diff --git a/404.html b/404.html
index 530d27a0..36a91cc1 100644
--- a/404.html
+++ b/404.html
@@ -12,7 +12,7 @@
 <link rel="apple-touch-icon" type="image/png" sizes="120x120" href="https://epiverse-trace.github.io/epichains/apple-touch-icon-120x120.png">
 <link rel="apple-touch-icon" type="image/png" sizes="76x76" href="https://epiverse-trace.github.io/epichains/apple-touch-icon-76x76.png">
 <link rel="apple-touch-icon" type="image/png" sizes="60x60" href="https://epiverse-trace.github.io/epichains/apple-touch-icon-60x60.png">
-<script src="https://epiverse-trace.github.io/epichains/deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
+<script src="https://epiverse-trace.github.io/epichains/lightswitch.js"></script><script src="https://epiverse-trace.github.io/epichains/deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
 <link href="https://epiverse-trace.github.io/epichains/deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet">
 <script src="https://epiverse-trace.github.io/epichains/deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="https://epiverse-trace.github.io/epichains/deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet">
 <link href="https://epiverse-trace.github.io/epichains/deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet">
@@ -22,18 +22,25 @@
   window.dataLayer = window.dataLayer || [];
   function gtag(){dataLayer.push(arguments);}
   gtag('js', new Date());
+
   gtag('config', 'G-XZ471458FQ');
 </script>
 </head>
 <body>
     <a href="https://epiverse-trace.github.io/epichains/#main" class="visually-hidden-focusable">Skip to contents</a>
-    <nav class="navbar navbar-expand-lg fixed-top bg-dark" data-bs-theme="dark" aria-label="Site navigation"><div class="container">
+
+
+    <nav class="navbar navbar-expand-lg fixed-top " aria-label="Site navigation"><div class="container">
     <a href="https://epiverse-trace.github.io/" class="external-link"><img src="https://epiverse-trace.github.io/blueprints/logo_white.svg" id="logo" alt="Epiverse-TRACE"></a>
     <a class="navbar-brand me-2" href="https://epiverse-trace.github.io/epichains/index.html">epichains</a>
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">0.1.0</small>
+
+    <small class="nav-text text-danger me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Unreleased version">0.1.0.9000</small>
+
+
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
       <span class="navbar-toggler-icon"></span>
     </button>
+
     <div id="navbar" class="collapse navbar-collapse ms-3">
       <ul class="navbar-nav me-auto">
 <li class="nav-item"><a class="nav-link" href="https://epiverse-trace.github.io/epichains/articles/epichains.html">Get started</a></li>
@@ -61,24 +68,46 @@
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="search.json">
 </form></li>
 <li class="nav-item"><a class="external-link nav-link" href="https://github.com/epiverse-trace/epichains/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item dropdown">
+  <button class="nav-link dropdown-toggle" type="button" id="dropdown-lightswitch" data-bs-toggle="dropdown" aria-expanded="false" aria-haspopup="true" aria-label="Light switch"><span class="fa fa-sun"></span></button>
+  <ul class="dropdown-menu dropdown-menu-end" aria-labelledby="dropdown-lightswitch">
+<li><button class="dropdown-item" data-bs-theme-value="light"><span class="fa fa-sun"></span> Light</button></li>
+    <li><button class="dropdown-item" data-bs-theme-value="dark"><span class="fa fa-moon"></span> Dark</button></li>
+    <li><button class="dropdown-item" data-bs-theme-value="auto"><span class="fa fa-adjust"></span> Auto</button></li>
+  </ul>
+</li>
       </ul>
 </div>
+
+
   </div>
 </nav><div class="container template-title-body">
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="https://epiverse-trace.github.io/epichains/logo.svg" class="logo" alt=""><h1>Page not found (404)</h1>
+
     </div>
+
 Content not found. Please use links in the navbar.
+
   </main>
 </div>
+
+
     <footer><div class="pkgdown-footer-left">
   <p>Developed by James M. Azam, Sebastian Funk, Flavio Finger.</p>
 </div>
+
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.9.9000.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
 </div>
+
     </footer>
 </div>
+
+
+
+
+
   </body>
 </html>
diff --git a/LICENSE-text.html b/LICENSE-text.html
index 8edda103..c5f85a27 100644
--- a/LICENSE-text.html
+++ b/LICENSE-text.html
@@ -1,18 +1,25 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>License • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="apple-touch-icon-60x60.png"><script src="deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="deps/headroom-0.11.0/headroom.min.js"></script><script src="deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="deps/search-1.0.0/fuse.min.js"></script><script src="deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="pkgdown.js"></script><meta property="og:title" content="License"><meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg"><!-- Google tag (gtag.js) --><script async src="https://www.googletagmanager.com/gtag/js?id=G-XZ471458FQ"></script><script>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>License • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="apple-touch-icon-60x60.png"><script src="lightswitch.js"></script><script src="deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="deps/headroom-0.11.0/headroom.min.js"></script><script src="deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="deps/search-1.0.0/fuse.min.js"></script><script src="deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="pkgdown.js"></script><meta property="og:title" content="License"><meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg"><!-- Google tag (gtag.js) --><script async src="https://www.googletagmanager.com/gtag/js?id=G-XZ471458FQ"></script><script>
   window.dataLayer = window.dataLayer || [];
   function gtag(){dataLayer.push(arguments);}
   gtag('js', new Date());
+
   gtag('config', 'G-XZ471458FQ');
 </script></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
-    <nav class="navbar navbar-expand-lg fixed-top bg-dark" data-bs-theme="dark" aria-label="Site navigation"><div class="container">
+
+
+    <nav class="navbar navbar-expand-lg fixed-top " aria-label="Site navigation"><div class="container">
     <a href="https://epiverse-trace.github.io/" class="external-link"><img src="https://epiverse-trace.github.io/blueprints/logo_white.svg" id="logo" alt="Epiverse-TRACE"></a>
     <a class="navbar-brand me-2" href="index.html">epichains</a>
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">0.1.0</small>
+
+    <small class="nav-text text-danger me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Unreleased version">0.1.0.9000</small>
+
+
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
       <span class="navbar-toggler-icon"></span>
     </button>
+
     <div id="navbar" class="collapse navbar-collapse ms-3">
       <ul class="navbar-nav me-auto"><li class="nav-item"><a class="nav-link" href="articles/epichains.html">Get started</a></li>
 <li class="nav-item"><a class="nav-link" href="reference/index.html">Reference</a></li>
@@ -34,23 +41,43 @@
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="search.json"></form></li>
 <li class="nav-item"><a class="external-link nav-link" href="https://github.com/epiverse-trace/epichains/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item dropdown">
+  <button class="nav-link dropdown-toggle" type="button" id="dropdown-lightswitch" data-bs-toggle="dropdown" aria-expanded="false" aria-haspopup="true" aria-label="Light switch"><span class="fa fa-sun"></span></button>
+  <ul class="dropdown-menu dropdown-menu-end" aria-labelledby="dropdown-lightswitch"><li><button class="dropdown-item" data-bs-theme-value="light"><span class="fa fa-sun"></span> Light</button></li>
+    <li><button class="dropdown-item" data-bs-theme-value="dark"><span class="fa fa-moon"></span> Dark</button></li>
+    <li><button class="dropdown-item" data-bs-theme-value="auto"><span class="fa fa-adjust"></span> Auto</button></li>
+  </ul></li>
       </ul></div>
+
+
   </div>
 </nav><div class="container template-title-body">
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="logo.svg" class="logo" alt=""><h1>License</h1>
+
     </div>
+
 <pre>YEAR: 2024
 COPYRIGHT HOLDER: epichains authors
 </pre>
+
   </main></div>
+
+
     <footer><div class="pkgdown-footer-left">
   <p>Developed by James M. Azam, Sebastian Funk, Flavio Finger.</p>
 </div>
+
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.9.9000.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
 </div>
+
     </footer></div>
+
+
+
+
+
   </body></html>
 
diff --git a/LICENSE.html b/LICENSE.html
index d73c6200..f728a0fa 100644
--- a/LICENSE.html
+++ b/LICENSE.html
@@ -1,18 +1,25 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>MIT License • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="apple-touch-icon-60x60.png"><script src="deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="deps/headroom-0.11.0/headroom.min.js"></script><script src="deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="deps/search-1.0.0/fuse.min.js"></script><script src="deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="pkgdown.js"></script><meta property="og:title" content="MIT License"><meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg"><!-- Google tag (gtag.js) --><script async src="https://www.googletagmanager.com/gtag/js?id=G-XZ471458FQ"></script><script>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>MIT License • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="apple-touch-icon-60x60.png"><script src="lightswitch.js"></script><script src="deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="deps/headroom-0.11.0/headroom.min.js"></script><script src="deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="deps/search-1.0.0/fuse.min.js"></script><script src="deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="pkgdown.js"></script><meta property="og:title" content="MIT License"><meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg"><!-- Google tag (gtag.js) --><script async src="https://www.googletagmanager.com/gtag/js?id=G-XZ471458FQ"></script><script>
   window.dataLayer = window.dataLayer || [];
   function gtag(){dataLayer.push(arguments);}
   gtag('js', new Date());
+
   gtag('config', 'G-XZ471458FQ');
 </script></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
-    <nav class="navbar navbar-expand-lg fixed-top bg-dark" data-bs-theme="dark" aria-label="Site navigation"><div class="container">
+
+
+    <nav class="navbar navbar-expand-lg fixed-top " aria-label="Site navigation"><div class="container">
     <a href="https://epiverse-trace.github.io/" class="external-link"><img src="https://epiverse-trace.github.io/blueprints/logo_white.svg" id="logo" alt="Epiverse-TRACE"></a>
     <a class="navbar-brand me-2" href="index.html">epichains</a>
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">0.1.0</small>
+
+    <small class="nav-text text-danger me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Unreleased version">0.1.0.9000</small>
+
+
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
       <span class="navbar-toggler-icon"></span>
     </button>
+
     <div id="navbar" class="collapse navbar-collapse ms-3">
       <ul class="navbar-nav me-auto"><li class="nav-item"><a class="nav-link" href="articles/epichains.html">Get started</a></li>
 <li class="nav-item"><a class="nav-link" href="reference/index.html">Reference</a></li>
@@ -34,27 +41,47 @@
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="search.json"></form></li>
 <li class="nav-item"><a class="external-link nav-link" href="https://github.com/epiverse-trace/epichains/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item dropdown">
+  <button class="nav-link dropdown-toggle" type="button" id="dropdown-lightswitch" data-bs-toggle="dropdown" aria-expanded="false" aria-haspopup="true" aria-label="Light switch"><span class="fa fa-sun"></span></button>
+  <ul class="dropdown-menu dropdown-menu-end" aria-labelledby="dropdown-lightswitch"><li><button class="dropdown-item" data-bs-theme-value="light"><span class="fa fa-sun"></span> Light</button></li>
+    <li><button class="dropdown-item" data-bs-theme-value="dark"><span class="fa fa-moon"></span> Dark</button></li>
+    <li><button class="dropdown-item" data-bs-theme-value="auto"><span class="fa fa-adjust"></span> Auto</button></li>
+  </ul></li>
       </ul></div>
+
+
   </div>
 </nav><div class="container template-title-body">
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="logo.svg" class="logo" alt=""><h1>MIT License</h1>
-      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/LICENSE.md" class="external-link"><code>LICENSE.md</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/LICENSE.md" class="external-link"><code>LICENSE.md</code></a></small>
     </div>
+
 <div id="mit-license" class="section level1">
+
 <p>Copyright (c) 2024 epichains authors</p>
 <p>Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the “Software”), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:</p>
 <p>The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.</p>
 <p>THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.</p>
 </div>
+
   </main></div>
+
+
     <footer><div class="pkgdown-footer-left">
   <p>Developed by James M. Azam, Sebastian Funk, Flavio Finger.</p>
 </div>
+
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.9.9000.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
 </div>
+
     </footer></div>
+
+
+
+
+
   </body></html>
 
diff --git a/articles/branching_process_literature.html b/articles/branching_process_literature.html
index f0cb02c9..c4af2a08 100644
--- a/articles/branching_process_literature.html
+++ b/articles/branching_process_literature.html
@@ -12,30 +12,34 @@
 <link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png">
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       <img src="../logo.svg" class="logo" alt=""><h1>Literature on branching process applications</h1>
-                        <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/vignettes/branching_process_literature.Rmd" class="external-link"><code>vignettes/branching_process_literature.Rmd</code></a></small>
+            
+      
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/vignettes/branching_process_literature.Rmd" class="external-link"><code>vignettes/branching_process_literature.Rmd</code></a></small>
       <div class="d-none name"><code>branching_process_literature.Rmd</code></div>
     </div>
-        <p>Below, we provide a bibliography on the application of branching processes to
-infectious disease modelling.</p>
-<p>It is our intention to grow this list to serve as a point of reference for
-budding modellers with an interest in the subject.</p>
-<p>If you would like to extend this list, the easiest way would be to <a href="https://github.com/epiverse-trace/epichains/issues/new/choose" class="external-link">file an issue</a>, listing the
-new additions and we’ll take it from there,
-or <a href="https://github.com/epiverse-trace/epichains/pulls" class="external-link">submit a pull request</a>
-with an updated version of the bibliography file found in
-“vignettes/branching_process_literature.json”.</p>
+
+    
+    
+<p>Below, we provide a bibliography on the application of branching
+processes to infectious disease modelling.</p>
+<p>It is our intention to grow this list to serve as a point of
+reference for budding modellers with an interest in the subject.</p>
+<p>If you would like to extend this list, the easiest way would be to <a href="https://github.com/epiverse-trace/epichains/issues/new/choose" class="external-link">file
+an issue</a>, listing the new additions and we’ll take it from there, or
+<a href="https://github.com/epiverse-trace/epichains/pulls" class="external-link">submit a
+pull request</a> with an updated version of the bibliography file found
+in “vignettes/branching_process_literature.json”.</p>
 <div class="section level2">
-<h2 id="bibliography">Bibliography<a class="anchor" aria-label="anchor" href="#bibliography"></a>
+<h2 class="unnumbered" id="bibliography">Bibliography<a class="anchor" aria-label="anchor" href="#bibliography"></a>
 </h2>
 <div id="refs" class="references csl-bib-body hanging-indent" entry-spacing="0">
 <div id="ref-abbott2020" class="csl-entry">
-Abbott, Sam, Joel Hellewell, James Munday, Sebastian Funk, CMMID nCoV working group, et al. 2020. <span>“The Transmissibility of Novel Coronavirus in the Early Stages of the 2019-20 Outbreak in Wuhan: Exploring Initial Point-Source Exposure Sizes and Durations Using Scenario Analysis.”</span> <em>Wellcome Open Research</em> 5.
+Abbott, Sam, Joel Hellewell, James Munday, Sebastian Funk, CMMID nCoV
+working group, et al. 2020. <span>“The Transmissibility of Novel
+Coronavirus in the Early Stages of the 2019-20 Outbreak in Wuhan:
+Exploring Initial Point-Source Exposure Sizes and Durations Using
+Scenario Analysis.”</span> <em>Wellcome Open Research</em> 5.
 </div>
 <div id="ref-becker1977" class="csl-entry">
-Becker, Niels, and International Biometric Society. 1977. <span>“Estimation for Discrete Time Branching Processes with Application to Epidemics.”</span> <em>Biometrics</em> 33 (3): 515–22.
+Becker, Niels, and International Biometric Society. 1977.
+<span>“Estimation for Discrete Time Branching Processes with Application
+to Epidemics.”</span> <em>Biometrics</em> 33 (3): 515–22.
 </div>
 <div id="ref-blumberg2013a" class="csl-entry">
-Blumberg, Seth, and James O. Lloyd-Smith. 2013. <span>“Inference of R0 and Transmission Heterogeneity from the Size Distribution of Stuttering Chains.”</span> <em>PLoS Computational Biology</em> 9 (5): 1–17. <a href="https://doi.org/10.1371/journal.pcbi.1002993" class="external-link">https://doi.org/10.1371/journal.pcbi.1002993</a>.
+Blumberg, Seth, and James O. Lloyd-Smith. 2013. <span>“Inference of R0
+and Transmission Heterogeneity from the Size Distribution of Stuttering
+Chains.”</span> <em>PLoS Computational Biology</em> 9 (5): 1–17. <a href="https://doi.org/10.1371/journal.pcbi.1002993" class="external-link">https://doi.org/10.1371/journal.pcbi.1002993</a>.
 </div>
 <div id="ref-blumberg2013" class="csl-entry">
-Blumberg, S., and J. O. Lloyd-Smith. 2013. <span>“Comparing Methods for Estimating R0 from the Size Distribution of Subcritical Transmission Chains.”</span> <em>Epidemics</em> 5 (3): 131–45. <a href="https://doi.org/10.1016/j.epidem.2013.05.002" class="external-link">https://doi.org/10.1016/j.epidem.2013.05.002</a>.
+Blumberg, S., and J. O. Lloyd-Smith. 2013. <span>“Comparing Methods for
+Estimating R0 from the Size Distribution of Subcritical Transmission
+Chains.”</span> <em>Epidemics</em> 5 (3): 131–45. <a href="https://doi.org/10.1016/j.epidem.2013.05.002" class="external-link">https://doi.org/10.1016/j.epidem.2013.05.002</a>.
 </div>
 <div id="ref-farrington1999" class="csl-entry">
-Farrington, C. P., and A. D. Grant. 1999. <span>“The Distribution of Time to Extinction in Subcritical Branching Processes: Applications to Outbreaks of Infectious Disease.”</span> <em>Journal of Applied Probability</em> 36 (3): 771–79. <a href="https://doi.org/10.1239/jap/1032374633" class="external-link">https://doi.org/10.1239/jap/1032374633</a>.
+Farrington, C. P., and A. D. Grant. 1999. <span>“The Distribution of
+Time to Extinction in Subcritical Branching Processes: Applications to
+Outbreaks of Infectious Disease.”</span> <em>Journal of Applied
+Probability</em> 36 (3): 771–79. <a href="https://doi.org/10.1239/jap/1032374633" class="external-link">https://doi.org/10.1239/jap/1032374633</a>.
 </div>
 <div id="ref-farrington2003" class="csl-entry">
-Farrington, C. P., M. N. Kanaan, and N. J. Gay. 2003. <span>“Branching Process Models for Surveillance of Infectious Diseases Controlled by Mass Vaccination.”</span> <em>Biostatistics (Oxford, England)</em> 4 (2): 279–95. <a href="https://doi.org/10.1093/biostatistics/4.2.279" class="external-link">https://doi.org/10.1093/biostatistics/4.2.279</a>.
+Farrington, C. P., M. N. Kanaan, and N. J. Gay. 2003. <span>“Branching
+Process Models for Surveillance of Infectious Diseases Controlled by
+Mass Vaccination.”</span> <em>Biostatistics (Oxford, England)</em> 4
+(2): 279–95. <a href="https://doi.org/10.1093/biostatistics/4.2.279" class="external-link">https://doi.org/10.1093/biostatistics/4.2.279</a>.
 </div>
 <div id="ref-hellewell2020" class="csl-entry">
-Hellewell, Joel, Sam Abbott, Amy Gimma, Nikos I. Bosse, Christopher I. Jarvis, Timothy W. Russell, James D. Munday, et al. 2020. <span>“Feasibility of controlling COVID-19 outbreaks by isolation of cases and contacts.”</span> <em>The Lancet Global Health</em> 8 (4): e488–96. <a href="https://doi.org/10.1016/S2214-109X(20)30074-7" class="external-link">https://doi.org/10.1016/S2214-109X(20)30074-7</a>.
+Hellewell, Joel, Sam Abbott, Amy Gimma, Nikos I. Bosse, Christopher I.
+Jarvis, Timothy W. Russell, James D. Munday, et al. 2020.
+<span>“Feasibility of controlling COVID-19 outbreaks by isolation of
+cases and contacts.”</span> <em>The Lancet Global Health</em> 8 (4):
+e488–96. <a href="https://doi.org/10.1016/S2214-109X(20)30074-7" class="external-link">https://doi.org/10.1016/S2214-109X(20)30074-7</a>.
 </div>
 <div id="ref-jacob2010" class="csl-entry">
-Jacob, Christine. 2010. <span>“Branching Processes: Their Role in Epidemiology.”</span> <em>International Journal of Environmental Research and Public Health</em> 7 (3): 1186–1204. <a href="https://doi.org/10.3390/ijerph7031204" class="external-link">https://doi.org/10.3390/ijerph7031204</a>.
+Jacob, Christine. 2010. <span>“Branching Processes: Their Role in
+Epidemiology.”</span> <em>International Journal of Environmental
+Research and Public Health</em> 7 (3): 1186–1204. <a href="https://doi.org/10.3390/ijerph7031204" class="external-link">https://doi.org/10.3390/ijerph7031204</a>.
 </div>
 <div id="ref-kucharski2015" class="csl-entry">
-Kucharski, Adam J., and W. John Edmunds. 2015. <span>“Characterizing the Transmission Potential of Zoonotic Infections from Minor Outbreaks.”</span> <em>PLOS Computational Biology</em> 11 (4): e1004154. <a href="https://doi.org/10.1371/journal.pcbi.1004154" class="external-link">https://doi.org/10.1371/journal.pcbi.1004154</a>.
+Kucharski, Adam J., and W. John Edmunds. 2015. <span>“Characterizing the
+Transmission Potential of Zoonotic Infections from Minor
+Outbreaks.”</span> <em>PLOS Computational Biology</em> 11 (4): e1004154.
+<a href="https://doi.org/10.1371/journal.pcbi.1004154" class="external-link">https://doi.org/10.1371/journal.pcbi.1004154</a>.
 </div>
 <div id="ref-kucharski2016" class="csl-entry">
-Kucharski, Adam J., Rosalind M. Eggo, Conall H. Watson, Anton Camacho, Sebastian Funk, and W. John Edmunds. 2016. <span>“Effectiveness of Ring Vaccination as Control Strategy for Ebola Virus Disease.”</span> <em>Emerging Infectious Diseases</em> 22 (1): 105–8. <a href="https://doi.org/10.3201/eid2201.151410" class="external-link">https://doi.org/10.3201/eid2201.151410</a>.
+Kucharski, Adam J., Rosalind M. Eggo, Conall H. Watson, Anton Camacho,
+Sebastian Funk, and W. John Edmunds. 2016. <span>“Effectiveness of Ring
+Vaccination as Control Strategy for Ebola Virus Disease.”</span>
+<em>Emerging Infectious Diseases</em> 22 (1): 105–8. <a href="https://doi.org/10.3201/eid2201.151410" class="external-link">https://doi.org/10.3201/eid2201.151410</a>.
 </div>
 <div id="ref-lloyd-smith2005" class="csl-entry">
-Lloyd-Smith, J. O., S. J. Schreiber, P. E. Kopp, and W. M. Getz. 2005. <span>“Superspreading and the Effect of Individual Variation on Disease Emergence.”</span> <em>Nature</em> 438 (7066): 355–59. <a href="https://doi.org/10.1038/nature04153" class="external-link">https://doi.org/10.1038/nature04153</a>.
+Lloyd-Smith, J. O., S. J. Schreiber, P. E. Kopp, and W. M. Getz. 2005.
+<span>“Superspreading and the Effect of Individual Variation on Disease
+Emergence.”</span> <em>Nature</em> 438 (7066): 355–59. <a href="https://doi.org/10.1038/nature04153" class="external-link">https://doi.org/10.1038/nature04153</a>.
 </div>
 <div id="ref-nishiura2012" class="csl-entry">
-Nishiura, Hiroshi, Ping Yan, Candace K. Sleeman, and Charles J. Mode. 2012. <span>“Estimating the Transmission Potential of Supercritical Processes Based on the Final Size Distribution of Minor Outbreaks.”</span> <em>Journal of Theoretical Biology</em> 294: 48–55. <a href="https://doi.org/10.1016/j.jtbi.2011.10.039" class="external-link">https://doi.org/10.1016/j.jtbi.2011.10.039</a>.
+Nishiura, Hiroshi, Ping Yan, Candace K. Sleeman, and Charles J. Mode.
+2012. <span>“Estimating the Transmission Potential of Supercritical
+Processes Based on the Final Size Distribution of Minor
+Outbreaks.”</span> <em>Journal of Theoretical Biology</em> 294: 48–55.
+<a href="https://doi.org/10.1016/j.jtbi.2011.10.039" class="external-link">https://doi.org/10.1016/j.jtbi.2011.10.039</a>.
 </div>
 <div id="ref-pearson2020" class="csl-entry">
-Pearson, Carl A.B., Cari van Schalkwyk, Anna M. Foss, Kathleen M. O’Reilly, and Juliet R.C. Pulliam. 2020. <span>“Projected Early Spread of COVID-19 in Africa Through 1 June 2020.”</span> <em>Eurosurveillance</em> 25 (18): 1–6. <a href="https://doi.org/10.2807/1560-7917.ES.2020.25.18.2000543" class="external-link">https://doi.org/10.2807/1560-7917.ES.2020.25.18.2000543</a>.
+Pearson, Carl A.B., Cari van Schalkwyk, Anna M. Foss, Kathleen M.
+O’Reilly, and Juliet R.C. Pulliam. 2020. <span>“Projected Early Spread
+of COVID-19 in Africa Through 1 June 2020.”</span>
+<em>Eurosurveillance</em> 25 (18): 1–6. <a href="https://doi.org/10.2807/1560-7917.ES.2020.25.18.2000543" class="external-link">https://doi.org/10.2807/1560-7917.ES.2020.25.18.2000543</a>.
 </div>
 <div id="ref-ratnayake2022" class="csl-entry">
-Ratnayake, Ruwan, Francesco Checchi, Christopher I. Jarvis, W. John Edmunds, and Flavio Finger. 2022. <span>“Inference Is Bliss: Simulation for Power Estimation for an Observational Study of a Cholera Outbreak Intervention.”</span> Edited by Ruifu Yang. <em>PLOS Neglected Tropical Diseases</em> 16 (2): e0010163. <a href="https://doi.org/10.1371/journal.pntd.0010163" class="external-link">https://doi.org/10.1371/journal.pntd.0010163</a>.
+Ratnayake, Ruwan, Francesco Checchi, Christopher I. Jarvis, W. John
+Edmunds, and Flavio Finger. 2022. <span>“Inference Is Bliss: Simulation
+for Power Estimation for an Observational Study of a Cholera Outbreak
+Intervention.”</span> Edited by Ruifu Yang. <em>PLOS Neglected Tropical
+Diseases</em> 16 (2): e0010163. <a href="https://doi.org/10.1371/journal.pntd.0010163" class="external-link">https://doi.org/10.1371/journal.pntd.0010163</a>.
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   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.svg" class="logo" alt=""><h1>Design Principles for {epichains}</h1>
             <h3 data-toc-skip class="subtitle">An R package for
 simulating, handling, and analysing transmission chains in R</h3>
-                        <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/vignettes/design-principles.Rmd" class="external-link"><code>vignettes/design-principles.Rmd</code></a></small>
+            
+      
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/vignettes/design-principles.Rmd" class="external-link"><code>vignettes/design-principles.Rmd</code></a></small>
       <div class="d-none name"><code>design-principles.Rmd</code></div>
     </div>
-        <p>This vignette outlines the design decisions that have been
-taken during the development of the <a href="https://github.com/epiverse-trace/epichains" class="external-link">epichains</a> R package,
-and provides some of the reasoning, and possible pros and cons of each
+
+    
+    
+<p>This vignette outlines the design decisions that have been taken
+during the development of the <a href="https://github.com/epiverse-trace/epichains" class="external-link">epichains</a> R package, and
+provides some of the reasoning, and possible pros and cons of each
 decision.</p>
 <p>The goal here is to make it easy to acquaint oneself with the code
 base in the absence of the current maintainer. This will ease future
@@ -335,13 +358,23 @@ <h2 id="development-journey">Development journey<a class="anchor" aria-label="an
   </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
     </nav></aside>
 </div>
+
+
+
     <footer><div class="pkgdown-footer-left">
   <p>Developed by James M. Azam, Sebastian Funk, Flavio Finger.</p>
 </div>
+
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.9.9000.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
 </div>
+
     </footer>
 </div>
+
+
+
+
+
   </body>
 </html>
diff --git a/articles/epichains.html b/articles/epichains.html
index 7f062d4a..0e0dfa47 100644
--- a/articles/epichains.html
+++ b/articles/epichains.html
@@ -12,30 +12,34 @@
 <link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png">
 <link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png">
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-<script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
+<script src="../lightswitch.js"></script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
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 <script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Getting started with epichains">
-<meta name="description" content="epichains">
-<meta property="og:description" content="epichains">
-<meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg">
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   gtag('js', new Date());
+
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 </script>
 </head>
 <body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
-    <nav class="navbar navbar-expand-lg fixed-top bg-dark" data-bs-theme="dark" aria-label="Site navigation"><div class="container">
+
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+    <nav class="navbar navbar-expand-lg fixed-top " aria-label="Site navigation"><div class="container">
     <a href="https://epiverse-trace.github.io/" class="external-link"><img src="https://epiverse-trace.github.io/blueprints/logo_white.svg" id="logo" alt="Epiverse-TRACE"></a>
     <a class="navbar-brand me-2" href="../index.html">epichains</a>
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">0.1.0</small>
+
+    <small class="nav-text text-danger me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Unreleased version">0.1.0.9000</small>
+
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@@ -63,8 +67,18 @@
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json">
 </form></li>
 <li class="nav-item"><a class="external-link nav-link" href="https://github.com/epiverse-trace/epichains/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item dropdown">
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 </nav><div class="container template-article">
 
@@ -77,10 +91,15 @@
       <img src="../logo.svg" class="logo" alt=""><h1>Getting started with epichains</h1>
                         <h4 data-toc-skip class="author">James M. Azam
 and Sebastian Funk</h4>
-                        <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/vignettes/epichains.Rmd" class="external-link"><code>vignettes/epichains.Rmd</code></a></small>
+            
+      
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/vignettes/epichains.Rmd" class="external-link"><code>vignettes/epichains.Rmd</code></a></small>
       <div class="d-none name"><code>epichains.Rmd</code></div>
     </div>
-        <p>This vignette demonstrates how get started with using the
+
+    
+    
+<p>This vignette demonstrates how get started with using the
 <em>epichains</em> package for simulating transmission chains or
 estimating the likelihood of observing a transmission chain.</p>
 <div class="alert alert-info">
@@ -207,9 +226,8 @@ <h3 id="likelihood">
 <span><span class="co"># randomly generate 20 chains of size between 1 to 10</span></span>
 <span><span class="va">chain_sizes</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/sample.html" class="external-link">sample</a></span><span class="op">(</span><span class="fl">1</span><span class="op">:</span><span class="fl">10</span>, <span class="fl">20</span>, replace <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span>
 <span><span class="va">chain_sizes</span></span>
-<span><span class="co">#&gt;  [1]  4  7  4  9  1  3  7  5  1  8 10  2  1  2  4  5 10  6  8  7</span></span></code></pre></div>
-<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="co"># estimate loglikelihood of the observed chain sizes for given lambda</span></span>
+<span><span class="co">#&gt;  [1]  4  7  4  9  1  3  7  5  1  8 10  2  1  2  4  5 10  6  8  7</span></span>
+<span><span class="co"># estimate loglikelihood of the observed chain sizes for given lambda</span></span>
 <span><span class="va">likelihood_eg</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/likelihood.html">likelihood</a></span><span class="op">(</span></span>
 <span>  chains <span class="op">=</span> <span class="va">chain_sizes</span>,</span>
 <span>  statistic <span class="op">=</span> <span class="st">"size"</span>,</span>
@@ -231,15 +249,14 @@ <h3 id="joint-and-individual-log-likelihoods">Joint and individual log-likelihoo
 information criterion</a> values, then the <code>individual</code>
 argument must be set to <code>TRUE</code>. To return likelihoods
 instead, set <code>log = FALSE</code>.</p>
-<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/Random.html" class="external-link">set.seed</a></span><span class="op">(</span><span class="fl">121</span><span class="op">)</span></span>
 <span><span class="co"># example of observed chain sizes</span></span>
 <span><span class="co"># randomly generate 20 chains of size between 1 to 10</span></span>
 <span><span class="va">chain_sizes</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/sample.html" class="external-link">sample</a></span><span class="op">(</span><span class="fl">1</span><span class="op">:</span><span class="fl">10</span>, <span class="fl">20</span>, replace <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span>
 <span><span class="va">chain_sizes</span></span>
-<span><span class="co">#&gt;  [1]  4  7  4  9  1  3  7  5  1  8 10  2  1  2  4  5 10  6  8  7</span></span></code></pre></div>
-<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span></span>
+<span><span class="co">#&gt;  [1]  4  7  4  9  1  3  7  5  1  8 10  2  1  2  4  5 10  6  8  7</span></span>
+<span></span>
 <span><span class="co"># estimate loglikelihood of the observed chain sizes</span></span>
 <span><span class="va">likelihood_ind_eg</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/likelihood.html">likelihood</a></span><span class="op">(</span></span>
 <span>  chains <span class="op">=</span> <span class="va">chain_sizes</span>,</span>
@@ -270,7 +287,7 @@ <h3 id="observation-probability">Observation probability<a class="anchor" aria-l
 calculated for each of the simulations.</p>
 <p>For example, if the probability of observing each case is
 <code>obs_prob = 0.30</code>, we use</p>
-<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/Random.html" class="external-link">set.seed</a></span><span class="op">(</span><span class="fl">121</span><span class="op">)</span></span>
 <span><span class="co"># example of observed chain sizes; randomly generate 20 chains of size 1 to 10</span></span>
 <span><span class="va">chain_sizes</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/sample.html" class="external-link">sample</a></span><span class="op">(</span><span class="fl">1</span><span class="op">:</span><span class="fl">10</span>, <span class="fl">20</span>, replace <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span>
@@ -329,7 +346,7 @@ <h3 id="how-likelihood-works">How <code>likelihood()</code> works<a class="ancho
 is observed and we want to calculate the likelihood of this being drawn
 from a binomial distribution with probability
 <code>prob = 0.9</code>.</p>
-<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/Random.html" class="external-link">set.seed</a></span><span class="op">(</span><span class="fl">121</span><span class="op">)</span></span>
 <span><span class="co"># example of observed chain sizes; randomly generate 20 chains of size 1 to 10</span></span>
 <span><span class="va">chain_sizes</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/sample.html" class="external-link">sample</a></span><span class="op">(</span><span class="fl">1</span><span class="op">:</span><span class="fl">10</span>, <span class="fl">20</span>, replace <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span>
@@ -408,7 +425,7 @@ <h3 id="simulate_chains">
 and a generation time of
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mn>3</mn><annotation encoding="application/x-tex">3</annotation></semantics></math>
 days:</p>
-<div class="sourceCode" id="cb8"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/Random.html" class="external-link">set.seed</a></span><span class="op">(</span><span class="fl">32</span><span class="op">)</span></span>
 <span><span class="co"># Define generation time</span></span>
 <span><span class="va">generation_time_fn</span> <span class="op">&lt;-</span> <span class="kw">function</span><span class="op">(</span><span class="va">n</span><span class="op">)</span> <span class="op">{</span></span>
@@ -452,7 +469,7 @@ <h3 id="simulate_chains">
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext mathvariant="normal">lambda</mtext><mo>=</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">\text{lambda} = 1</annotation></semantics></math>,
 and fixed generation time of
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mn>3</mn><annotation encoding="application/x-tex">3</annotation></semantics></math>:</p>
-<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/Random.html" class="external-link">set.seed</a></span><span class="op">(</span><span class="fl">32</span><span class="op">)</span></span>
 <span><span class="co"># Define generation time</span></span>
 <span><span class="va">generation_time_fn</span> <span class="op">&lt;-</span> <span class="kw">function</span><span class="op">(</span><span class="va">n</span><span class="op">)</span> <span class="op">{</span></span>
@@ -496,7 +513,7 @@ <h3 id="simulate_chain_stats">
 chains. It assumes a Poisson offspring distribution distribution with
 mean of
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mn>0.9</mn><annotation encoding="application/x-tex">0.9</annotation></semantics></math>.</p>
-<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb8"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/Random.html" class="external-link">set.seed</a></span><span class="op">(</span><span class="fl">123</span><span class="op">)</span></span>
 <span></span>
 <span><span class="va">simulate_chain_stats_eg</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/simulate_chain_stats.html">simulate_chain_stats</a></span><span class="op">(</span></span>
@@ -528,7 +545,7 @@ <h3 id="summarising">Summarising<a class="anchor" aria-label="anchor" href="#sum
 <p>You can run <code><a href="https://rdrr.io/r/base/summary.html" class="external-link">summary()</a></code> on the object returned by
 <code><a href="../reference/simulate_chains.html">simulate_chains()</a></code> to obtain the chain summaries per index
 case.</p>
-<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/Random.html" class="external-link">set.seed</a></span><span class="op">(</span><span class="fl">32</span><span class="op">)</span></span>
 <span><span class="co"># Define generation time</span></span>
 <span><span class="va">generation_time_fn</span> <span class="op">&lt;-</span> <span class="kw">function</span><span class="op">(</span><span class="va">n</span><span class="op">)</span> <span class="op">{</span></span>
@@ -553,9 +570,8 @@ <h3 id="summarising">Summarising<a class="anchor" aria-label="anchor" href="#sum
 <span><span class="co">#&gt;  Simulated sizes: </span></span>
 <span><span class="co">#&gt; </span></span>
 <span><span class="co">#&gt; Max: &gt;=10</span></span>
-<span><span class="co">#&gt; Min: 1</span></span></code></pre></div>
-<div class="sourceCode" id="cb12"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span></span>
+<span><span class="co">#&gt; Min: 1</span></span>
+<span></span>
 <span><span class="co"># Example with simulate_chain_stats()</span></span>
 <span><span class="fu"><a href="https://rdrr.io/r/base/Random.html" class="external-link">set.seed</a></span><span class="op">(</span><span class="fl">32</span><span class="op">)</span></span>
 <span></span>
@@ -586,7 +602,7 @@ <h3 id="summarising">Summarising<a class="anchor" aria-label="anchor" href="#sum
 <p>We can confirm if the two outputs are the same using
 <code><a href="https://rdrr.io/r/base/sets.html" class="external-link">base::setequal()</a></code>, which checks if two objects are equal and
 returns <code>TRUE/FALSE</code>.</p>
-<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/sets.html" class="external-link">setequal</a></span><span class="op">(</span></span>
 <span>  <span class="co"># summary of output from simulate_chains()</span></span>
 <span>  <span class="fu"><a href="https://rdrr.io/r/base/summary.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">sim_chains</span><span class="op">)</span>,</span>
@@ -604,7 +620,7 @@ <h3 id="aggregating">Aggregating<a class="anchor" aria-label="anchor" href="#agg
 “generation” or “time”, depending on the value of <code>by</code>.</p>
 <p>To aggregate over “time”, you must have specified a generation time
 distribution (<code>generation_time</code>) in the simulation step.</p>
-<div class="sourceCode" id="cb14"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="co"># Example with simulate_chains()</span></span>
 <span><span class="fu"><a href="https://rdrr.io/r/base/Random.html" class="external-link">set.seed</a></span><span class="op">(</span><span class="fl">32</span><span class="op">)</span></span>
 <span></span>
@@ -676,7 +692,7 @@ <h3 id="some-notes-about-interoperability-between-epicontacts-and-epichains-obje
 </div>
 <p>Let’s subset one of the chains with the biggest size from the
 <code>sim_chains</code> object created above.</p>
-<div class="sourceCode" id="cb15"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb12"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="co"># Get the biggest chain</span></span>
 <span><span class="va">longest_chain</span> <span class="op">&lt;-</span> <span class="va">sim_chains</span><span class="op">[</span><span class="va">sim_chains</span><span class="op">$</span><span class="va">chain</span> <span class="op">==</span> <span class="fu"><a href="https://rdrr.io/r/base/which.min.html" class="external-link">which.max</a></span><span class="op">(</span></span>
 <span>  <span class="fu"><a href="https://rdrr.io/r/base/unname.html" class="external-link">unname</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/table.html" class="external-link">table</a></span><span class="op">(</span><span class="va">sim_chains</span><span class="op">$</span><span class="va">chain</span><span class="op">)</span><span class="op">)</span></span>
@@ -699,7 +715,7 @@ <h3 id="some-notes-about-interoperability-between-epicontacts-and-epichains-obje
 <span><span class="co">#&gt; 45     6        8       12          4    9</span></span></code></pre></div>
 <p>Now, we can plot the chain using the <a href="https://www.repidemicsconsortium.org/epicontacts/" class="external-link">epicontacts</a>
 package.</p>
-<div class="sourceCode" id="cb16"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="co"># Create an `&lt;epicontacts&gt;` object</span></span>
 <span><span class="va">epc</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://www.repidemicsconsortium.org/epicontacts/reference/make_epicontacts.html" class="external-link">make_epicontacts</a></span><span class="op">(</span></span>
 <span>  linelist <span class="op">=</span> <span class="va">longest_chain</span>,</span>
@@ -718,7 +734,7 @@ <h3 id="some-notes-about-interoperability-between-epicontacts-and-epichains-obje
 manipulation.</p>
 <p>Here is an end-to-end example from simulation through aggregation to
 plotting.</p>
-<div class="sourceCode" id="cb17"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb14"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="co"># Run simulation with simulate_chains()</span></span>
 <span><span class="fu"><a href="https://rdrr.io/r/base/Random.html" class="external-link">set.seed</a></span><span class="op">(</span><span class="fl">32</span><span class="op">)</span></span>
 <span><span class="co"># Define generation time</span></span>
@@ -770,13 +786,23 @@ <h2 class="unnumbered" id="references">References<a class="anchor" aria-label="a
   </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
     </nav></aside>
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+
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     <footer><div class="pkgdown-footer-left">
   <p>Developed by James M. Azam, Sebastian Funk, Flavio Finger.</p>
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+
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-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.9.9000.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
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diff --git a/articles/index.html b/articles/index.html
index 55570648..330210fc 100644
--- a/articles/index.html
+++ b/articles/index.html
@@ -1,18 +1,25 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Articles • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Articles"><meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg"><!-- Google tag (gtag.js) --><script async src="https://www.googletagmanager.com/gtag/js?id=G-XZ471458FQ"></script><script>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Articles • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../lightswitch.js"></script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Articles"><meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg"><!-- Google tag (gtag.js) --><script async src="https://www.googletagmanager.com/gtag/js?id=G-XZ471458FQ"></script><script>
   window.dataLayer = window.dataLayer || [];
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 </script></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
-    <nav class="navbar navbar-expand-lg fixed-top bg-dark" data-bs-theme="dark" aria-label="Site navigation"><div class="container">
+
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+    <nav class="navbar navbar-expand-lg fixed-top " aria-label="Site navigation"><div class="container">
     <a href="https://epiverse-trace.github.io/" class="external-link"><img src="https://epiverse-trace.github.io/blueprints/logo_white.svg" id="logo" alt="Epiverse-TRACE"></a>
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-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">0.1.0</small>
+
+    <small class="nav-text text-danger me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Unreleased version">0.1.0.9000</small>
+
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 <li class="nav-item"><a class="nav-link" href="../reference/index.html">Reference</a></li>
@@ -34,16 +41,26 @@
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
 <li class="nav-item"><a class="external-link nav-link" href="https://github.com/epiverse-trace/epichains/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item dropdown">
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       <img src="../logo.svg" class="logo" alt=""><h1>Articles</h1>
     </div>
+
     <div class="section ">
       <h3>Package vignettes</h3>
       <div class="section-desc"></div>
+
       <dl><dt><a href="projecting_incidence.html">Projecting infectious disease incidence: a COVID-19 example</a></dt>
         <dd>
         </dd><dt><a href="interventions.html">Modelling disease control interventions</a></dt>
@@ -52,6 +69,7 @@ <h3>Package vignettes</h3>
     <div class="section ">
       <h3>Modelling guides and background</h3>
       <div class="section-desc"></div>
+
       <dl><dt><a href="branching_process_literature.html">Literature on branching process applications</a></dt>
         <dd>
         </dd><dt><a href="theoretical_background.html">Theoretical background for epichains</a></dt>
@@ -60,17 +78,27 @@ <h3>Modelling guides and background</h3>
     <div class="section ">
       <h3>Developer Documentation</h3>
       <div class="section-desc"></div>
+
       <dl><dt><a href="design-principles.html">Design Principles for {epichains}</a></dt>
         <dd>
       </dd></dl></div>
   </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
     </nav></aside></div>
+
+
     <footer><div class="pkgdown-footer-left">
   <p>Developed by James M. Azam, Sebastian Funk, Flavio Finger.</p>
 </div>
+
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.9.9000.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
 </div>
+
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+
+
+
+
+
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diff --git a/articles/interventions.html b/articles/interventions.html
index aab81a80..54bd162f 100644
--- a/articles/interventions.html
+++ b/articles/interventions.html
@@ -12,30 +12,34 @@
 <link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png">
 <link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png">
 <link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png">
-<script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
+<script src="../lightswitch.js"></script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
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 <script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Modelling disease control interventions">
-<meta name="description" content="epichains">
-<meta property="og:description" content="epichains">
-<meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg">
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+
   gtag('config', 'G-XZ471458FQ');
 </script>
 </head>
 <body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
-    <nav class="navbar navbar-expand-lg fixed-top bg-dark" data-bs-theme="dark" aria-label="Site navigation"><div class="container">
+
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+    <nav class="navbar navbar-expand-lg fixed-top " aria-label="Site navigation"><div class="container">
     <a href="https://epiverse-trace.github.io/" class="external-link"><img src="https://epiverse-trace.github.io/blueprints/logo_white.svg" id="logo" alt="Epiverse-TRACE"></a>
     <a class="navbar-brand me-2" href="../index.html">epichains</a>
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">0.1.0</small>
+
+    <small class="nav-text text-danger me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Unreleased version">0.1.0.9000</small>
+
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     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
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+
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       <ul class="navbar-nav me-auto">
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@@ -63,61 +67,94 @@
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json">
 </form></li>
 <li class="nav-item"><a class="external-link nav-link" href="https://github.com/epiverse-trace/epichains/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item dropdown">
+  <button class="nav-link dropdown-toggle" type="button" id="dropdown-lightswitch" data-bs-toggle="dropdown" aria-expanded="false" aria-haspopup="true" aria-label="Light switch"><span class="fa fa-sun"></span></button>
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+  </ul>
+</li>
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+
+
+
+
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.svg" class="logo" alt=""><h1>Modelling disease control interventions</h1>
-                        <h4 data-toc-skip class="author">Sebastian Funk and James M. Azam</h4>
-                        <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/vignettes/interventions.Rmd" class="external-link"><code>vignettes/interventions.Rmd</code></a></small>
+                        <h4 data-toc-skip class="author">Sebastian Funk
+and James M. Azam</h4>
+            
+      
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/vignettes/interventions.Rmd" class="external-link"><code>vignettes/interventions.Rmd</code></a></small>
       <div class="d-none name"><code>interventions.Rmd</code></div>
     </div>
-        <p><em>epichains</em> does not provide any direct functionality for studying reductions in transmission (e.g. from public health interventions).
-However, the flexible simulation functionality that it includes can be used to consider some specific changes to the parameters that can be interpreted as the result of changes in social behaviour or control measures.
-Here we investigate the effect on outbreak sizes, but the same approaches could be used for investigating chain lengths (using the <code>statistic</code> argument to <code><a href="../reference/simulate_chain_stats.html">simulate_chain_stats()</a></code>) or the time progression of outbreaks (using the <code><a href="../reference/simulate_chains.html">simulate_chains()</a></code> function).</p>
+
+    
+    
+<p><em>epichains</em> does not provide any direct functionality for
+studying reductions in transmission (e.g. from public health
+interventions). However, the flexible simulation functionality that it
+includes can be used to consider some specific changes to the parameters
+that can be interpreted as the result of changes in social behaviour or
+control measures. Here we investigate the effect on outbreak sizes, but
+the same approaches could be used for investigating chain lengths (using
+the <code>statistic</code> argument to
+<code><a href="../reference/simulate_chain_stats.html">simulate_chain_stats()</a></code>) or the time progression of
+outbreaks (using the <code><a href="../reference/simulate_chains.html">simulate_chains()</a></code> function).</p>
 <div class="alert alert-info">
-<p>Some of the ideas presented here can be achieved using closed-form solutions
-of the probability of an epidemic growing out of proportion or going extinct,
-and the impact of heterogeneities in individual-level transmission. For
-examples of this, see the <a href="https://epiverse-trace.github.io/superspreading/articles/epidemic_risk.html" class="external-link">vignette on epidemic risk</a>
-in the <a href="https://epiverse-trace.github.io/superspreading/index.html" class="external-link">superspreading</a>
+<p>Some of the ideas presented here can be achieved using closed-form
+solutions of the probability of an epidemic growing out of proportion or
+going extinct, and the impact of heterogeneities in individual-level
+transmission. For examples of this, see the <a href="https://epiverse-trace.github.io/superspreading/articles/epidemic_risk.html" class="external-link">vignette
+on epidemic risk</a> in the <a href="https://epiverse-trace.github.io/superspreading/index.html" class="external-link">superspreading</a>
 package, which is part of the Epiverse-TRACE Initiative.</p>
 </div>
-<details class="chunk-details" open><summary class="chunk-summary"><span class="chunk-summary-text">Code</span></summary><div class="sourceCode" id="cb1"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb1"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="co">## main package</span></span>
 <span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="st"><a href="https://github.com/epiverse-trace/epichains" class="external-link">"epichains"</a></span><span class="op">)</span></span>
 <span><span class="co">## for plotting</span></span>
 <span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="st"><a href="https://ggplot2.tidyverse.org" class="external-link">"ggplot2"</a></span><span class="op">)</span></span>
 <span><span class="co">## for truncating the offspring distribution later</span></span>
 <span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="st">"truncdist"</span><span class="op">)</span></span></code></pre></div>
-</details><p>As a base case we consider the spread of an infection with a negative binomial offspring distribution with mean 1.2 and overdispersion parameter 0.5.
-We simulate 200 chains tracking up to 99 infections:</p>
-<details class="chunk-details" open><summary class="chunk-summary"><span class="chunk-summary-text">Code</span></summary><div class="sourceCode" id="cb2"><pre class="downlit sourceCode r">
+<p>As a base case we consider the spread of an infection with a negative
+binomial offspring distribution with mean 1.2 and overdispersion
+parameter 0.5. We simulate 200 chains tracking up to 99 infections:</p>
+<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">sims</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/simulate_chain_stats.html">simulate_chain_stats</a></span><span class="op">(</span></span>
 <span>  n_chains <span class="op">=</span> <span class="fl">200</span>, offspring_dist <span class="op">=</span> <span class="va">rnbinom</span>, stat_threshold <span class="op">=</span> <span class="fl">99</span>, mu <span class="op">=</span> <span class="fl">1.2</span>,</span>
 <span>  size <span class="op">=</span> <span class="fl">0.5</span>, statistic <span class="op">=</span> <span class="st">"size"</span></span>
 <span><span class="op">)</span></span></code></pre></div>
-</details><p>We then plot the resulting distribution of chain sizes</p>
-<details class="chunk-details" open><summary class="chunk-summary"><span class="chunk-summary-text">Code</span></summary><div class="sourceCode" id="cb3"><pre class="downlit sourceCode r">
+<p>We then plot the resulting distribution of chain sizes</p>
+<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">sims</span><span class="op">[</span><span class="fu"><a href="https://rdrr.io/r/base/is.finite.html" class="external-link">is.infinite</a></span><span class="op">(</span><span class="va">sims</span><span class="op">)</span><span class="op">]</span> <span class="op">&lt;-</span> <span class="fl">100</span> <span class="co"># Replace infections &gt; 99 with 100 for plotting.</span></span>
 <span><span class="fu"><a href="https://ggplot2.tidyverse.org/reference/ggplot.html" class="external-link">ggplot</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/data.frame.html" class="external-link">data.frame</a></span><span class="op">(</span>x <span class="op">=</span> <span class="va">sims</span><span class="op">)</span>, <span class="fu"><a href="https://ggplot2.tidyverse.org/reference/aes.html" class="external-link">aes</a></span><span class="op">(</span>x <span class="op">=</span> <span class="va">x</span><span class="op">)</span><span class="op">)</span> <span class="op">+</span></span>
 <span>  <span class="fu"><a href="https://ggplot2.tidyverse.org/reference/geom_histogram.html" class="external-link">geom_histogram</a></span><span class="op">(</span>breaks <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/seq.html" class="external-link">seq</a></span><span class="op">(</span><span class="fl">0</span>, <span class="fl">100</span>, by <span class="op">=</span> <span class="fl">5</span><span class="op">)</span>, closed <span class="op">=</span> <span class="st">"left"</span><span class="op">)</span> <span class="op">+</span></span>
 <span>  <span class="fu"><a href="https://ggplot2.tidyverse.org/reference/scale_continuous.html" class="external-link">scale_x_continuous</a></span><span class="op">(</span>breaks <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0</span>, <span class="fl">25</span>, <span class="fl">50</span>, <span class="fl">75</span>, <span class="fl">100</span><span class="op">)</span>,</span>
 <span>                     labels <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0</span>, <span class="fl">25</span>, <span class="fl">50</span>, <span class="fl">75</span>, <span class="st">"&gt;99"</span><span class="op">)</span><span class="op">)</span> <span class="op">+</span></span>
 <span>  <span class="fu"><a href="https://ggplot2.tidyverse.org/reference/ggtheme.html" class="external-link">theme_bw</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
-</details><p><img src="interventions_files/figure-html/uncontrolled_chains_plot-1.png"><!-- --></p>
+<p><img src="interventions_files/figure-html/uncontrolled_chains_plot-1.png" width="768"></p>
 <div class="section level2">
 <h2 id="reducing-the-strength-of-transmission">Reducing the strength of transmission<a class="anchor" aria-label="anchor" href="#reducing-the-strength-of-transmission"></a>
 </h2>
-<p>Following <span class="citation">(<a href="#ref-lloyd-smith2005">Lloyd-Smith et al. 2005</a>)</span> we consider two ways in which disease control interventions can reduce the reproduction number: <em>population-wide</em> and <em>individual-specific</em> control.</p>
+<p>Following <span class="citation">(<a href="#ref-lloyd-smith2005">Lloyd-Smith et al. 2005</a>)</span> we
+consider two ways in which disease control interventions can reduce the
+reproduction number: <em>population-wide</em> and
+<em>individual-specific</em> control.</p>
 <div class="section level3">
 <h3 id="population-wide-control">Population-wide control<a class="anchor" aria-label="anchor" href="#population-wide-control"></a>
 </h3>
-<p>By population-level control we mean an intervention that reduces the mean number of offspring (i.e. the reproduction number) by a fixed proportion.
-For example, to reduce R by 25% at the population level we scale the <code>mu</code> parameter from 1.2 to 0.9:</p>
-<details class="chunk-details" open><summary class="chunk-summary"><span class="chunk-summary-text">Code</span></summary><div class="sourceCode" id="cb4"><pre class="downlit sourceCode r">
+<p>By population-level control we mean an intervention that reduces the
+mean number of offspring (i.e. the reproduction number) by a fixed
+proportion. For example, to reduce R by 25% at the population level we
+scale the <code>mu</code> parameter from 1.2 to 0.9:</p>
+<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">sims</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/simulate_chain_stats.html">simulate_chain_stats</a></span><span class="op">(</span></span>
 <span>  n_chains <span class="op">=</span> <span class="fl">200</span>, offspring_dist <span class="op">=</span> <span class="va">rnbinom</span>, stat_threshold <span class="op">=</span> <span class="fl">99</span>, mu <span class="op">=</span> <span class="fl">0.9</span>,</span>
 <span>  size <span class="op">=</span> <span class="fl">0.5</span>, statistic <span class="op">=</span> <span class="st">"size"</span></span>
@@ -128,15 +165,23 @@ <h3 id="population-wide-control">Population-wide control<a class="anchor" aria-l
 <span>  <span class="fu"><a href="https://ggplot2.tidyverse.org/reference/scale_continuous.html" class="external-link">scale_x_continuous</a></span><span class="op">(</span>breaks <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0</span>, <span class="fl">25</span>, <span class="fl">50</span>, <span class="fl">75</span>, <span class="fl">100</span><span class="op">)</span>,</span>
 <span>                     labels <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0</span>, <span class="fl">25</span>, <span class="fl">50</span>, <span class="fl">75</span>, <span class="st">"&gt;99"</span><span class="op">)</span><span class="op">)</span> <span class="op">+</span></span>
 <span>  <span class="fu"><a href="https://ggplot2.tidyverse.org/reference/ggtheme.html" class="external-link">theme_bw</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
-</details><p><img src="interventions_files/figure-html/simulate_chains_pop_control-1.png"><!-- --></p>
+<p><img src="interventions_files/figure-html/simulate_chains_pop_control-1.png" width="768"></p>
 </div>
 <div class="section level3">
 <h3 id="individual-level-control-">Individual-level control.<a class="anchor" aria-label="anchor" href="#individual-level-control-"></a>
 </h3>
-<p>In simulating population-level control we now apply the same reduction as before (25%) but instead of assuming that the mean is reduced we apply this such that 25% of individuals do not transmit further at all, whereas the remaining 75% generate offspring as in the uncontrolled case.</p>
-<p>To do this, we can no longer use the standard negative binomial distribution that comes with R.
-Instead, we define a random generator from a modified negative binomial distribution that includes our individual-level control as a <code>control</code> argument indicating the level of individual-level control (0: no control; 1: full control):</p>
-<details class="chunk-details" open><summary class="chunk-summary"><span class="chunk-summary-text">Code</span></summary><div class="sourceCode" id="cb5"><pre class="downlit sourceCode r">
+<p>In simulating population-level control we now apply the same
+reduction as before (25%) but instead of assuming that the mean is
+reduced we apply this such that 25% of individuals do not transmit
+further at all, whereas the remaining 75% generate offspring as in the
+uncontrolled case.</p>
+<p>To do this, we can no longer use the standard negative binomial
+distribution that comes with R. Instead, we define a random generator
+from a modified negative binomial distribution that includes our
+individual-level control as a <code>control</code> argument indicating
+the level of individual-level control (0: no control; 1: full
+control):</p>
+<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">rnbinom_ind</span> <span class="op">&lt;-</span> <span class="kw">function</span><span class="op">(</span><span class="va">n</span>, <span class="va">...</span>, <span class="va">control</span> <span class="op">=</span> <span class="fl">0</span><span class="op">)</span> <span class="op">{</span></span>
 <span>  <span class="co">## initialise number of offspring to 0</span></span>
 <span>  <span class="va">offspring</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/rep.html" class="external-link">rep</a></span><span class="op">(</span><span class="fl">0L</span>, <span class="va">n</span><span class="op">)</span></span>
@@ -150,8 +195,8 @@ <h3 id="individual-level-control-">Individual-level control.<a class="anchor" ar
 <span>  <span class="op">}</span></span>
 <span>  <span class="kw"><a href="https://rdrr.io/r/base/function.html" class="external-link">return</a></span><span class="op">(</span><span class="va">offspring</span><span class="op">)</span></span>
 <span><span class="op">}</span></span></code></pre></div>
-</details><p>Having defined this, we can generate simulations as before:</p>
-<details class="chunk-details" open><summary class="chunk-summary"><span class="chunk-summary-text">Code</span></summary><div class="sourceCode" id="cb6"><pre class="downlit sourceCode r">
+<p>Having defined this, we can generate simulations as before:</p>
+<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">sims</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/simulate_chain_stats.html">simulate_chain_stats</a></span><span class="op">(</span></span>
 <span>  n_chains <span class="op">=</span> <span class="fl">200</span>, offspring_dist <span class="op">=</span> <span class="va">rnbinom_ind</span>, stat_threshold <span class="op">=</span> <span class="fl">99</span>, mu <span class="op">=</span> <span class="fl">1.2</span>,</span>
 <span>  size <span class="op">=</span> <span class="fl">0.5</span>, control <span class="op">=</span> <span class="fl">0.25</span>, statistic <span class="op">=</span> <span class="st">"size"</span></span>
@@ -162,23 +207,29 @@ <h3 id="individual-level-control-">Individual-level control.<a class="anchor" ar
 <span>  <span class="fu"><a href="https://ggplot2.tidyverse.org/reference/scale_continuous.html" class="external-link">scale_x_continuous</a></span><span class="op">(</span>breaks <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0</span>, <span class="fl">25</span>, <span class="fl">50</span>, <span class="fl">75</span>, <span class="fl">100</span><span class="op">)</span>,</span>
 <span>                     labels <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0</span>, <span class="fl">25</span>, <span class="fl">50</span>, <span class="fl">75</span>, <span class="st">"&gt;99"</span><span class="op">)</span><span class="op">)</span> <span class="op">+</span></span>
 <span>  <span class="fu"><a href="https://ggplot2.tidyverse.org/reference/ggtheme.html" class="external-link">theme_bw</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
-</details><p><img src="interventions_files/figure-html/simulate_chains_ind_control-1.png"><!-- --></p>
+<p><img src="interventions_files/figure-html/simulate_chains_ind_control-1.png" width="768"></p>
 </div>
 </div>
 <div class="section level2">
 <h2 id="preventing-superspreading-events">Preventing superspreading events<a class="anchor" aria-label="anchor" href="#preventing-superspreading-events"></a>
 </h2>
-<p>Another way of controlling a disease would be to prevent individuals from spreading to a large number of others, for example by preventing mass gatherings or, more generally, settings where superspreading events can occur.</p>
-<p>We can model this by truncating the offspring distribution at a certain size.
-This can be done, for example, using the <a href="https://cran.r-project.org/package=truncdist" class="external-link">truncdist</a> R package.
-We use this to define a truncated negative binomial offspring distribution:</p>
-<details class="chunk-details" open><summary class="chunk-summary"><span class="chunk-summary-text">Code</span></summary><div class="sourceCode" id="cb7"><pre class="downlit sourceCode r">
+<p>Another way of controlling a disease would be to prevent individuals
+from spreading to a large number of others, for example by preventing
+mass gatherings or, more generally, settings where superspreading events
+can occur.</p>
+<p>We can model this by truncating the offspring distribution at a
+certain size. This can be done, for example, using the <a href="https://cran.r-project.org/package=truncdist" class="external-link">truncdist</a> R
+package. We use this to define a truncated negative binomial offspring
+distribution:</p>
+<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">rnbinom_truncated</span> <span class="op">&lt;-</span> <span class="kw">function</span><span class="op">(</span><span class="va">n</span>, <span class="va">...</span>, <span class="va">max</span> <span class="op">=</span> <span class="cn">Inf</span><span class="op">)</span> <span class="op">{</span></span>
 <span>  <span class="kw"><a href="https://rdrr.io/r/base/function.html" class="external-link">return</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/pkg/truncdist/man/rtrunc.html" class="external-link">rtrunc</a></span><span class="op">(</span>n <span class="op">=</span> <span class="va">n</span>, spec <span class="op">=</span> <span class="st">"nbinom"</span>, b <span class="op">=</span> <span class="va">max</span>, <span class="va">...</span><span class="op">)</span><span class="op">)</span></span>
 <span><span class="op">}</span></span></code></pre></div>
-</details><p>We use this to simulate chains in a situation where the maximum of secondary cases that each infected person can generate is 10.
-This can be likened to a disease control strategy where gatherings are limited to 10 people.</p>
-<details class="chunk-details" open><summary class="chunk-summary"><span class="chunk-summary-text">Code</span></summary><div class="sourceCode" id="cb8"><pre class="downlit sourceCode r">
+<p>We use this to simulate chains in a situation where the maximum of
+secondary cases that each infected person can generate is 10. This can
+be likened to a disease control strategy where gatherings are limited to
+10 people.</p>
+<div class="sourceCode" id="cb8"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">sims</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/simulate_chain_stats.html">simulate_chain_stats</a></span><span class="op">(</span></span>
 <span>  n_chains <span class="op">=</span> <span class="fl">200</span>, offspring_dist <span class="op">=</span> <span class="va">rnbinom_truncated</span>, stat_threshold <span class="op">=</span> <span class="fl">99</span>,</span>
 <span>  mu <span class="op">=</span> <span class="fl">1.2</span>, size <span class="op">=</span> <span class="fl">0.5</span>, max <span class="op">=</span>  <span class="fl">10</span>, statistic <span class="op">=</span> <span class="st">"size"</span></span>
@@ -189,40 +240,58 @@ <h2 id="preventing-superspreading-events">Preventing superspreading events<a cla
 <span>  <span class="fu"><a href="https://ggplot2.tidyverse.org/reference/scale_continuous.html" class="external-link">scale_x_continuous</a></span><span class="op">(</span>breaks <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0</span>, <span class="fl">25</span>, <span class="fl">50</span>, <span class="fl">75</span>, <span class="fl">100</span><span class="op">)</span>,</span>
 <span>                     labels <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0</span>, <span class="fl">25</span>, <span class="fl">50</span>, <span class="fl">75</span>, <span class="st">"&gt;99"</span><span class="op">)</span><span class="op">)</span> <span class="op">+</span></span>
 <span>  <span class="fu"><a href="https://ggplot2.tidyverse.org/reference/ggtheme.html" class="external-link">theme_bw</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
-</details><p><img src="interventions_files/figure-html/simulate_chains_truncated-1.png"><!-- --></p>
+<p><img src="interventions_files/figure-html/simulate_chains_truncated-1.png" width="768"></p>
 </div>
 <div class="section level2">
 <h2 id="truncating-the-generation-interval">Truncating the generation interval<a class="anchor" aria-label="anchor" href="#truncating-the-generation-interval"></a>
 </h2>
-<p>Lastly, we consider a situation where the generation interval is shortened.
-We do not model this explicitly but instead consider the effect on the offspring distribution.</p>
-<p>For example, if our generation interval is from a gamma distribution with shape = 25 and rate = 5 (corresponding to a mean of 5 and standard deviation of 1), and we stop all transmission that would normally occur more than 6 days after infection, we can calculate the proportion of transmissions that are prevented as</p>
-<details class="chunk-details" open><summary class="chunk-summary"><span class="chunk-summary-text">Code</span></summary><div class="sourceCode" id="cb9"><pre class="downlit sourceCode r">
+<p>Lastly, we consider a situation where the generation interval is
+shortened. We do not model this explicitly but instead consider the
+effect on the offspring distribution.</p>
+<p>For example, if our generation interval is from a gamma distribution
+with shape = 25 and rate = 5 (corresponding to a mean of 5 and standard
+deviation of 1), and we stop all transmission that would normally occur
+more than 6 days after infection, we can calculate the proportion of
+transmissions that are prevented as</p>
+<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">control</span> <span class="op">&lt;-</span> <span class="fl">1</span> <span class="op">-</span> <span class="fu"><a href="https://rdrr.io/r/stats/GammaDist.html" class="external-link">pgamma</a></span><span class="op">(</span><span class="fl">6</span>, shape <span class="op">=</span> <span class="fl">25</span>, rate <span class="op">=</span> <span class="fl">5</span><span class="op">)</span></span>
 <span><span class="fu"><a href="https://rdrr.io/r/base/Round.html" class="external-link">signif</a></span><span class="op">(</span><span class="va">control</span>, <span class="fl">2</span><span class="op">)</span></span>
 <span><span class="co">#&gt; [1] 0.16</span></span></code></pre></div>
-</details><p>In other words, this would prevent 16% of infections in this example.
-The value of <code>control</code> can be used in the examples above to study the effect on outbreak sizes.</p>
+<p>In other words, this would prevent 16% of infections in this example.
+The value of <code>control</code> can be used in the examples above to
+study the effect on outbreak sizes.</p>
 </div>
 <div class="section level2">
-<h2 id="references">References<a class="anchor" aria-label="anchor" href="#references"></a>
+<h2 class="unnumbered" id="references">References<a class="anchor" aria-label="anchor" href="#references"></a>
 </h2>
 <div id="refs" class="references csl-bib-body hanging-indent" entry-spacing="0">
 <div id="ref-lloyd-smith2005" class="csl-entry">
-Lloyd-Smith, J. O., S. J. Schreiber, P. E. Kopp, and W. M. Getz. 2005. <span>“Superspreading and the Effect of Individual Variation on Disease Emergence.”</span> <em>Nature</em> 438 (7066): 355–59. <a href="https://doi.org/10.1038/nature04153" class="external-link">https://doi.org/10.1038/nature04153</a>.
+Lloyd-Smith, J. O., S. J. Schreiber, P. E. Kopp, and W. M. Getz. 2005.
+<span>“Superspreading and the Effect of Individual Variation on Disease
+Emergence.”</span> <em>Nature</em> 438 (7066): 355–59. <a href="https://doi.org/10.1038/nature04153" class="external-link">https://doi.org/10.1038/nature04153</a>.
 </div>
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diff --git a/articles/projecting_incidence.html b/articles/projecting_incidence.html
index 36b231da..11896adc 100644
--- a/articles/projecting_incidence.html
+++ b/articles/projecting_incidence.html
@@ -12,30 +12,34 @@
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       <img src="../logo.svg" class="logo" alt=""><h1>Projecting infectious disease incidence: a COVID-19 example</h1>
-                        <h4 data-toc-skip class="author">James Azam, Sebastian Funk</h4>
-                        <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/vignettes/projecting_incidence.Rmd" class="external-link"><code>vignettes/projecting_incidence.Rmd</code></a></small>
+                        <h4 data-toc-skip class="author">James Azam,
+Sebastian Funk</h4>
+            
+      
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/vignettes/projecting_incidence.Rmd" class="external-link"><code>vignettes/projecting_incidence.Rmd</code></a></small>
       <div class="d-none name"><code>projecting_incidence.Rmd</code></div>
     </div>
-        <div class="section level2">
+
+    
+    
+<div class="section level2">
 <h2 id="overview">Overview<a class="anchor" aria-label="anchor" href="#overview"></a>
 </h2>
-<p>Branching processes can be used to project stochastic infectious disease trends in time
-provided we can characterize the distribution of times between
-successive cases (serial interval), and the distribution of secondary cases
-produced by a single individual (offspring distribution). Such simulations can
-be achieved in <em>epichains</em> with the <code><a href="../reference/simulate_chains.html">simulate_chains()</a></code> function and
-<span class="citation">Pearson et al. (<a href="#ref-pearson2020">2020</a>)</span>, and <span class="citation">Abbott et al. (<a href="#ref-abbott2020">2020</a>)</span> illustrate its application to COVID-19.</p>
-<p>The purpose of this vignette is to use early data on COVID-19 in South Africa
-<span class="citation">(<a href="#ref-marivate2020">Marivate and Combrink 2020</a>)</span> to illustrate how <em>epichains</em> can be used to project an
+<p>Branching processes can be used to project stochastic infectious
+disease trends in time provided we can characterize the distribution of
+times between successive cases (serial interval), and the distribution
+of secondary cases produced by a single individual (offspring
+distribution). Such simulations can be achieved in <em>epichains</em>
+with the <code><a href="../reference/simulate_chains.html">simulate_chains()</a></code> function and <span class="citation">Pearson et al. (<a href="#ref-pearson2020">2020</a>)</span>, and <span class="citation">Abbott et al. (<a href="#ref-abbott2020">2020</a>)</span> illustrate its application to
+COVID-19.</p>
+<p>The purpose of this vignette is to use early data on COVID-19 in
+South Africa <span class="citation">(<a href="#ref-marivate2020">Marivate and Combrink 2020</a>)</span> to
+illustrate how <em>epichains</em> can be used to project an
 outbreak.</p>
 <p>Let’s load the required packages</p>
-<details class="chunk-details" open><summary class="chunk-summary"><span class="chunk-summary-text">Code</span></summary><div class="sourceCode" id="cb1"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb1"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="st"><a href="https://github.com/epiverse-trace/epichains" class="external-link">"epichains"</a></span><span class="op">)</span></span>
 <span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="st"><a href="https://dplyr.tidyverse.org" class="external-link">"dplyr"</a></span><span class="op">)</span></span>
 <span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="st"><a href="https://ggplot2.tidyverse.org" class="external-link">"ggplot2"</a></span><span class="op">)</span></span>
 <span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="st"><a href="https://lubridate.tidyverse.org" class="external-link">"lubridate"</a></span><span class="op">)</span></span></code></pre></div>
-</details>
 </div>
 <div class="section level2">
 <h2 id="data">Data<a class="anchor" aria-label="anchor" href="#data"></a>
 </h2>
-<p>Included in <em>epichains</em> is a cleaned time series of the first 15 days of
-the COVID-19 outbreak in South Africa. This can be loaded into
-memory as follows:</p>
-<details class="chunk-details" open><summary class="chunk-summary"><span class="chunk-summary-text">Code</span></summary><div class="sourceCode" id="cb2"><pre class="downlit sourceCode r">
+<p>Included in <em>epichains</em> is a cleaned time series of the first
+15 days of the COVID-19 outbreak in South Africa. This can be loaded
+into memory as follows:</p>
+<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/utils/data.html" class="external-link">data</a></span><span class="op">(</span><span class="st">"covid19_sa"</span>, package <span class="op">=</span> <span class="st">"epichains"</span><span class="op">)</span></span></code></pre></div>
-</details><p>We will use the first <span class="math inline">\(5\)</span> observations for this demonstration. We will assume
-that all the cases in that subset are imported and did not infect each other.</p>
+<p>We will use the first
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mn>5</mn><annotation encoding="application/x-tex">5</annotation></semantics></math>
+observations for this demonstration. We will assume that all the cases
+in that subset are imported and did not infect each other.</p>
 <p>Let us subset and view that aspect of the data.</p>
-<details class="chunk-details" open><summary class="chunk-summary"><span class="chunk-summary-text">Code</span></summary><div class="sourceCode" id="cb3"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">seed_cases</span> <span class="op">&lt;-</span> <span class="va">covid19_sa</span><span class="op">[</span><span class="fl">1</span><span class="op">:</span><span class="fl">5</span>, <span class="op">]</span></span>
 <span><span class="fu"><a href="https://rdrr.io/r/utils/head.html" class="external-link">head</a></span><span class="op">(</span><span class="va">seed_cases</span><span class="op">)</span></span>
 <span><span class="co">#&gt; <span style="color: #949494;"># A tibble: 5 × 2</span></span></span>
@@ -116,71 +143,83 @@ <h2 id="data">Data<a class="anchor" aria-label="anchor" href="#data"></a>
 <span><span class="co">#&gt; <span style="color: #BCBCBC;">3</span> 2020-03-08     1</span></span>
 <span><span class="co">#&gt; <span style="color: #BCBCBC;">4</span> 2020-03-09     4</span></span>
 <span><span class="co">#&gt; <span style="color: #BCBCBC;">5</span> 2020-03-11     6</span></span></code></pre></div>
-</details>
 </div>
 <div class="section level2">
 <h2 id="setting-up-the-inputs">Setting up the inputs<a class="anchor" aria-label="anchor" href="#setting-up-the-inputs"></a>
 </h2>
-<p>We will now proceed to set up <code><a href="../reference/simulate_chains.html">simulate_chains()</a></code> for the simulations.</p>
+<p>We will now proceed to set up <code><a href="../reference/simulate_chains.html">simulate_chains()</a></code> for the
+simulations.</p>
 <div class="section level3">
 <h3 id="onset-times">Onset times<a class="anchor" aria-label="anchor" href="#onset-times"></a>
 </h3>
-<p><code><a href="../reference/simulate_chains.html">simulate_chains()</a></code> requires a vector of seeding times, <code>t0</code>, for each
-chain/individual/simulation.</p>
-<p>To get this, we will use the observation date of the index case as the
-reference and find the difference between the other observed dates and the reference.</p>
-<details class="chunk-details" open><summary class="chunk-summary"><span class="chunk-summary-text">Code</span></summary><div class="sourceCode" id="cb4"><pre class="downlit sourceCode r">
+<p><code><a href="../reference/simulate_chains.html">simulate_chains()</a></code> requires a vector of seeding times,
+<code>t0</code>, for each chain/individual/simulation.</p>
+<p>To get this, we will use the observation date of the index case as
+the reference and find the difference between the other observed dates
+and the reference.</p>
+<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">days_since_index</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/integer.html" class="external-link">as.integer</a></span><span class="op">(</span><span class="va">seed_cases</span><span class="op">$</span><span class="va">date</span> <span class="op">-</span> <span class="fu"><a href="https://rdrr.io/r/base/Extremes.html" class="external-link">min</a></span><span class="op">(</span><span class="va">seed_cases</span><span class="op">$</span><span class="va">date</span><span class="op">)</span><span class="op">)</span></span>
 <span><span class="va">days_since_index</span></span>
 <span><span class="co">#&gt; [1] 0 2 3 4 6</span></span></code></pre></div>
-</details><p>Using the vector of start times from the time series, we will then
-create a corresponding seeding time for each individual, which we’ll call
-<code>t0</code>.</p>
-<details class="chunk-details" open><summary class="chunk-summary"><span class="chunk-summary-text">Code</span></summary><div class="sourceCode" id="cb5"><pre class="downlit sourceCode r">
+<p>Using the vector of start times from the time series, we will then
+create a corresponding seeding time for each individual, which we’ll
+call <code>t0</code>.</p>
+<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">t0</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/rep.html" class="external-link">rep</a></span><span class="op">(</span><span class="va">days_since_index</span>, <span class="va">seed_cases</span><span class="op">$</span><span class="va">cases</span><span class="op">)</span></span>
 <span><span class="va">t0</span></span>
 <span><span class="co">#&gt;  [1] 0 2 3 4 4 4 4 6 6 6 6 6 6</span></span></code></pre></div>
-</details>
 </div>
 <div class="section level3">
 <h3 id="generation-time">Generation time<a class="anchor" aria-label="anchor" href="#generation-time"></a>
 </h3>
-<p>In epidemiology, the generation time (also called the generation interval) is
-the duration between successive infectious events in a chain of transmission.
-Similarly, the serial interval is the duration between observed symptom onset
-times between successive cases in a transmission chain. The generation
-interval is often hard to observe because exact times of infection are hard to
-measure hence, the serial interval is often used instead. Here, we
-use the serial interval and interpret the simulated case data to represent
-symptom onset.</p>
+<p>In epidemiology, the generation time (also called the generation
+interval) is the duration between successive infectious events in a
+chain of transmission. Similarly, the serial interval is the duration
+between observed symptom onset times between successive cases in a
+transmission chain. The generation interval is often hard to observe
+because exact times of infection are hard to measure hence, the serial
+interval is often used instead. Here, we use the serial interval and
+interpret the simulated case data to represent symptom onset.</p>
 <p>In this example, we will assume based on COVID-19 literature that the
 serial interval, S, is log-normal distributed with parameters,
-<span class="math inline">\(\mu = 4.7\)</span> and <span class="math inline">\(\sigma = 2.9\)</span> <span class="citation">(<a href="#ref-pearson2020">Pearson et al. 2020</a>)</span>. The log-normal distribution is
-commonly used in epidemiology to characterise quantities such as the serial
-interval because it has a large variance and can only be positive-valued
-<span class="citation">(<a href="#ref-nishiura2007">Nishiura 2007</a>; <a href="#ref-limpert2001">Limpert, Stahel, and Abbt 2001</a>)</span>.</p>
-<p>Note that when the distribution is described this way, it means <span class="math inline">\(\mu\)</span> and
-<span class="math inline">\(\sigma\)</span> are the expected value and standard deviation of the natural
-logarithm of the serial interval. Hence, in order to sample the
-“back-transformed” measured serial interval with expectation/mean, <span class="math inline">\(E[S]\)</span>
-and standard deviation, <span class="math inline">\(SD [S]\)</span>, we can use the following parametrisation:</p>
-<p><span class="math display">\[\begin{align}
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>μ</mi><mo>=</mo><mn>4.7</mn></mrow><annotation encoding="application/x-tex">\mu = 4.7</annotation></semantics></math>
+and
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>σ</mi><mo>=</mo><mn>2.9</mn></mrow><annotation encoding="application/x-tex">\sigma = 2.9</annotation></semantics></math><span class="citation">(<a href="#ref-pearson2020">Pearson et al.
+2020</a>)</span>. The log-normal distribution is commonly used in
+epidemiology to characterise quantities such as the serial interval
+because it has a large variance and can only be positive-valued <span class="citation">(<a href="#ref-nishiura2007">Nishiura 2007</a>; <a href="#ref-limpert2001">Limpert, Stahel, and Abbt 2001</a>)</span>.</p>
+<p>Note that when the distribution is described this way, it means
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>μ</mi><annotation encoding="application/x-tex">\mu</annotation></semantics></math>
+and
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>σ</mi><annotation encoding="application/x-tex">\sigma</annotation></semantics></math>
+are the expected value and standard deviation of the natural logarithm
+of the serial interval. Hence, in order to sample the “back-transformed”
+measured serial interval with expectation/mean,
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>E</mi><mrow><mo stretchy="true" form="prefix">[</mo><mi>S</mi><mo stretchy="true" form="postfix">]</mo></mrow></mrow><annotation encoding="application/x-tex">E[S]</annotation></semantics></math>
+and standard deviation,
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>S</mi><mi>D</mi><mrow><mo stretchy="true" form="prefix">[</mo><mi>S</mi><mo stretchy="true" form="postfix">]</mo></mrow></mrow><annotation encoding="application/x-tex">SD [S]</annotation></semantics></math>,
+we can use the following parametrisation:</p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable><mtr><mtd columnalign="right" style="text-align: right"><mi>E</mi><mrow><mo stretchy="true" form="prefix">[</mo><mi>S</mi><mo stretchy="true" form="postfix">]</mo></mrow></mtd><mtd columnalign="left" style="text-align: left"><mo>=</mo><mo>ln</mo><mrow><mo stretchy="true" form="prefix">(</mo><mfrac displaystyle="true"><msup><mi>μ</mi><mn>2</mn></msup><mrow><mo stretchy="false" form="prefix">(</mo><msqrt><mrow><msup><mi>μ</mi><mn>2</mn></msup><mo>+</mo><msup><mi>σ</mi><mn>2</mn></msup></mrow></msqrt></mrow></mfrac><mo stretchy="true" form="postfix">)</mo></mrow></mtd></mtr><mtr><mtd columnalign="right" style="text-align: right"><mi>S</mi><mi>D</mi><mrow><mo stretchy="true" form="prefix">[</mo><mi>S</mi><mo stretchy="true" form="postfix">]</mo></mrow></mtd><mtd columnalign="left" style="text-align: left"><mo>=</mo><msqrt><mrow><mo>ln</mo><mrow><mo stretchy="true" form="prefix">(</mo><mn>1</mn><mo>+</mo><mfrac displaystyle="true"><msup><mi>σ</mi><mn>2</mn></msup><msup><mi>μ</mi><mn>2</mn></msup></mfrac><mo stretchy="true" form="postfix">)</mo></mrow></mrow></msqrt></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{align}
 E[S] &amp;= \ln \left( \dfrac{\mu^2}{(\sqrt{\mu^2 + \sigma^2}} \right) \\
 
 SD [S] &amp;= \sqrt {\ln \left(1 + \dfrac{\sigma^2}{\mu^2} \right)}
-\end{align}\]</span>
-See <a href="https://en.wikipedia.org/wiki/Log-normal_distribution" class="external-link">“log-normal_distribution” on Wikipedia</a> for a
-detailed explanation of this parametrisation.
-We will now set up the generation time function with the appropriate inputs.
-We adopt R’s random lognormal distribution generator (<code><a href="https://rdrr.io/r/stats/Lognormal.html" class="external-link">rlnorm()</a></code>) that
-takes <code>meanlog</code> and <code>sdlog</code> as arguments, which we define with the
-parametrisation above as <code>log_mean()</code> and <code>log_sd()</code> respectively and wrap it in
-the <code>generation_time_fn()</code> function. Moreover, <code>generation_time_fn()</code> takes one
-argument <code>n</code> as is required by <em>epichains</em> (See <code><a href="../reference/simulate_chains.html">?epichains::simulate_chains</a></code>),
-which is further passed to <code><a href="https://rdrr.io/r/stats/Lognormal.html" class="external-link">rlnorm()</a></code> as the
-first argument to determine the number of observations to sample
-(See <code><a href="https://rdrr.io/r/stats/Lognormal.html" class="external-link">?rlnorm</a></code>).
-<details class="chunk-details" open><summary class="chunk-summary"><span class="chunk-summary-text">Code</span></summary><div class="sourceCode" id="cb6"><pre class="downlit sourceCode r">
+ 
+\end{align}</annotation></semantics></math></p>
+<p>See <a href="https://en.wikipedia.org/wiki/Log-normal_distribution" class="external-link">“log-normal_distribution”
+on Wikipedia</a> for a detailed explanation of this parametrisation.</p>
+<p>We will now set up the generation time function with the appropriate
+inputs. We adopt R’s random lognormal distribution generator
+(<code><a href="https://rdrr.io/r/stats/Lognormal.html" class="external-link">rlnorm()</a></code>) that takes <code>meanlog</code> and
+<code>sdlog</code> as arguments, which we define with the
+parametrisation above as <code>log_mean()</code> and
+<code>log_sd()</code> respectively and wrap it in the
+<code>generation_time_fn()</code> function. Moreover,
+<code>generation_time_fn()</code> takes one argument <code>n</code> as
+is required by <em>epichains</em> (See
+<code><a href="../reference/simulate_chains.html">?epichains::simulate_chains</a></code>), which is further passed to
+<code><a href="https://rdrr.io/r/stats/Lognormal.html" class="external-link">rlnorm()</a></code> as the first argument to determine the number of
+observations to sample (See <code><a href="https://rdrr.io/r/stats/Lognormal.html" class="external-link">?rlnorm</a></code>).</p>
+<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">mu</span> <span class="op">&lt;-</span> <span class="fl">4.7</span></span>
 <span><span class="va">sgma</span> <span class="op">&lt;-</span> <span class="fl">2.9</span></span>
 <span></span>
@@ -192,58 +231,72 @@ <h3 id="generation-time">Generation time<a class="anchor" aria-label="anchor" hr
 <span>  <span class="va">gt</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/stats/Lognormal.html" class="external-link">rlnorm</a></span><span class="op">(</span><span class="va">n</span>, meanlog <span class="op">=</span> <span class="va">log_mean</span>, sdlog <span class="op">=</span> <span class="va">log_sd</span><span class="op">)</span></span>
 <span>  <span class="kw"><a href="https://rdrr.io/r/base/function.html" class="external-link">return</a></span><span class="op">(</span><span class="va">gt</span><span class="op">)</span></span>
 <span><span class="op">}</span></span></code></pre></div>
-</details>
 </div>
 <div class="section level3">
 <h3 id="offspring-distribution">Offspring distribution<a class="anchor" aria-label="anchor" href="#offspring-distribution"></a>
 </h3>
-<p>Let us now set up the offspring distribution, that is the distribution that
-drives the mechanism behind how individual cases infect other cases. The
-appropriate way to model the offspring distribution is to capture both the
-population-level transmissibility (<span class="math inline">\(R0\)</span>) and the individual-level heterogeneity
-in transmission (“superspreading”). The negative binomial distribution is
-commonly used in this case <span class="citation">(<a href="#ref-lloyd-smith2005">Lloyd-Smith et al. 2005</a>)</span>.</p>
+<p>Let us now set up the offspring distribution, that is the
+distribution that drives the mechanism behind how individual cases
+infect other cases. The appropriate way to model the offspring
+distribution is to capture both the population-level transmissibility
+(<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>R</mi><mn>0</mn></mrow><annotation encoding="application/x-tex">R0</annotation></semantics></math>)
+and the individual-level heterogeneity in transmission
+(“superspreading”). The negative binomial distribution is commonly used
+in this case <span class="citation">(<a href="#ref-lloyd-smith2005">Lloyd-Smith et al. 2005</a>)</span>.</p>
 <p>For this example, we will assume that the offspring distribution is
-characterised by a negative binomial with <span class="math inline">\(mu = 2.5\)</span> <span class="citation">(<a href="#ref-abbott2020">Abbott et al. 2020</a>)</span> and
-<span class="math inline">\(size = 0.58\)</span> <span class="citation">(<a href="#ref-wang2020">Wang et al. 2020</a>)</span>.</p>
-<details class="chunk-details" open><summary class="chunk-summary"><span class="chunk-summary-text">Code</span></summary><div class="sourceCode" id="cb7"><pre class="downlit sourceCode r">
+characterised by a negative binomial with
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>m</mi><mi>u</mi><mo>=</mo><mn>2.5</mn></mrow><annotation encoding="application/x-tex">mu = 2.5</annotation></semantics></math><span class="citation">(<a href="#ref-abbott2020">Abbott et al.
+2020</a>)</span> and
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>s</mi><mi>i</mi><mi>z</mi><mi>e</mi><mo>=</mo><mn>0.58</mn></mrow><annotation encoding="application/x-tex">size = 0.58</annotation></semantics></math><span class="citation">(<a href="#ref-wang2020">Wang et al.
+2020</a>)</span>.</p>
+<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">mu</span> <span class="op">&lt;-</span> <span class="fl">2.5</span></span>
 <span><span class="va">size</span> <span class="op">&lt;-</span> <span class="fl">0.58</span></span></code></pre></div>
-</details><p>In this parameterization, <span class="math inline">\(mu\)</span>
-represents the <span class="math inline">\(R_0\)</span>, which is defined as the average number of
-cases produced by a single individual in an entirely susceptible population.
-The parameter <span class="math inline">\(size\)</span> represents superspreading, that is, the degree of
-heterogeneity in transmission by single individuals.</p>
+<p>In this parameterization,
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>m</mi><mi>u</mi></mrow><annotation encoding="application/x-tex">mu</annotation></semantics></math>
+represents the
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>R</mi><mn>0</mn></msub><annotation encoding="application/x-tex">R_0</annotation></semantics></math>,
+which is defined as the average number of cases produced by a single
+individual in an entirely susceptible population. The parameter
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>s</mi><mi>i</mi><mi>z</mi><mi>e</mi></mrow><annotation encoding="application/x-tex">size</annotation></semantics></math>
+represents superspreading, that is, the degree of heterogeneity in
+transmission by single individuals.</p>
 </div>
 <div class="section level3">
 <h3 id="simulation-controls">Simulation controls<a class="anchor" aria-label="anchor" href="#simulation-controls"></a>
 </h3>
-<p>For this example, we will simulate outbreaks that end <span class="math inline">\(21\)</span> days after the last
-date of observations in the <code>seed_cases</code> dataset.</p>
-<details class="chunk-details" open><summary class="chunk-summary"><span class="chunk-summary-text">Code</span></summary><div class="sourceCode" id="cb8"><pre class="downlit sourceCode r">
+<p>For this example, we will simulate outbreaks that end
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mn>21</mn><annotation encoding="application/x-tex">21</annotation></semantics></math>
+days after the last date of observations in the <code>seed_cases</code>
+dataset.</p>
+<div class="sourceCode" id="cb8"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="co">#' Date to end simulation</span></span>
 <span><span class="va">projection_window</span> <span class="op">&lt;-</span> <span class="fl">21</span></span>
 <span><span class="va">tf</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/Extremes.html" class="external-link">max</a></span><span class="op">(</span><span class="va">days_since_index</span><span class="op">)</span> <span class="op">+</span> <span class="va">projection_window</span></span>
 <span><span class="va">tf</span></span>
 <span><span class="co">#&gt; [1] 27</span></span></code></pre></div>
-</details><p><code><a href="../reference/simulate_chains.html">simulate_chains()</a></code> is stochastic, meaning the results are different every
-time it is run for the same set of parameters. We will, therefore, run the
-simulations <span class="math inline">\(100\)</span> times and aggregate the results.</p>
+<p><code><a href="../reference/simulate_chains.html">simulate_chains()</a></code> is stochastic, meaning the results are
+different every time it is run for the same set of parameters. We will,
+therefore, run the simulations
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mn>100</mn><annotation encoding="application/x-tex">100</annotation></semantics></math>
+times and aggregate the results.</p>
 <p>Let us specify that.</p>
-<details class="chunk-details" open><summary class="chunk-summary"><span class="chunk-summary-text">Code</span></summary><div class="sourceCode" id="cb9"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="co">#' Number of simulations</span></span>
 <span><span class="va">sim_rep</span> <span class="op">&lt;-</span> <span class="fl">100</span></span></code></pre></div>
-</details><p>Lastly, since, we have specified that <span class="math inline">\(R0 &gt; 1\)</span>, it means the epidemic could
-potentially grow without end. Hence, we must specify an end point for the
-simulations.</p>
-<p><code><a href="../reference/simulate_chains.html">simulate_chains()</a></code> provides the <code>stat_threshold</code> argument for this purpose.
-Above <code>stat_threshold</code>, the simulation is cut off. If this value is
-not specified, it assumes a value of infinity. Here, we will
-assume a maximum chain size of <span class="math inline">\(1000\)</span>.</p>
-<details class="chunk-details" open><summary class="chunk-summary"><span class="chunk-summary-text">Code</span></summary><div class="sourceCode" id="cb10"><pre class="downlit sourceCode r">
+<p>Lastly, since, we have specified that
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>R</mi><mn>0</mn><mo>&gt;</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">R0 &gt; 1</annotation></semantics></math>,
+it means the epidemic could potentially grow without end. Hence, we must
+specify an end point for the simulations.</p>
+<p><code><a href="../reference/simulate_chains.html">simulate_chains()</a></code> provides the
+<code>stat_threshold</code> argument for this purpose. Above
+<code>stat_threshold</code>, the simulation is cut off. If this value is
+not specified, it assumes a value of infinity. Here, we will assume a
+maximum chain size of
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mn>1000</mn><annotation encoding="application/x-tex">1000</annotation></semantics></math>.</p>
+<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="co">#' Maximum chain size allowed</span></span>
 <span><span class="va">stat_threshold</span> <span class="op">&lt;-</span> <span class="fl">1000</span></span></code></pre></div>
-</details>
 </div>
 </div>
 <div class="section level2">
@@ -258,17 +311,16 @@ <h2 id="modelling-assumptions">Modelling assumptions<a class="anchor" aria-label
 <li>No interventions have been implemented.</li>
 <li>Population is homogeneous and well-mixed.</li>
 </ol>
-<p>To summarise the whole set up so far, we are going to simulate
-each chain 100 times, projecting cases over
-21 days after the first 6 days, and
-assuming that no outbreak size exceeds 1000 cases.</p>
+<p>To summarise the whole set up so far, we are going to simulate each
+chain 100 times, projecting cases over 21 days after the first 6 days,
+and assuming that no outbreak size exceeds 1000 cases.</p>
 </div>
 <div class="section level2">
 <h2 id="running-the-simulations">Running the simulations<a class="anchor" aria-label="anchor" href="#running-the-simulations"></a>
 </h2>
-<p>We will use the function <code><a href="https://rdrr.io/r/base/lapply.html" class="external-link">lapply()</a></code> to run the simulations and bind them
-by rows with <code><a href="https://dplyr.tidyverse.org/reference/bind_rows.html" class="external-link">dplyr::bind_rows()</a></code>.</p>
-<details class="chunk-details" open><summary class="chunk-summary"><span class="chunk-summary-text">Code</span></summary><div class="sourceCode" id="cb11"><pre class="downlit sourceCode r">
+<p>We will use the function <code><a href="https://rdrr.io/r/base/lapply.html" class="external-link">lapply()</a></code> to run the simulations
+and bind them by rows with <code><a href="https://dplyr.tidyverse.org/reference/bind_rows.html" class="external-link">dplyr::bind_rows()</a></code>.</p>
+<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/Random.html" class="external-link">set.seed</a></span><span class="op">(</span><span class="fl">1234</span><span class="op">)</span></span>
 <span><span class="va">sim_chain_sizes</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">lapply</a></span><span class="op">(</span></span>
 <span>  <span class="fu"><a href="https://rdrr.io/r/base/seq.html" class="external-link">seq_len</a></span><span class="op">(</span><span class="va">sim_rep</span><span class="op">)</span>,</span>
@@ -289,8 +341,8 @@ <h2 id="running-the-simulations">Running the simulations<a class="anchor" aria-l
 <span><span class="op">)</span></span>
 <span></span>
 <span><span class="va">sim_output</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://dplyr.tidyverse.org/reference/bind_rows.html" class="external-link">bind_rows</a></span><span class="op">(</span><span class="va">sim_chain_sizes</span><span class="op">)</span></span></code></pre></div>
-</details><p>Let us view the first few rows of the simulation results.</p>
-<details class="chunk-details" open><summary class="chunk-summary"><span class="chunk-summary-text">Code</span></summary><div class="sourceCode" id="cb12"><pre class="downlit sourceCode r">
+<p>Let us view the first few rows of the simulation results.</p>
+<div class="sourceCode" id="cb12"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/utils/head.html" class="external-link">head</a></span><span class="op">(</span><span class="va">sim_output</span><span class="op">)</span></span>
 <span><span class="co">#&gt;    chain infector infectee generation      time sim</span></span>
 <span><span class="co">#&gt; 14     3        1        2          2  8.123133   1</span></span>
@@ -299,7 +351,6 @@ <h2 id="running-the-simulations">Running the simulations<a class="anchor" aria-l
 <span><span class="co">#&gt; 17     3        1        5          2 11.244838   1</span></span>
 <span><span class="co">#&gt; 18     7        1        2          2  7.022334   1</span></span>
 <span><span class="co">#&gt; 19     7        1        3          2 12.182368   1</span></span></code></pre></div>
-</details>
 </div>
 <div class="section level2">
 <h2 id="post-processing">Post-processing<a class="anchor" aria-label="anchor" href="#post-processing"></a>
@@ -309,7 +360,7 @@ <h2 id="post-processing">Post-processing<a class="anchor" aria-label="anchor" hr
 the median cases per day aggregated over all simulations.</p>
 <p>First, we will create the daily time series per simulation by
 aggregating the number of cases per day of each simulation.</p>
-<details class="chunk-details" open><summary class="chunk-summary"><span class="chunk-summary-text">Code</span></summary><div class="sourceCode" id="cb13"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="co"># Daily number of cases for each simulation</span></span>
 <span><span class="va">incidence_ts</span> <span class="op">&lt;-</span> <span class="va">sim_output</span> <span class="op"><a href="https://magrittr.tidyverse.org/reference/pipe.html" class="external-link">%&gt;%</a></span></span>
 <span>  <span class="fu"><a href="https://dplyr.tidyverse.org/reference/mutate.html" class="external-link">mutate</a></span><span class="op">(</span>day <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/Round.html" class="external-link">ceiling</a></span><span class="op">(</span><span class="va">time</span><span class="op">)</span><span class="op">)</span> <span class="op"><a href="https://magrittr.tidyverse.org/reference/pipe.html" class="external-link">%&gt;%</a></span></span>
@@ -326,16 +377,15 @@ <h2 id="post-processing">Post-processing<a class="anchor" aria-label="anchor" hr
 <span><span class="co">#&gt; <span style="color: #BCBCBC;">4</span>     1     4     4</span></span>
 <span><span class="co">#&gt; <span style="color: #BCBCBC;">5</span>     1     6     6</span></span>
 <span><span class="co">#&gt; <span style="color: #BCBCBC;">6</span>     1     7     1</span></span></code></pre></div>
-</details><p>Next, we will add a date column to the results of each simulation
-set. We will use the date of the first case in the observed data
-as the reference start date.</p>
-<details class="chunk-details" open><summary class="chunk-summary"><span class="chunk-summary-text">Code</span></summary><div class="sourceCode" id="cb14"><pre class="downlit sourceCode r">
+<p>Next, we will add a date column to the results of each simulation
+set. We will use the date of the first case in the observed data as the
+reference start date.</p>
+<div class="sourceCode" id="cb14"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="co"># Get start date from the observed data</span></span>
 <span><span class="va">index_date</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/Extremes.html" class="external-link">min</a></span><span class="op">(</span><span class="va">seed_cases</span><span class="op">$</span><span class="va">date</span><span class="op">)</span></span>
 <span><span class="va">index_date</span></span>
-<span><span class="co">#&gt; [1] "2020-03-05"</span></span></code></pre></div>
-</details><details class="chunk-details" open><summary class="chunk-summary"><span class="chunk-summary-text">Code</span></summary><div class="sourceCode" id="cb15"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span></span>
+<span><span class="co">#&gt; [1] "2020-03-05"</span></span>
+<span></span>
 <span><span class="co"># Add a dates column to each simulation result</span></span>
 <span><span class="va">incidence_ts_by_date</span> <span class="op">&lt;-</span> <span class="va">incidence_ts</span> <span class="op"><a href="https://magrittr.tidyverse.org/reference/pipe.html" class="external-link">%&gt;%</a></span></span>
 <span>  <span class="fu"><a href="https://dplyr.tidyverse.org/reference/group_by.html" class="external-link">group_by</a></span><span class="op">(</span><span class="va">sim</span><span class="op">)</span> <span class="op"><a href="https://magrittr.tidyverse.org/reference/pipe.html" class="external-link">%&gt;%</a></span></span>
@@ -352,9 +402,9 @@ <h2 id="post-processing">Post-processing<a class="anchor" aria-label="anchor" hr
 <span><span class="co">#&gt; <span style="color: #BCBCBC;">4</span>     1     4     4 2020-03-08</span></span>
 <span><span class="co">#&gt; <span style="color: #BCBCBC;">5</span>     1     6     6 2020-03-09</span></span>
 <span><span class="co">#&gt; <span style="color: #BCBCBC;">6</span>     1     7     1 2020-03-10</span></span></code></pre></div>
-</details><p>Now we will aggregate the simulations by day and evaluate the median
+<p>Now we will aggregate the simulations by day and evaluate the median
 daily cases across all simulations.</p>
-<details class="chunk-details" open><summary class="chunk-summary"><span class="chunk-summary-text">Code</span></summary><div class="sourceCode" id="cb16"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb15"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="co"># Median daily number of cases aggregated across all simulations</span></span>
 <span><span class="va">median_daily_cases</span> <span class="op">&lt;-</span> <span class="va">incidence_ts_by_date</span> <span class="op"><a href="https://magrittr.tidyverse.org/reference/pipe.html" class="external-link">%&gt;%</a></span></span>
 <span>  <span class="fu"><a href="https://dplyr.tidyverse.org/reference/group_by.html" class="external-link">group_by</a></span><span class="op">(</span><span class="va">date</span><span class="op">)</span> <span class="op"><a href="https://magrittr.tidyverse.org/reference/pipe.html" class="external-link">%&gt;%</a></span></span>
@@ -372,14 +422,13 @@ <h2 id="post-processing">Post-processing<a class="anchor" aria-label="anchor" hr
 <span><span class="co">#&gt; <span style="color: #BCBCBC;">4</span> 2020-03-08            4</span></span>
 <span><span class="co">#&gt; <span style="color: #BCBCBC;">5</span> 2020-03-09            5</span></span>
 <span><span class="co">#&gt; <span style="color: #BCBCBC;">6</span> 2020-03-10            8</span></span></code></pre></div>
-</details>
 </div>
 <div class="section level2">
 <h2 id="visualization">Visualization<a class="anchor" aria-label="anchor" href="#visualization"></a>
 </h2>
-<p>We will now plot the individual simulation results alongside the median
-of the aggregated results.</p>
-<details class="chunk-details" open><summary class="chunk-summary"><span class="chunk-summary-text">Code</span></summary><div class="sourceCode" id="cb17"><pre class="downlit sourceCode r">
+<p>We will now plot the individual simulation results alongside the
+median of the aggregated results.</p>
+<div class="sourceCode" id="cb16"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span></span>
 <span><span class="co"># since all simulations may end at a different date, we will find the minimum</span></span>
 <span><span class="co"># final date for all simulations for the purposes of visualisation.</span></span>
@@ -463,50 +512,82 @@ <h2 id="visualization">Visualization<a class="anchor" aria-label="anchor" href="
 <span>    linetype <span class="op">=</span> <span class="st">"dashed"</span></span>
 <span>  <span class="op">)</span> <span class="op">+</span></span>
 <span>  <span class="fu"><a href="https://ggplot2.tidyverse.org/reference/labs.html" class="external-link">labs</a></span><span class="op">(</span>x <span class="op">=</span> <span class="st">"Date"</span>, y <span class="op">=</span> <span class="st">"Daily cases"</span><span class="op">)</span></span></code></pre></div>
-</details><div class="figure">
-<span style="display:block;" id="fig:viz"></span>
-<img src="projecting_incidence_files/figure-html/viz-1.png" alt="COVID-19 incidence in South Africa projected over a two week window in 2020. The light gray lines represent the individual simulations, the red line represents the median daily cases across all simulations, the black connected dots represent the observed data, and the dashed vertical line marks the beginning of the projection."><p class="caption">
-Figure 1: COVID-19 incidence in South Africa projected over a two week window in 2020. The light gray lines represent the individual simulations, the red line represents the median daily cases across all simulations, the black connected dots represent the observed data, and the dashed vertical line marks the beginning of the projection.
+<div class="figure">
+<img src="projecting_incidence_files/figure-html/viz-1.png" alt="COVID-19 incidence in South Africa projected over a two week window in 2020. The light gray lines represent the individual simulations, the red line represents the median daily cases across all simulations, the black connected dots represent the observed data, and the dashed vertical line marks the beginning of the projection." width="576"><p class="caption">
+COVID-19 incidence in South Africa projected over a two week window in
+2020. The light gray lines represent the individual simulations, the red
+line represents the median daily cases across all simulations, the black
+connected dots represent the observed data, and the dashed vertical line
+marks the beginning of the projection.
 </p>
 </div>
 </div>
 <div class="section level2 unnumbered">
-<h2 id="references">References<a class="anchor" aria-label="anchor" href="#references"></a>
+<h2 class="unnumbered" id="references">References<a class="anchor" aria-label="anchor" href="#references"></a>
 </h2>
 <div id="refs" class="references csl-bib-body hanging-indent" entry-spacing="0">
 <div id="ref-abbott2020" class="csl-entry">
-Abbott, Sam, Joel Hellewell, James Munday, Sebastian Funk, CMMID nCoV working group, et al. 2020. <span>“The Transmissibility of Novel Coronavirus in the Early Stages of the 2019-20 Outbreak in Wuhan: Exploring Initial Point-Source Exposure Sizes and Durations Using Scenario Analysis.”</span> <em>Wellcome Open Research</em> 5.
+Abbott, Sam, Joel Hellewell, James Munday, Sebastian Funk, CMMID nCoV
+working group, et al. 2020. <span>“The Transmissibility of Novel
+Coronavirus in the Early Stages of the 2019-20 Outbreak in Wuhan:
+Exploring Initial Point-Source Exposure Sizes and Durations Using
+Scenario Analysis.”</span> <em>Wellcome Open Research</em> 5.
 </div>
 <div id="ref-limpert2001" class="csl-entry">
-Limpert, Eckhard, Werner A. Stahel, and Markus Abbt. 2001. <span>“Log-Normal Distributions Across the Sciences: Keys and Clues.”</span> <em>BioScience</em> 51 (5): 341–52. <a href="https://doi.org/10.1641/0006-3568(2001)051%5B0341:LNDATS%5D2.0.CO;2" class="external-link">https://doi.org/10.1641/0006-3568(2001)051[0341:LNDATS]2.0.CO;2</a>.
+Limpert, Eckhard, Werner A. Stahel, and Markus Abbt. 2001.
+<span>“Log-Normal Distributions Across the Sciences: Keys and
+Clues.”</span> <em>BioScience</em> 51 (5): 341–52. <a href="https://doi.org/10.1641/0006-3568(2001)051%5B0341:LNDATS%5D2.0.CO;2" class="external-link">https://doi.org/10.1641/0006-3568(2001)051[0341:LNDATS]2.0.CO;2</a>.
 </div>
 <div id="ref-lloyd-smith2005" class="csl-entry">
-Lloyd-Smith, J. O., S. J. Schreiber, P. E. Kopp, and W. M. Getz. 2005. <span>“Superspreading and the Effect of Individual Variation on Disease Emergence.”</span> <em>Nature</em> 438 (7066): 355–59. <a href="https://doi.org/10.1038/nature04153" class="external-link">https://doi.org/10.1038/nature04153</a>.
+Lloyd-Smith, J. O., S. J. Schreiber, P. E. Kopp, and W. M. Getz. 2005.
+<span>“Superspreading and the Effect of Individual Variation on Disease
+Emergence.”</span> <em>Nature</em> 438 (7066): 355–59. <a href="https://doi.org/10.1038/nature04153" class="external-link">https://doi.org/10.1038/nature04153</a>.
 </div>
 <div id="ref-marivate2020" class="csl-entry">
-Marivate, Vukosi, and Herkulaas MvE Combrink. 2020. <span>“Use of Available Data to Inform the COVID-19 Outbreak in South Africa: A Case Study.”</span> <em>arXiv Preprint arXiv:2004.04813</em>.
+Marivate, Vukosi, and Herkulaas MvE Combrink. 2020. <span>“Use of
+Available Data to Inform the COVID-19 Outbreak in South Africa: A Case
+Study.”</span> <em>arXiv Preprint arXiv:2004.04813</em>.
 </div>
 <div id="ref-nishiura2007" class="csl-entry">
-Nishiura, Hiroshi. 2007. <span>“Early Efforts in Modeling the Incubation Period of Infectious Diseases with an Acute Course of Illness.”</span> <em>Emerging Themes in Epidemiology</em> 4: 1–12. <a href="https://doi.org/10.1186/1742-7622-4-2" class="external-link">https://doi.org/10.1186/1742-7622-4-2</a>.
+Nishiura, Hiroshi. 2007. <span>“Early Efforts in Modeling the Incubation
+Period of Infectious Diseases with an Acute Course of Illness.”</span>
+<em>Emerging Themes in Epidemiology</em> 4: 1–12. <a href="https://doi.org/10.1186/1742-7622-4-2" class="external-link">https://doi.org/10.1186/1742-7622-4-2</a>.
 </div>
 <div id="ref-pearson2020" class="csl-entry">
-Pearson, Carl A.B., Cari van Schalkwyk, Anna M. Foss, Kathleen M. O’Reilly, and Juliet R.C. Pulliam. 2020. <span>“Projected Early Spread of COVID-19 in Africa Through 1 June 2020.”</span> <em>Eurosurveillance</em> 25 (18): 1–6. <a href="https://doi.org/10.2807/1560-7917.ES.2020.25.18.2000543" class="external-link">https://doi.org/10.2807/1560-7917.ES.2020.25.18.2000543</a>.
+Pearson, Carl A.B., Cari van Schalkwyk, Anna M. Foss, Kathleen M.
+O’Reilly, and Juliet R.C. Pulliam. 2020. <span>“Projected Early Spread
+of COVID-19 in Africa Through 1 June 2020.”</span>
+<em>Eurosurveillance</em> 25 (18): 1–6. <a href="https://doi.org/10.2807/1560-7917.ES.2020.25.18.2000543" class="external-link">https://doi.org/10.2807/1560-7917.ES.2020.25.18.2000543</a>.
 </div>
 <div id="ref-wang2020" class="csl-entry">
-Wang, Liang, Xavier Didelot, Jing Yang, Gary Wong, Yi Shi, Wenjun Liu, George F. Gao, and Yuhai Bi. 2020. <span>“Inference of Person-to-Person Transmission of COVID-19 Reveals Hidden Super-Spreading Events During the Early Outbreak Phase.”</span> <em>Nature Communications</em> 11 (1): 1–6. <a href="https://doi.org/10.1038/s41467-020-18836-4" class="external-link">https://doi.org/10.1038/s41467-020-18836-4</a>.
+Wang, Liang, Xavier Didelot, Jing Yang, Gary Wong, Yi Shi, Wenjun Liu,
+George F. Gao, and Yuhai Bi. 2020. <span>“Inference of Person-to-Person
+Transmission of COVID-19 Reveals Hidden Super-Spreading Events During
+the Early Outbreak Phase.”</span> <em>Nature Communications</em> 11 (1):
+1–6. <a href="https://doi.org/10.1038/s41467-020-18836-4" class="external-link">https://doi.org/10.1038/s41467-020-18836-4</a>.
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       <img src="../logo.svg" class="logo" alt=""><h1>Theoretical background for epichains</h1>
-                        <h4 data-toc-skip class="author">Sebastian Funk and James Azam</h4>
-                        <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/vignettes/theoretical_background.Rmd" class="external-link"><code>vignettes/theoretical_background.Rmd</code></a></small>
+                        <h4 data-toc-skip class="author">Sebastian Funk
+and James Azam</h4>
+            
+      
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/vignettes/theoretical_background.Rmd" class="external-link"><code>vignettes/theoretical_background.Rmd</code></a></small>
       <div class="d-none name"><code>theoretical_background.Rmd</code></div>
     </div>
-        <p><em>epichains</em> provides methods to analyse and simulate the size and length of branching processes with an arbitrary offspring distribution.
-In this vignette we lay out the mathematical concepts behind the functionality available
-in the package.</p>
+
+    
+    
+<p><em>epichains</em> provides methods to analyse and simulate the size
+and length of branching processes with an arbitrary offspring
+distribution. In this vignette we lay out the mathematical concepts
+behind the functionality available in the package.</p>
 <div class="section level2">
 <h2 id="branching-processes">Branching processes<a class="anchor" aria-label="anchor" href="#branching-processes"></a>
 </h2>
-<p><a href="https://en.wikipedia.org/wiki/Branching_process" class="external-link">Branching processes</a> are a class of models that are used to model the growth of populations. They assume that each member of the population produces a number of offspring, <span class="math inline">\(Z\)</span>, that is a random variable with probability mass function <span class="math inline">\(p(Z = z | \theta)\)</span>, called the <em>offspring distribution</em>.
-Their use has a long history in epidemiology, where the population is interpreted as a pathogen, and the offspring as new hosts that it infects <span class="citation">(<a href="#ref-farrington2003">Farrington, Kanaan, and Gay 2003</a>)</span>.
-Below we will call these infected individuals <em>cases</em> but the methods could be applied in other contexts where branching processes are to be used.</p>
+<p><a href="https://en.wikipedia.org/wiki/Branching_process" class="external-link">Branching
+processes</a> are a class of models that are used to model the growth of
+populations. They assume that each member of the population produces a
+number of offspring,
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>Z</mi><annotation encoding="application/x-tex">Z</annotation></semantics></math>,
+that is a random variable with probability mass function
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>Z</mi><mo>=</mo><mi>z</mi><mo stretchy="false" form="prefix">|</mo><mi>θ</mi><mo stretchy="true" form="postfix">)</mo></mrow></mrow><annotation encoding="application/x-tex">p(Z = z | \theta)</annotation></semantics></math>,
+called the <em>offspring distribution</em>. Their use has a long history
+in epidemiology, where the population is interpreted as a pathogen, and
+the offspring as new hosts that it infects <span class="citation">(<a href="#ref-farrington2003">Farrington, Kanaan, and Gay 2003</a>)</span>.
+Below we will call these infected individuals <em>cases</em> but the
+methods could be applied in other contexts where branching processes are
+to be used.</p>
 </div>
 <div class="section level2">
 <h2 id="simulation">Simulation<a class="anchor" aria-label="anchor" href="#simulation"></a>
 </h2>
-<p>To simulate from a branching process, we start with a single case and proceed in discrete steps or generations, drawing from the offspring distribution <span class="math inline">\(p(Z=z | \theta)\)</span> to generate new cases from each case.</p>
-<p>Given an infector <span class="math inline">\(i\)</span> and infectee <span class="math inline">\(j\)</span>, we can additionally assign them a distribution of times <span class="math inline">\(T\)</span> that approximates when the infection event occurred. If we define <span class="math inline">\(T\)</span> as a random variable with distribution <span class="math inline">\(f(T = t; \theta)\)</span> we can assign each case <span class="math inline">\(j\)</span> a time <span class="math inline">\(t_{j}\)</span> which, if case <span class="math inline">\(j\)</span> has been affected by case <span class="math inline">\(i\)</span> is given by <span class="math inline">\(f(t_{j} - t_{i} | \theta)\)</span>.
-If we identify the timing of cases by the time of their symptom onset this is the <a href="https://en.wikipedia.org/wiki/Serial_interval" class="external-link">serial interval</a>, but depending on case definitions this could be another interval.</p>
+<p>To simulate from a branching process, we start with a single case and
+proceed in discrete steps or generations, drawing from the offspring
+distribution
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>Z</mi><mo>=</mo><mi>z</mi><mo stretchy="false" form="prefix">|</mo><mi>θ</mi><mo stretchy="true" form="postfix">)</mo></mrow></mrow><annotation encoding="application/x-tex">p(Z=z | \theta)</annotation></semantics></math>
+to generate new cases from each case.</p>
+<p>Given an infector
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>i</mi><annotation encoding="application/x-tex">i</annotation></semantics></math>
+and infectee
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>j</mi><annotation encoding="application/x-tex">j</annotation></semantics></math>,
+we can additionally assign them a distribution of times
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>T</mi><annotation encoding="application/x-tex">T</annotation></semantics></math>
+that approximates when the infection event occurred. If we define
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>T</mi><annotation encoding="application/x-tex">T</annotation></semantics></math>
+as a random variable with distribution
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>f</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>T</mi><mo>=</mo><mi>t</mi><mo>;</mo><mi>θ</mi><mo stretchy="true" form="postfix">)</mo></mrow></mrow><annotation encoding="application/x-tex">f(T = t; \theta)</annotation></semantics></math>
+we can assign each case
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>j</mi><annotation encoding="application/x-tex">j</annotation></semantics></math>
+a time
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>t</mi><mi>j</mi></msub><annotation encoding="application/x-tex">t_{j}</annotation></semantics></math>
+which, if case
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>j</mi><annotation encoding="application/x-tex">j</annotation></semantics></math>
+has been affected by case
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>i</mi><annotation encoding="application/x-tex">i</annotation></semantics></math>
+is given by
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>f</mi><mrow><mo stretchy="true" form="prefix">(</mo><msub><mi>t</mi><mi>j</mi></msub><mo>−</mo><msub><mi>t</mi><mi>i</mi></msub><mo stretchy="false" form="prefix">|</mo><mi>θ</mi><mo stretchy="true" form="postfix">)</mo></mrow></mrow><annotation encoding="application/x-tex">f(t_{j} - t_{i} | \theta)</annotation></semantics></math>.
+If we identify the timing of cases by the time of their symptom onset
+this is the <a href="https://en.wikipedia.org/wiki/Serial_interval" class="external-link">serial
+interval</a>, but depending on case definitions this could be another
+interval.</p>
 <div class="section level3">
 <h3 id="summary-statistics">Summary statistics<a class="anchor" aria-label="anchor" href="#summary-statistics"></a>
 </h3>
-<p>Branching process simulations end when they have gone extinct, that is, no more offspring are being produced, or because of some stopping criterion. To summarise the simulations, we either study the <em>size</em> or <em>length</em> of the resulting <em>chain</em> of cases.
-The size <span class="math inline">\(S\)</span> of a chain is the number of cases that have occurred over the course of the simulation including the initial case so that <span class="math inline">\(S \geq 1\)</span>.
-The length <span class="math inline">\(L\)</span> of a chain is the number of generations that have been simulated including the initial case so that <span class="math inline">\(L \geq 1\)</span>.</p>
+<p>Branching process simulations end when they have gone extinct, that
+is, no more offspring are being produced, or because of some stopping
+criterion. To summarise the simulations, we either study the
+<em>size</em> or <em>length</em> of the resulting <em>chain</em> of
+cases. The size
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>S</mi><annotation encoding="application/x-tex">S</annotation></semantics></math>
+of a chain is the number of cases that have occurred over the course of
+the simulation including the initial case so that
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>S</mi><mo>≥</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">S \geq 1</annotation></semantics></math>.
+The length
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>L</mi><annotation encoding="application/x-tex">L</annotation></semantics></math>
+of a chain is the number of generations that have been simulated
+including the initial case so that
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>L</mi><mo>≥</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">L \geq 1</annotation></semantics></math>.</p>
 </div>
 </div>
 <div class="section level2">
 <h2 id="inference">Inference<a class="anchor" aria-label="anchor" href="#inference"></a>
 </h2>
-<p>By characterising a chains of cases by their size of length we can conduct inference to learn about the underlying parameters <span class="math inline">\(\theta\)</span> from observation of chain sizes or chain lengths <span class="citation">(<a href="#ref-blumberg2013">Blumberg and Lloyd-Smith 2013</a>)</span>.
-In general this is only possible for <em>subcritical</em> branching processes, i.e. ones where the mean number of offspring is less than 1, as otherwise the branching process could grow forever.
-However, we can expand the theory to <em>supercritical</em> branching processes, i.e. ones where the mean number of offspring is greater than 1, by defining a cut off of chain size or length beyond which we treat the chain as if it had infinite size or length, respectively.</p>
+<p>By characterising a chains of cases by their size of length we can
+conduct inference to learn about the underlying parameters
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>θ</mi><annotation encoding="application/x-tex">\theta</annotation></semantics></math>
+from observation of chain sizes or chain lengths <span class="citation">(<a href="#ref-blumberg2013">Blumberg and Lloyd-Smith
+2013</a>)</span>. In general this is only possible for
+<em>subcritical</em> branching processes, i.e. ones where the mean
+number of offspring is less than 1, as otherwise the branching process
+could grow forever. However, we can expand the theory to
+<em>supercritical</em> branching processes, i.e. ones where the mean
+number of offspring is greater than 1, by defining a cut off of chain
+size or length beyond which we treat the chain as if it had infinite
+size or length, respectively.</p>
 <div class="section level3">
 <h3 id="size-and-length-distributions-for-some-offspring-distributions">Size and length distributions for some offspring distributions<a class="anchor" aria-label="anchor" href="#size-and-length-distributions-for-some-offspring-distributions"></a>
 </h3>
-<p>We show the equations for the size and length distributions for some offspring distributions where they can be derived analytically:
-<a href="https://en.wikipedia.org/wiki/Poisson_distribution" class="external-link">Poisson</a>,
-<a href="https://en.wikipedia.org/wiki/Negative_binomial_distribution" class="external-link">negative binomial</a>,
-<a href="https://en.wikipedia.org/wiki/Geometric_distribution" class="external-link">geometric</a>,
-and a <a href="https://en.wikipedia.org/wiki/Gamma_distribution" class="external-link">gamma</a>-<a href="https://en.wikipedia.org/wiki/Borel_distribution" class="external-link">Borel</a> mixture.</p>
+<p>We show the equations for the size and length distributions for some
+offspring distributions where they can be derived analytically: <a href="https://en.wikipedia.org/wiki/Poisson_distribution" class="external-link">Poisson</a>,
+<a href="https://en.wikipedia.org/wiki/Negative_binomial_distribution" class="external-link">negative
+binomial</a>, <a href="https://en.wikipedia.org/wiki/Geometric_distribution" class="external-link">geometric</a>,
+and a <a href="https://en.wikipedia.org/wiki/Gamma_distribution" class="external-link">gamma</a>-<a href="https://en.wikipedia.org/wiki/Borel_distribution" class="external-link">Borel</a>
+mixture.</p>
 <div class="section level4">
 <h4 id="negative-binomial-and-special-cases">Negative binomial and special cases<a class="anchor" aria-label="anchor" href="#negative-binomial-and-special-cases"></a>
 </h4>
-<p>If the offspring distribution is a Poisson distribution, we can interpret its rate parameter <span class="math inline">\(\lambda\)</span> as the basic reproduction number <span class="math inline">\(R_{0}\)</span> of the pathogen.
-In the more general case where the offspring definition can be <em>overdispersed</em> leading to <em>superspreading</em> we can use a negative binomial offspring distribution with mean <span class="math inline">\(\mu\)</span> and overdispersion <span class="math inline">\(k\)</span> <span class="citation">Blumberg and Lloyd-Smith (<a href="#ref-blumberg2013">2013</a>)</span>.
-In that case, the mean parameter <span class="math inline">\(\mu\)</span> is interpreted as the basic reproduction number <span class="math inline">\(R_0\)</span> of the pathogen.
-The negative binomial distribution arises from a Poisson-gamma mixture and thus a branching process with negative binomial distributed offspring can be interpreted as one with Poisson distributed offspring where the basic reproduction number <span class="math inline">\(R_0\)</span> itself varies according to a gamma distribution.
-The amount of variation in <span class="math inline">\(R_0\)</span> is then interpreted as individual-level variation in transmission representing overdispersion or superspreading, and the degree to which this happens is given by the overdispersion parameter <span class="math inline">\(k\)</span>.</p>
+<p>If the offspring distribution is a Poisson distribution, we can
+interpret its rate parameter
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>λ</mi><annotation encoding="application/x-tex">\lambda</annotation></semantics></math>
+as the basic reproduction number
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>R</mi><mn>0</mn></msub><annotation encoding="application/x-tex">R_{0}</annotation></semantics></math>
+of the pathogen. In the more general case where the offspring definition
+can be <em>overdispersed</em> leading to <em>superspreading</em> we can
+use a negative binomial offspring distribution with mean
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>μ</mi><annotation encoding="application/x-tex">\mu</annotation></semantics></math>
+and overdispersion
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>k</mi><annotation encoding="application/x-tex">k</annotation></semantics></math><span class="citation">Blumberg and Lloyd-Smith (<a href="#ref-blumberg2013">2013</a>)</span>. In that case, the mean
+parameter
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>μ</mi><annotation encoding="application/x-tex">\mu</annotation></semantics></math>
+is interpreted as the basic reproduction number
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>R</mi><mn>0</mn></msub><annotation encoding="application/x-tex">R_0</annotation></semantics></math>
+of the pathogen. The negative binomial distribution arises from a
+Poisson-gamma mixture and thus a branching process with negative
+binomial distributed offspring can be interpreted as one with Poisson
+distributed offspring where the basic reproduction number
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>R</mi><mn>0</mn></msub><annotation encoding="application/x-tex">R_0</annotation></semantics></math>
+itself varies according to a gamma distribution. The amount of variation
+in
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>R</mi><mn>0</mn></msub><annotation encoding="application/x-tex">R_0</annotation></semantics></math>
+is then interpreted as individual-level variation in transmission
+representing overdispersion or superspreading, and the degree to which
+this happens is given by the overdispersion parameter
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>k</mi><annotation encoding="application/x-tex">k</annotation></semantics></math>.</p>
 <div class="section level5">
 <h5 id="size-distributions">Size distributions<a class="anchor" aria-label="anchor" href="#size-distributions"></a>
 </h5>
-<p>The probability <span class="math inline">\(p\)</span> of a chain of size <span class="math inline">\(S\)</span> given <span class="math inline">\(R_0\)</span> and <span class="math inline">\(k\)</span> in a branching process with negative binomial offspring distribution is given in Eq. 9 of <span class="citation">Blumberg and Lloyd-Smith (<a href="#ref-blumberg2013">2013</a>)</span></p>
-<p><span class="math display">\[
+<p>The probability
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>p</mi><annotation encoding="application/x-tex">p</annotation></semantics></math>
+of a chain of size
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>S</mi><annotation encoding="application/x-tex">S</annotation></semantics></math>
+given
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>R</mi><mn>0</mn></msub><annotation encoding="application/x-tex">R_0</annotation></semantics></math>
+and
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>k</mi><annotation encoding="application/x-tex">k</annotation></semantics></math>
+in a branching process with negative binomial offspring distribution is
+given in Eq. 9 of <span class="citation">Blumberg and Lloyd-Smith (<a href="#ref-blumberg2013">2013</a>)</span></p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>S</mi><mo stretchy="false" form="prefix">|</mo><msub><mi>R</mi><mn>0</mn></msub><mo>,</mo><mi>k</mi><mo stretchy="true" form="postfix">)</mo></mrow><mo>=</mo><mfrac><mrow><mi>Γ</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>k</mi><mi>S</mi><mo>+</mo><mi>S</mi><mo>−</mo><mn>1</mn><mo stretchy="true" form="postfix">)</mo></mrow></mrow><mrow><mi>Γ</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>k</mi><mi>S</mi><mo stretchy="true" form="postfix">)</mo></mrow><mi>Γ</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>S</mi><mo>+</mo><mn>1</mn><mo stretchy="true" form="postfix">)</mo></mrow></mrow></mfrac><mfrac><msup><mrow><mo stretchy="true" form="prefix">(</mo><mfrac><msub><mi>R</mi><mn>0</mn></msub><mi>k</mi></mfrac><mo stretchy="true" form="postfix">)</mo></mrow><mrow><mi>S</mi><mo>−</mo><mn>1</mn></mrow></msup><msup><mrow><mo stretchy="true" form="prefix">(</mo><mn>1</mn><mo>+</mo><mfrac><msub><mi>R</mi><mn>0</mn></msub><mi>k</mi></mfrac><mo stretchy="true" form="postfix">)</mo></mrow><mrow><mi>k</mi><mi>S</mi><mo>+</mo><mi>S</mi><mo>−</mo><mn>1</mn></mrow></msup></mfrac></mrow><annotation encoding="application/x-tex">
 p(S|R_0, k) = \frac{\Gamma(kS + S - 1)}{\Gamma(kS)\Gamma(S + 1)} \frac{\left(\frac{R_0}{k}\right)^{S - 1}}{\left( 1 + \frac{R_0}{k} \right)^{kS + S - 1}}
-\]</span>
-where <span class="math inline">\(\Gamma\)</span> is the gamma function.
-In order to estimate <span class="math inline">\(S\)</span> from a given <span class="math inline">\(R_0\)</span> and <span class="math inline">\(k\)</span> we can define a likelihood function <span class="math inline">\(L(S) = p(S|R_0, k)\)</span>.
+</annotation></semantics></math></p>
+<p>where
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>Γ</mi><annotation encoding="application/x-tex">\Gamma</annotation></semantics></math>
+is the gamma function. In order to estimate
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>S</mi><annotation encoding="application/x-tex">S</annotation></semantics></math>
+from a given
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>R</mi><mn>0</mn></msub><annotation encoding="application/x-tex">R_0</annotation></semantics></math>
+and
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>k</mi><annotation encoding="application/x-tex">k</annotation></semantics></math>
+we can define a likelihood function
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>L</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>S</mi><mo stretchy="true" form="postfix">)</mo></mrow><mo>=</mo><mi>p</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>S</mi><mo stretchy="false" form="prefix">|</mo><msub><mi>R</mi><mn>0</mn></msub><mo>,</mo><mi>k</mi><mo stretchy="true" form="postfix">)</mo></mrow></mrow><annotation encoding="application/x-tex">L(S) = p(S|R_0, k)</annotation></semantics></math>.
 The corresponding log-likelihood is</p>
-<p><span class="math display">\[\begin{align}
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable><mtr><mtd columnalign="right" style="text-align: right"><mrow><mi mathvariant="normal">L</mi><mi mathvariant="normal">L</mi></mrow><mrow><mo stretchy="true" form="prefix">(</mo><mi>S</mi><mo stretchy="true" form="postfix">)</mo></mrow><mo>=</mo></mtd><mtd columnalign="left" style="text-align: left"><mo>log</mo><mi>Γ</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>k</mi><mi>S</mi><mo>+</mo><mi>S</mi><mo>−</mo><mn>1</mn><mo stretchy="true" form="postfix">)</mo></mrow><mo>−</mo><mrow><mo stretchy="true" form="prefix">(</mo><mo>log</mo><mi>Γ</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>k</mi><mi>S</mi><mo stretchy="true" form="postfix">)</mo></mrow><mo>+</mo><mo>log</mo><mi>Γ</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>S</mi><mo>−</mo><mn>1</mn><mo stretchy="true" form="postfix">)</mo></mrow><mo stretchy="true" form="postfix">)</mo></mrow></mtd></mtr><mtr><mtd columnalign="right" style="text-align: right"></mtd><mtd columnalign="left" style="text-align: left"><mo>+</mo><mrow><mo stretchy="true" form="prefix">(</mo><mi>S</mi><mo>−</mo><mn>1</mn><mo stretchy="true" form="postfix">)</mo></mrow><mo>log</mo><mfrac><msub><mi>R</mi><mn>0</mn></msub><mi>k</mi></mfrac><mo>−</mo><mrow><mo stretchy="true" form="prefix">(</mo><mi>S</mi><msub><mi>R</mi><mn>0</mn></msub><mo>+</mo><mrow><mo stretchy="true" form="prefix">(</mo><mi>S</mi><mo>−</mo><mn>1</mn><mo stretchy="true" form="postfix">)</mo></mrow><mo stretchy="true" form="postfix">)</mo></mrow><mo>log</mo><mrow><mo stretchy="true" form="prefix">(</mo><mn>1</mn><mo>+</mo><mfrac><msub><mi>R</mi><mn>0</mn></msub><mi>k</mi></mfrac><mo stretchy="true" form="postfix">)</mo></mrow></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{align}
 \mathrm{LL}(S) = &amp;\log\Gamma(kS + S  - 1) - \left(\log\Gamma(kS) + \log\Gamma(S - 1) \right) \\
 &amp; + (S-1) \log \frac{R_0}{k} - (SR_0 + (S - 1)) \log \left(1 + \frac{R_0}{k}\right)
-\end{align}\]</span>
-The log-likelihood for Poisson distributed offspring follows from this where <span class="math inline">\(k\)</span> tends to infinity (corresponding to Eq. 2.2 in <span class="citation">Farrington, Kanaan, and Gay (<a href="#ref-farrington2003">2003</a>)</span>)
-<span class="math display">\[
+\end{align}</annotation></semantics></math></p>
+<p>The log-likelihood for Poisson distributed offspring follows from
+this where
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>k</mi><annotation encoding="application/x-tex">k</annotation></semantics></math>
+tends to infinity (corresponding to Eq. 2.2 in <span class="citation">Farrington, Kanaan, and Gay (<a href="#ref-farrington2003">2003</a>)</span>)</p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi mathvariant="normal">L</mi><mi mathvariant="normal">L</mi></mrow><mrow><mo stretchy="true" form="prefix">(</mo><mi>S</mi><mo stretchy="true" form="postfix">)</mo></mrow><mo>=</mo><mrow><mo stretchy="true" form="prefix">(</mo><mi>S</mi><mo>−</mo><mn>1</mn><mo stretchy="true" form="postfix">)</mo></mrow><mo>log</mo><msub><mi>R</mi><mn>0</mn></msub><mo>−</mo><mi>S</mi><msub><mi>R</mi><mn>0</mn></msub><mo>+</mo><mrow><mo stretchy="true" form="prefix">(</mo><mi>S</mi><mo>−</mo><mn>2</mn><mo stretchy="true" form="postfix">)</mo></mrow><mo>log</mo><mi>S</mi><mo>−</mo><mo>log</mo><mi>Γ</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>S</mi><mo stretchy="true" form="postfix">)</mo></mrow></mrow><annotation encoding="application/x-tex">
 \mathrm{LL}(S) = (S - 1) \log R_0 - S R_0 + (S - 2) \log S - \log\Gamma(S)
-\]</span>
-In all cases the point estimate for the basic reproduction number <span class="math inline">\(\hat{R_0}\)</span> is related to the mean chain size <span class="math inline">\(\bar{S}\)</span> by
-<span class="math display">\[
+</annotation></semantics></math></p>
+<p>In all cases the point estimate for the basic reproduction number
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mover><msub><mi>R</mi><mn>0</mn></msub><mo accent="true">̂</mo></mover><annotation encoding="application/x-tex">\hat{R_0}</annotation></semantics></math>
+is related to the mean chain size
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mover><mi>S</mi><mo accent="true">‾</mo></mover><annotation encoding="application/x-tex">\bar{S}</annotation></semantics></math>
+by</p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover><msub><mi>R</mi><mn>0</mn></msub><mo accent="true">̂</mo></mover><mo>=</mo><mn>1</mn><mo>−</mo><mfrac><mn>1</mn><mover><mi>S</mi><mo accent="true">‾</mo></mover></mfrac></mrow><annotation encoding="application/x-tex">
 \hat{R_0} = 1 - \frac{1}{\bar{S}}
-\]</span>
+</annotation></semantics></math></p>
 </div>
 <div class="section level5">
 <h5 id="length-distributions">Length distributions<a class="anchor" aria-label="anchor" href="#length-distributions"></a>
 </h5>
-<p>The cumulative mass function <span class="math inline">\(F(L)\)</span> of observing a chain of length <span class="math inline">\(L\)</span> when offspring is Poisson distributed is given by Eq. (2.5) in <span class="citation">Farrington, Kanaan, and Gay (<a href="#ref-farrington2003">2003</a>)</span> (there called “outbreak duration”):</p>
-<p><span class="math display">\[
+<p>The cumulative mass function
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>L</mi><mo stretchy="true" form="postfix">)</mo></mrow></mrow><annotation encoding="application/x-tex">F(L)</annotation></semantics></math>
+of observing a chain of length
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>L</mi><annotation encoding="application/x-tex">L</annotation></semantics></math>
+when offspring is Poisson distributed is given by Eq. (2.5) in <span class="citation">Farrington, Kanaan, and Gay (<a href="#ref-farrington2003">2003</a>)</span> (there called “outbreak
+duration”):</p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>L</mi><mo stretchy="true" form="postfix">)</mo></mrow><mo>=</mo><msup><mi>e</mi><mrow><mo>−</mo><msub><mi>R</mi><mn>0</mn></msub></mrow></msup><msub><mi>E</mi><mi>L</mi></msub><mrow><mo stretchy="true" form="prefix">(</mo><msup><mi>e</mi><mrow><msub><mi>R</mi><mn>0</mn></msub><msup><mi>e</mi><mrow><mo>−</mo><msub><mi>R</mi><mn>0</mn></msub></mrow></msup></mrow></msup><mo stretchy="true" form="postfix">)</mo></mrow></mrow><annotation encoding="application/x-tex">
 F(L) = e^{-R_0} E_L \left( e^{R_0 e^{-R_0} } \right)
-\]</span>
-where <span class="math inline">\(E_L(x)\)</span> is the iterated exponential function, <span class="math inline">\(E_0(x) = 1\)</span>, <span class="math inline">\(E_{L + 1}(x) = x^{E_L(x)}\)</span>.
-For geometric distributed offspring (corresponding to a negative Binomial with <span class="math inline">\(k=1\)</span>) this function is given by
-<span class="math display">\[
+</annotation></semantics></math></p>
+<p>where
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>E</mi><mi>L</mi></msub><mrow><mo stretchy="true" form="prefix">(</mo><mi>x</mi><mo stretchy="true" form="postfix">)</mo></mrow></mrow><annotation encoding="application/x-tex">E_L(x)</annotation></semantics></math>
+is the iterated exponential function,
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>E</mi><mn>0</mn></msub><mrow><mo stretchy="true" form="prefix">(</mo><mi>x</mi><mo stretchy="true" form="postfix">)</mo></mrow><mo>=</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">E_0(x) = 1</annotation></semantics></math>,
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>E</mi><mrow><mi>L</mi><mo>+</mo><mn>1</mn></mrow></msub><mrow><mo stretchy="true" form="prefix">(</mo><mi>x</mi><mo stretchy="true" form="postfix">)</mo></mrow><mo>=</mo><msup><mi>x</mi><mrow><msub><mi>E</mi><mi>L</mi></msub><mrow><mo stretchy="true" form="prefix">(</mo><mi>x</mi><mo stretchy="true" form="postfix">)</mo></mrow></mrow></msup></mrow><annotation encoding="application/x-tex">E_{L + 1}(x) = x^{E_L(x)}</annotation></semantics></math>.</p>
+<p>For geometric distributed offspring (corresponding to a negative
+Binomial with
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">k=1</annotation></semantics></math>)
+this function is given by</p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>L</mi><mo stretchy="true" form="postfix">)</mo></mrow><mo>=</mo><mfrac><mrow><mn>1</mn><mo>−</mo><msubsup><mi>R</mi><mn>0</mn><mrow><mi>L</mi><mo>+</mo><mn>1</mn></mrow></msubsup></mrow><mrow><mn>1</mn><mo>−</mo><msubsup><mi>R</mi><mn>0</mn><mrow><mi>L</mi><mo>−</mo><mn>2</mn></mrow></msubsup></mrow></mfrac></mrow><annotation encoding="application/x-tex">
 F(L) = \frac{ 1- R_0^{L + 1} } {1 - R_0^{L - 2}}
-\]</span>
-In both cases <span class="math inline">\(f(L)\)</span> denotes cumulative mass functions and therefore the probability of observing a chain of length <span class="math inline">\(L\)</span> is therefore <span class="math inline">\(f(L) - f(L - 1)\)</span>.
+</annotation></semantics></math></p>
+<p>In both cases
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>f</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>L</mi><mo stretchy="true" form="postfix">)</mo></mrow></mrow><annotation encoding="application/x-tex">f(L)</annotation></semantics></math>
+denotes cumulative mass functions and therefore the probability of
+observing a chain of length
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>L</mi><annotation encoding="application/x-tex">L</annotation></semantics></math>
+is therefore
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>f</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>L</mi><mo stretchy="true" form="postfix">)</mo></mrow><mo>−</mo><mi>f</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>L</mi><mo>−</mo><mn>1</mn><mo stretchy="true" form="postfix">)</mo></mrow></mrow><annotation encoding="application/x-tex">f(L) - f(L - 1)</annotation></semantics></math>.</p>
 </div>
 </div>
 <div class="section level4">
 <h4 id="gamma-borel-mixture">Gamma-Borel mixture<a class="anchor" aria-label="anchor" href="#gamma-borel-mixture"></a>
 </h4>
-<p>The probability distribution of outbreak sizes from a branching process with a Poisson offspring distribution (Eq. 2.2 in <span class="citation">Farrington, Kanaan, and Gay (<a href="#ref-farrington2003">2003</a>)</span>) is a special case of the <a href="https://en.wikipedia.org/wiki/Borel_distribution#Borel%E2%80%93Tanner_distribution" class="external-link">Borel-Tanner distribution</a> starting with 1 individual.
-An alternative to the negative binomial offspring distribution which represents a Poisson-gamma mixture is a Borel-gamma mixture.
-This could represent situations where the variation is not at the <em>individual level</em> but at the <em>chain level</em>, i.e. transmission chains is homogeneous but there is heterogeneity between chains.
-In that case, it can be shown that the resulting log-likelihood of chain sizes is</p>
-<p><span class="math display">\[\begin{align}
+<p>The probability distribution of outbreak sizes from a branching
+process with a Poisson offspring distribution (Eq. 2.2 in <span class="citation">Farrington, Kanaan, and Gay (<a href="#ref-farrington2003">2003</a>)</span>) is a special case of the <a href="https://en.wikipedia.org/wiki/Borel_distribution#Borel%E2%80%93Tanner_distribution" class="external-link">Borel-Tanner
+distribution</a> starting with 1 individual. An alternative to the
+negative binomial offspring distribution which represents a
+Poisson-gamma mixture is a Borel-gamma mixture. This could represent
+situations where the variation is not at the <em>individual level</em>
+but at the <em>chain level</em>, i.e. transmission chains is homogeneous
+but there is heterogeneity between chains. In that case, it can be shown
+that the resulting log-likelihood of chain sizes is</p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable><mtr><mtd columnalign="right" style="text-align: right"><mrow><mi mathvariant="normal">L</mi><mi mathvariant="normal">L</mi></mrow><mrow><mo stretchy="true" form="prefix">(</mo><mi>S</mi><mo stretchy="true" form="postfix">)</mo></mrow><mo>=</mo></mtd><mtd columnalign="left" style="text-align: left"><mo>log</mo><mi>Γ</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>k</mi><mo>+</mo><mi>S</mi><mo>−</mo><mn>1</mn><mo stretchy="true" form="postfix">)</mo></mrow><mo>−</mo><mrow><mo stretchy="true" form="prefix">(</mo><mo>log</mo><mi>Γ</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>k</mi><mo stretchy="true" form="postfix">)</mo></mrow><mo>+</mo><mo>log</mo><mi>Γ</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>S</mi><mo>+</mo><mn>1</mn><mo stretchy="true" form="postfix">)</mo></mrow><mo stretchy="true" form="postfix">)</mo></mrow></mtd></mtr><mtr><mtd columnalign="right" style="text-align: right"></mtd><mtd columnalign="left" style="text-align: left"><mo>+</mo><mrow><mo stretchy="true" form="prefix">(</mo><mi>S</mi><mo>−</mo><mn>1</mn><mo stretchy="true" form="postfix">)</mo></mrow><mo>log</mo><mi>S</mi><mo>−</mo><mi>k</mi><mo>log</mo><mrow><mo stretchy="true" form="prefix">(</mo><mi>S</mi><mo>+</mo><mfrac><msub><mi>R</mi><mn>0</mn></msub><mi>k</mi></mfrac><mo stretchy="true" form="postfix">)</mo></mrow></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{align}
 \mathrm{LL}(S) = &amp;\log\Gamma(k + S - 1) - \left(\log\Gamma(k) + \log\Gamma(S + 1) \right) \\
 &amp; + (S-1) \log S - k \log \left(S + \frac{R_0}{k}\right)
-\end{align}\]</span>
+\end{align}</annotation></semantics></math></p>
 </div>
 </div>
 <div class="section level3">
 <h3 id="numerical-approximations-of-chain-size-and-length-distributions">Numerical approximations of chain size and length distributions<a class="anchor" aria-label="anchor" href="#numerical-approximations-of-chain-size-and-length-distributions"></a>
 </h3>
-<p>When analytic likelihoods are not available a numerical approximation is used to derive the distributions.
-In order to do this, the simulation functionality is be used to generate <span class="math inline">\(n\)</span> simulated chains and the value of the cumulative mass function <span class="math inline">\(P(S|\theta)\)</span> at the observed <span class="math inline">\(S\)</span> approximated by the empirical cumulative distribution function:
-<span class="math display">\[
+<p>When analytic likelihoods are not available a numerical approximation
+is used to derive the distributions. In order to do this, the simulation
+functionality is be used to generate
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>n</mi><annotation encoding="application/x-tex">n</annotation></semantics></math>
+simulated chains and the value of the cumulative mass function
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>S</mi><mo stretchy="false" form="prefix">|</mo><mi>θ</mi><mo stretchy="true" form="postfix">)</mo></mrow></mrow><annotation encoding="application/x-tex">P(S|\theta)</annotation></semantics></math>
+at the observed
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>S</mi><annotation encoding="application/x-tex">S</annotation></semantics></math>
+approximated by the empirical cumulative distribution function:
+<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>S</mi><mo stretchy="false" form="prefix">|</mo><mi>θ</mi><mo stretchy="true" form="postfix">)</mo></mrow><mo>≈</mo><munder><mo>∑</mo><mi>i</mi></munder><mn>𝟏</mn><mrow><mo stretchy="true" form="prefix">(</mo><msub><mi>x</mi><mi>i</mi></msub><mo>&lt;</mo><mo>=</mo><mi>S</mi><mo stretchy="true" form="postfix">)</mo></mrow></mrow><annotation encoding="application/x-tex">
 P(S|\theta) \approx \sum_i \mathbf{1}(x_i &lt;= S)
-\]</span>
-where <span class="math inline">\(\mathbf{1}\)</span> is the indicator function and <span class="math inline">\(x_i\)</span> the i-th observed chain size (or length, if the interest is in <span class="math inline">\(L\)</span>).
-In order to improve this approximation a linear approximation is applied to the values of the empirical distribution function (at the expense of normalisation to 1).
-The (unnormalised) probability of observing <span class="math inline">\(S\)</span> is then given by
-<span class="math display">\[
+</annotation></semantics></math> where
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mn>𝟏</mn><annotation encoding="application/x-tex">\mathbf{1}</annotation></semantics></math>
+is the indicator function and
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>x</mi><mi>i</mi></msub><annotation encoding="application/x-tex">x_i</annotation></semantics></math>
+the i-th observed chain size (or length, if the interest is in
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>L</mi><annotation encoding="application/x-tex">L</annotation></semantics></math>).
+In order to improve this approximation a linear approximation is applied
+to the values of the empirical distribution function (at the expense of
+normalisation to 1).</p>
+<p>The (unnormalised) probability of observing
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>S</mi><annotation encoding="application/x-tex">S</annotation></semantics></math>
+is then given by
+<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>S</mi><mo stretchy="false" form="prefix">|</mo><mi>θ</mi><mo stretchy="true" form="postfix">)</mo></mrow><mo>=</mo><mi>P</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>S</mi><mo stretchy="false" form="prefix">|</mo><mi>θ</mi><mo stretchy="true" form="postfix">)</mo></mrow><mo>−</mo><mi>P</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>S</mi><mo>−</mo><mn>1</mn><mo stretchy="false" form="prefix">|</mo><mi>θ</mi><mo stretchy="true" form="postfix">)</mo></mrow></mrow><annotation encoding="application/x-tex">
 p(S|\theta) = P(S|\theta) - P(S - 1|\theta)
-\]</span>
-and a an equivalent relationship is used for <span class="math inline">\(L\)</span>.
+</annotation></semantics></math> and a an equivalent relationship is
+used for
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>L</mi><annotation encoding="application/x-tex">L</annotation></semantics></math>.</p>
 <div id="refs" class="references csl-bib-body hanging-indent" entry-spacing="0">
 <div id="ref-blumberg2013" class="csl-entry">
-Blumberg, S., and J. O. Lloyd-Smith. 2013. <span>“Comparing Methods for Estimating R0 from the Size Distribution of Subcritical Transmission Chains.”</span> <em>Epidemics</em> 5 (3): 131–45. <a href="https://doi.org/10.1016/j.epidem.2013.05.002" class="external-link">https://doi.org/10.1016/j.epidem.2013.05.002</a>.
+Blumberg, S., and J. O. Lloyd-Smith. 2013. <span>“Comparing Methods for
+Estimating R0 from the Size Distribution of Subcritical Transmission
+Chains.”</span> <em>Epidemics</em> 5 (3): 131–45. <a href="https://doi.org/10.1016/j.epidem.2013.05.002" class="external-link">https://doi.org/10.1016/j.epidem.2013.05.002</a>.
 </div>
 <div id="ref-farrington2003" class="csl-entry">
-Farrington, C. P., M. N. Kanaan, and N. J. Gay. 2003. <span>“Branching Process Models for Surveillance of Infectious Diseases Controlled by Mass Vaccination.”</span> <em>Biostatistics (Oxford, England)</em> 4 (2): 279–95. <a href="https://doi.org/10.1093/biostatistics/4.2.279" class="external-link">https://doi.org/10.1093/biostatistics/4.2.279</a>.
+Farrington, C. P., M. N. Kanaan, and N. J. Gay. 2003. <span>“Branching
+Process Models for Surveillance of Infectious Diseases Controlled by
+Mass Vaccination.”</span> <em>Biostatistics (Oxford, England)</em> 4
+(2): 279–95. <a href="https://doi.org/10.1093/biostatistics/4.2.279" class="external-link">https://doi.org/10.1093/biostatistics/4.2.279</a>.
 </div>
 <div id="ref-lloyd-smith2005" class="csl-entry">
-Lloyd-Smith, J. O., S. J. Schreiber, P. E. Kopp, and W. M. Getz. 2005. <span>“Superspreading and the Effect of Individual Variation on Disease Emergence.”</span> <em>Nature</em> 438 (7066): 355–59. <a href="https://doi.org/10.1038/nature04153" class="external-link">https://doi.org/10.1038/nature04153</a>.
+Lloyd-Smith, J. O., S. J. Schreiber, P. E. Kopp, and W. M. Getz. 2005.
+<span>“Superspreading and the Effect of Individual Variation on Disease
+Emergence.”</span> <em>Nature</em> 438 (7066): 355–59. <a href="https://doi.org/10.1038/nature04153" class="external-link">https://doi.org/10.1038/nature04153</a>.
 </div>
 </div>
 </div>
@@ -202,13 +376,23 @@ <h3 id="numerical-approximations-of-chain-size-and-length-distributions">Numeric
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 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Authors and Citation • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="apple-touch-icon-60x60.png"><script src="deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="deps/headroom-0.11.0/headroom.min.js"></script><script src="deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="deps/search-1.0.0/fuse.min.js"></script><script src="deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="pkgdown.js"></script><meta property="og:title" content="Authors and Citation"><meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg"><!-- Google tag (gtag.js) --><script async src="https://www.googletagmanager.com/gtag/js?id=G-XZ471458FQ"></script><script>
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+
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       <h2>Authors</h2>
+
       <ul class="list-unstyled"><li>
           <p><strong>James M. Azam</strong>. Author, maintainer, copyright holder. <a href="https://orcid.org/0000-0001-5782-7330" target="orcid.widget" aria-label="ORCID" class="external-link"><span class="fab fa-orcid orcid" aria-hidden="true"></span></a>
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@@ -76,31 +93,43 @@ <h2>Authors</h2>
           </p>
         </li>
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+
     <div class="section level2">
       <h2 id="citation">Citation</h2>
-      <p><small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/DESCRIPTION" class="external-link"><code>DESCRIPTION</code></a></small></p>
+      <p><small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/DESCRIPTION" class="external-link"><code>DESCRIPTION</code></a></small></p>
+
       <p>Azam J, Funk S, Finger F (2024).
 <em>epichains: Simulating and Analysing Transmission Chain Statistics Using Branching Process Models</em>.
-R package version 0.1.0,
+R package version 0.1.0.9000,
 https://epiverse-trace.github.io/epichains/, <a href="https://github.com/epiverse-trace/epichains" class="external-link">https://github.com/epiverse-trace/epichains</a>.
 </p>
       <pre>@Manual{,
   title = {epichains: Simulating and Analysing Transmission Chain Statistics Using Branching Process Models},
   author = {James M. Azam and Sebastian Funk and Flavio Finger},
   year = {2024},
-  note = {R package version 0.1.0,
-https://epiverse-trace.github.io/epichains/},
+  note = {R package version 0.1.0.9000,
+    https://epiverse-trace.github.io/epichains/},
   url = {https://github.com/epiverse-trace/epichains},
 }</pre>
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992px){.navbar-expand-lg{flex-wrap:nowrap;-webkit-flex-wrap:nowrap;justify-content:flex-start;-webkit-justify-content:flex-start}.navbar-expand-lg .navbar-nav{flex-direction:row;-webkit-flex-direction:row}.navbar-expand-lg .navbar-nav .dropdown-menu{position:absolute}.navbar-expand-lg .navbar-nav .nav-link{padding-right:var(--bs-navbar-nav-link-padding-x);padding-left:var(--bs-navbar-nav-link-padding-x)}.navbar-expand-lg .navbar-nav-scroll{overflow:visible}.navbar-expand-lg .navbar-collapse{display:flex !important;display:-webkit-flex !important;flex-basis:auto;-webkit-flex-basis:auto}.navbar-expand-lg .navbar-toggler{display:none}.navbar-expand-lg .offcanvas{position:static;z-index:auto;flex-grow:1;-webkit-flex-grow:1;width:auto !important;height:auto !important;visibility:visible !important;background-color:transparent !important;border:0 !important;transform:none !important;transition:none}.navbar-expand-lg .offcanvas .offcanvas-header{display:none}.navbar-expand-lg .offcanvas 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.offcanvas{position:static;z-index:auto;flex-grow:1;-webkit-flex-grow:1;width:auto !important;height:auto !important;visibility:visible !important;background-color:transparent !important;border:0 !important;transform:none !important;transition:none}.navbar-expand-xxl .offcanvas .offcanvas-header{display:none}.navbar-expand-xxl .offcanvas .offcanvas-body{display:flex;display:-webkit-flex;flex-grow:0;-webkit-flex-grow:0;padding:0;overflow-y:visible}}.navbar-expand{flex-wrap:nowrap;-webkit-flex-wrap:nowrap;justify-content:flex-start;-webkit-justify-content:flex-start}.navbar-expand .navbar-nav{flex-direction:row;-webkit-flex-direction:row}.navbar-expand .navbar-nav .dropdown-menu{position:absolute}.navbar-expand .navbar-nav .nav-link{padding-right:var(--bs-navbar-nav-link-padding-x);padding-left:var(--bs-navbar-nav-link-padding-x)}.navbar-expand .navbar-nav-scroll{overflow:visible}.navbar-expand .navbar-collapse{display:flex !important;display:-webkit-flex !important;flex-basis:auto;-webkit-flex-basis:auto}.navbar-expand .navbar-toggler{display:none}.navbar-expand .offcanvas{position:static;z-index:auto;flex-grow:1;-webkit-flex-grow:1;width:auto !important;height:auto !important;visibility:visible !important;background-color:transparent !important;border:0 !important;transform:none !important;transition:none}.navbar-expand .offcanvas .offcanvas-header{display:none}.navbar-expand .offcanvas .offcanvas-body{display:flex;display:-webkit-flex;flex-grow:0;-webkit-flex-grow:0;padding:0;overflow-y:visible}.navbar-dark,.navbar[data-bs-theme="dark"]{--bs-navbar-color: rgba(var(--bs-emphasis-color-rgb), 0.55);--bs-navbar-hover-color: rgba(var(--bs-emphasis-color-rgb), 0.75);--bs-navbar-disabled-color: rgba(var(--bs-emphasis-color-rgb), 0.25);--bs-navbar-active-color: rgba(var(--bs-emphasis-color-rgb), 1);--bs-navbar-brand-color: rgba(var(--bs-emphasis-color-rgb), 1);--bs-navbar-brand-hover-color: rgba(var(--bs-emphasis-color-rgb), 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url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%23052c65'%3e%3cpath fill-rule='evenodd' d='M1.646 4.646a.5.5 0 0 1 .708 0L8 10.293l5.646-5.647a.5.5 0 0 1 .708.708l-6 6a.5.5 0 0 1-.708 0l-6-6a.5.5 0 0 1 0-.708z'/%3e%3c/svg%3e");--bs-accordion-btn-focus-border-color: #86b7fe;--bs-accordion-btn-focus-box-shadow: 0 0 0 .25rem rgba(13,110,253,0.25);--bs-accordion-body-padding-x: 1.25rem;--bs-accordion-body-padding-y: 1rem;--bs-accordion-active-color: var(--bs-primary-text-emphasis);--bs-accordion-active-bg: var(--bs-primary-bg-subtle)}.accordion-button{position:relative;display:flex;display:-webkit-flex;align-items:center;-webkit-align-items:center;width:100%;padding:var(--bs-accordion-btn-padding-y) var(--bs-accordion-btn-padding-x);font-size:1rem;color:var(--bs-accordion-btn-color);text-align:left;background-color:var(--bs-accordion-btn-bg);border:0;border-radius:0;overflow-anchor:none;transition:var(--bs-accordion-transition)}@media (prefers-reduced-motion: reduce){.accordion-button{transition:none}}.accordion-button:not(.collapsed){color:var(--bs-accordion-active-color);background-color:var(--bs-accordion-active-bg);box-shadow:inset 0 calc(-1 * var(--bs-accordion-border-width)) 0 var(--bs-accordion-border-color)}.accordion-button:not(.collapsed)::after{background-image:var(--bs-accordion-btn-active-icon);transform:var(--bs-accordion-btn-icon-transform)}.accordion-button::after{flex-shrink:0;-webkit-flex-shrink:0;width:var(--bs-accordion-btn-icon-width);height:var(--bs-accordion-btn-icon-width);margin-left:auto;content:"";background-image:var(--bs-accordion-btn-icon);background-repeat:no-repeat;background-size:var(--bs-accordion-btn-icon-width);transition:var(--bs-accordion-btn-icon-transition)}@media (prefers-reduced-motion: reduce){.accordion-button::after{transition:none}}.accordion-button:hover{z-index:2}.accordion-button:focus{z-index:3;border-color:var(--bs-accordion-btn-focus-border-color);outline:0;box-shadow:var(--bs-accordion-btn-focus-box-shadow)}.accordion-header{margin-bottom:0}.accordion-item{color:var(--bs-accordion-color);background-color:var(--bs-accordion-bg);border:var(--bs-accordion-border-width) solid var(--bs-accordion-border-color)}.accordion-item:first-of-type{border-top-left-radius:var(--bs-accordion-border-radius);border-top-right-radius:var(--bs-accordion-border-radius)}.accordion-item:first-of-type .accordion-button{border-top-left-radius:var(--bs-accordion-inner-border-radius);border-top-right-radius:var(--bs-accordion-inner-border-radius)}.accordion-item:not(:first-of-type){border-top:0}.accordion-item:last-of-type{border-bottom-right-radius:var(--bs-accordion-border-radius);border-bottom-left-radius:var(--bs-accordion-border-radius)}.accordion-item:last-of-type .accordion-button.collapsed{border-bottom-right-radius:var(--bs-accordion-inner-border-radius);border-bottom-left-radius:var(--bs-accordion-inner-border-radius)}.accordion-item:last-of-type .accordion-collapse{border-bottom-right-radius:var(--bs-accordion-border-radius);border-bottom-left-radius:var(--bs-accordion-border-radius)}.accordion-body{padding:var(--bs-accordion-body-padding-y) var(--bs-accordion-body-padding-x)}.accordion-flush .accordion-collapse{border-width:0}.accordion-flush .accordion-item{border-right:0;border-left:0;border-radius:0}.accordion-flush .accordion-item:first-child{border-top:0}.accordion-flush .accordion-item:last-child{border-bottom:0}.accordion-flush .accordion-item .accordion-button,.accordion-flush .accordion-item .accordion-button.collapsed{border-radius:0}[data-bs-theme="dark"] .accordion-button::after{--bs-accordion-btn-icon: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%236ea8fe'%3e%3cpath fill-rule='evenodd' d='M1.646 4.646a.5.5 0 0 1 .708 0L8 10.293l5.646-5.647a.5.5 0 0 1 .708.708l-6 6a.5.5 0 0 1-.708 0l-6-6a.5.5 0 0 1 0-.708z'/%3e%3c/svg%3e");--bs-accordion-btn-active-icon: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%236ea8fe'%3e%3cpath fill-rule='evenodd' d='M1.646 4.646a.5.5 0 0 1 .708 0L8 10.293l5.646-5.647a.5.5 0 0 1 .708.708l-6 6a.5.5 0 0 1-.708 0l-6-6a.5.5 0 0 1 0-.708z'/%3e%3c/svg%3e")}.breadcrumb{--bs-breadcrumb-padding-x: 0;--bs-breadcrumb-padding-y: 0;--bs-breadcrumb-margin-bottom: 1rem;--bs-breadcrumb-bg: ;--bs-breadcrumb-border-radius: ;--bs-breadcrumb-divider-color: var(--bs-secondary-color);--bs-breadcrumb-item-padding-x: .5rem;--bs-breadcrumb-item-active-color: var(--bs-secondary-color);display:flex;display:-webkit-flex;flex-wrap:wrap;-webkit-flex-wrap:wrap;padding:var(--bs-breadcrumb-padding-y) var(--bs-breadcrumb-padding-x);margin-bottom:var(--bs-breadcrumb-margin-bottom);font-size:var(--bs-breadcrumb-font-size);list-style:none;background-color:var(--bs-breadcrumb-bg);border-radius:var(--bs-breadcrumb-border-radius)}.breadcrumb-item+.breadcrumb-item{padding-left:var(--bs-breadcrumb-item-padding-x)}.breadcrumb-item+.breadcrumb-item::before{float:left;padding-right:var(--bs-breadcrumb-item-padding-x);color:var(--bs-breadcrumb-divider-color);content:var(--bs-breadcrumb-divider, "/") /* rtl: var(--bs-breadcrumb-divider, "/") */}.breadcrumb-item.active{color:var(--bs-breadcrumb-item-active-color)}.pagination{--bs-pagination-padding-x: .75rem;--bs-pagination-padding-y: .375rem;--bs-pagination-font-size:1rem;--bs-pagination-color: var(--bs-link-color);--bs-pagination-bg: var(--bs-body-bg);--bs-pagination-border-width: var(--bs-border-width);--bs-pagination-border-color: var(--bs-border-color);--bs-pagination-border-radius: var(--bs-border-radius);--bs-pagination-hover-color: var(--bs-link-hover-color);--bs-pagination-hover-bg: var(--bs-tertiary-bg);--bs-pagination-hover-border-color: var(--bs-border-color);--bs-pagination-focus-color: var(--bs-link-hover-color);--bs-pagination-focus-bg: var(--bs-secondary-bg);--bs-pagination-focus-box-shadow: 0 0 0 .25rem rgba(13,110,253,0.25);--bs-pagination-active-color: #fff;--bs-pagination-active-bg: #0d6efd;--bs-pagination-active-border-color: #0d6efd;--bs-pagination-disabled-color: var(--bs-secondary-color);--bs-pagination-disabled-bg: var(--bs-secondary-bg);--bs-pagination-disabled-border-color: var(--bs-border-color);display:flex;display:-webkit-flex;padding-left:0;list-style:none}.page-link{position:relative;display:block;padding:var(--bs-pagination-padding-y) var(--bs-pagination-padding-x);font-size:var(--bs-pagination-font-size);color:var(--bs-pagination-color);text-decoration:none;-webkit-text-decoration:none;-moz-text-decoration:none;-ms-text-decoration:none;-o-text-decoration:none;background-color:var(--bs-pagination-bg);border:var(--bs-pagination-border-width) solid var(--bs-pagination-border-color);transition:color 0.15s ease-in-out,background-color 0.15s ease-in-out,border-color 0.15s ease-in-out,box-shadow 0.15s ease-in-out}@media (prefers-reduced-motion: reduce){.page-link{transition:none}}.page-link:hover{z-index:2;color:var(--bs-pagination-hover-color);background-color:var(--bs-pagination-hover-bg);border-color:var(--bs-pagination-hover-border-color)}.page-link:focus{z-index:3;color:var(--bs-pagination-focus-color);background-color:var(--bs-pagination-focus-bg);outline:0;box-shadow:var(--bs-pagination-focus-box-shadow)}.page-link.active,.active>.page-link{z-index:3;color:var(--bs-pagination-active-color);background-color:var(--bs-pagination-active-bg);border-color:var(--bs-pagination-active-border-color)}.page-link.disabled,.disabled>.page-link{color:var(--bs-pagination-disabled-color);pointer-events:none;background-color:var(--bs-pagination-disabled-bg);border-color:var(--bs-pagination-disabled-border-color)}.page-item:not(:first-child) .page-link{margin-left:calc(var(--bs-border-width) * -1)}.page-item:first-child .page-link{border-top-left-radius:var(--bs-pagination-border-radius);border-bottom-left-radius:var(--bs-pagination-border-radius)}.page-item:last-child .page-link{border-top-right-radius:var(--bs-pagination-border-radius);border-bottom-right-radius:var(--bs-pagination-border-radius)}.pagination-lg{--bs-pagination-padding-x: 1.5rem;--bs-pagination-padding-y: .75rem;--bs-pagination-font-size:1.25rem;--bs-pagination-border-radius: var(--bs-border-radius-lg)}.pagination-sm{--bs-pagination-padding-x: .5rem;--bs-pagination-padding-y: .25rem;--bs-pagination-font-size:.875rem;--bs-pagination-border-radius: var(--bs-border-radius-sm)}.badge{--bs-badge-padding-x: .65em;--bs-badge-padding-y: .35em;--bs-badge-font-size:.75em;--bs-badge-font-weight: 700;--bs-badge-color: #fff;--bs-badge-border-radius: var(--bs-border-radius);display:inline-block;padding:var(--bs-badge-padding-y) var(--bs-badge-padding-x);font-size:var(--bs-badge-font-size);font-weight:var(--bs-badge-font-weight);line-height:1;color:var(--bs-badge-color);text-align:center;white-space:nowrap;vertical-align:baseline;border-radius:var(--bs-badge-border-radius)}.badge:empty{display:none}.btn .badge{position:relative;top:-1px}.alert{--bs-alert-bg: transparent;--bs-alert-padding-x: 1rem;--bs-alert-padding-y: 1rem;--bs-alert-margin-bottom: 1rem;--bs-alert-color: inherit;--bs-alert-border-color: transparent;--bs-alert-border: var(--bs-border-width) solid var(--bs-alert-border-color);--bs-alert-border-radius: var(--bs-border-radius);--bs-alert-link-color: inherit;position:relative;padding:var(--bs-alert-padding-y) var(--bs-alert-padding-x);margin-bottom:var(--bs-alert-margin-bottom);color:var(--bs-alert-color);background-color:var(--bs-alert-bg);border:var(--bs-alert-border);border-radius:var(--bs-alert-border-radius)}.alert-heading{color:inherit}.alert-link{font-weight:700;color:var(--bs-alert-link-color)}.alert-dismissible{padding-right:3rem}.alert-dismissible .btn-close{position:absolute;top:0;right:0;z-index:2;padding:1.25rem 1rem}.alert-default{--bs-alert-color: var(--bs-default-text-emphasis);--bs-alert-bg: var(--bs-default-bg-subtle);--bs-alert-border-color: var(--bs-default-border-subtle);--bs-alert-link-color: var(--bs-default-text-emphasis)}.alert-primary{--bs-alert-color: var(--bs-primary-text-emphasis);--bs-alert-bg: var(--bs-primary-bg-subtle);--bs-alert-border-color: var(--bs-primary-border-subtle);--bs-alert-link-color: var(--bs-primary-text-emphasis)}.alert-secondary{--bs-alert-color: var(--bs-secondary-text-emphasis);--bs-alert-bg: var(--bs-secondary-bg-subtle);--bs-alert-border-color: var(--bs-secondary-border-subtle);--bs-alert-link-color: var(--bs-secondary-text-emphasis)}.alert-success{--bs-alert-color: var(--bs-success-text-emphasis);--bs-alert-bg: var(--bs-success-bg-subtle);--bs-alert-border-color: var(--bs-success-border-subtle);--bs-alert-link-color: var(--bs-success-text-emphasis)}.alert-info{--bs-alert-color: var(--bs-info-text-emphasis);--bs-alert-bg: var(--bs-info-bg-subtle);--bs-alert-border-color: var(--bs-info-border-subtle);--bs-alert-link-color: var(--bs-info-text-emphasis)}.alert-warning{--bs-alert-color: var(--bs-warning-text-emphasis);--bs-alert-bg: var(--bs-warning-bg-subtle);--bs-alert-border-color: var(--bs-warning-border-subtle);--bs-alert-link-color: var(--bs-warning-text-emphasis)}.alert-danger{--bs-alert-color: var(--bs-danger-text-emphasis);--bs-alert-bg: var(--bs-danger-bg-subtle);--bs-alert-border-color: var(--bs-danger-border-subtle);--bs-alert-link-color: var(--bs-danger-text-emphasis)}.alert-light{--bs-alert-color: var(--bs-light-text-emphasis);--bs-alert-bg: var(--bs-light-bg-subtle);--bs-alert-border-color: var(--bs-light-border-subtle);--bs-alert-link-color: var(--bs-light-text-emphasis)}.alert-dark{--bs-alert-color: var(--bs-dark-text-emphasis);--bs-alert-bg: var(--bs-dark-bg-subtle);--bs-alert-border-color: var(--bs-dark-border-subtle);--bs-alert-link-color: var(--bs-dark-text-emphasis)}@keyframes progress-bar-stripes{0%{background-position-x:1rem}}.progress,.progress-stacked{--bs-progress-height: 1rem;--bs-progress-font-size:.75rem;--bs-progress-bg: var(--bs-secondary-bg);--bs-progress-border-radius: var(--bs-border-radius);--bs-progress-box-shadow: var(--bs-box-shadow-inset);--bs-progress-bar-color: #fff;--bs-progress-bar-bg: #0d6efd;--bs-progress-bar-transition: width 0.6s ease;display:flex;display:-webkit-flex;height:var(--bs-progress-height);overflow:hidden;font-size:var(--bs-progress-font-size);background-color:var(--bs-progress-bg);border-radius:var(--bs-progress-border-radius)}.progress-bar{display:flex;display:-webkit-flex;flex-direction:column;-webkit-flex-direction:column;justify-content:center;-webkit-justify-content:center;overflow:hidden;color:var(--bs-progress-bar-color);text-align:center;white-space:nowrap;background-color:var(--bs-progress-bar-bg);transition:var(--bs-progress-bar-transition)}@media (prefers-reduced-motion: reduce){.progress-bar{transition:none}}.progress-bar-striped{background-image:linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent);background-size:var(--bs-progress-height) var(--bs-progress-height)}.progress-stacked>.progress{overflow:visible}.progress-stacked>.progress>.progress-bar{width:100%}.progress-bar-animated{animation:1s linear infinite progress-bar-stripes}@media (prefers-reduced-motion: reduce){.progress-bar-animated{animation:none}}.list-group{--bs-list-group-color: var(--bs-body-color);--bs-list-group-bg: var(--bs-body-bg);--bs-list-group-border-color: var(--bs-border-color);--bs-list-group-border-width: var(--bs-border-width);--bs-list-group-border-radius: var(--bs-border-radius);--bs-list-group-item-padding-x: 1rem;--bs-list-group-item-padding-y: .5rem;--bs-list-group-action-color: var(--bs-secondary-color);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-tertiary-bg);--bs-list-group-action-active-color: var(--bs-body-color);--bs-list-group-action-active-bg: var(--bs-secondary-bg);--bs-list-group-disabled-color: var(--bs-secondary-color);--bs-list-group-disabled-bg: var(--bs-body-bg);--bs-list-group-active-color: #fff;--bs-list-group-active-bg: #0d6efd;--bs-list-group-active-border-color: #0d6efd;display:flex;display:-webkit-flex;flex-direction:column;-webkit-flex-direction:column;padding-left:0;margin-bottom:0;border-radius:var(--bs-list-group-border-radius)}.list-group-numbered{list-style-type:none;counter-reset:section}.list-group-numbered>.list-group-item::before{content:counters(section, ".") 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";counter-increment:section}.list-group-item-action{width:100%;color:var(--bs-list-group-action-color);text-align:inherit}.list-group-item-action:hover,.list-group-item-action:focus{z-index:1;color:var(--bs-list-group-action-hover-color);text-decoration:none;background-color:var(--bs-list-group-action-hover-bg)}.list-group-item-action:active{color:var(--bs-list-group-action-active-color);background-color:var(--bs-list-group-action-active-bg)}.list-group-item{position:relative;display:block;padding:var(--bs-list-group-item-padding-y) var(--bs-list-group-item-padding-x);color:var(--bs-list-group-color);text-decoration:none;-webkit-text-decoration:none;-moz-text-decoration:none;-ms-text-decoration:none;-o-text-decoration:none;background-color:var(--bs-list-group-bg);border:var(--bs-list-group-border-width) solid var(--bs-list-group-border-color)}.list-group-item:first-child{border-top-left-radius:inherit;border-top-right-radius:inherit}.list-group-item:last-child{border-bottom-right-radius:inherit;border-bottom-left-radius:inherit}.list-group-item.disabled,.list-group-item:disabled{color:var(--bs-list-group-disabled-color);pointer-events:none;background-color:var(--bs-list-group-disabled-bg)}.list-group-item.active{z-index:2;color:var(--bs-list-group-active-color);background-color:var(--bs-list-group-active-bg);border-color:var(--bs-list-group-active-border-color)}.list-group-item+.list-group-item{border-top-width:0}.list-group-item+.list-group-item.active{margin-top:calc(-1 * var(--bs-list-group-border-width));border-top-width:var(--bs-list-group-border-width)}.list-group-horizontal{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal>.list-group-item.active{margin-top:0}.list-group-horizontal>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal>.list-group-item+.list-group-item.active{margin-left:calc(-1 * var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}@media (min-width: 576px){.list-group-horizontal-sm{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-sm>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-sm>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-sm>.list-group-item.active{margin-top:0}.list-group-horizontal-sm>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-sm>.list-group-item+.list-group-item.active{margin-left:calc(-1 * var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media (min-width: 768px){.list-group-horizontal-md{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-md>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-md>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-md>.list-group-item.active{margin-top:0}.list-group-horizontal-md>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-md>.list-group-item+.list-group-item.active{margin-left:calc(-1 * var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media (min-width: 992px){.list-group-horizontal-lg{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-lg>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-lg>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-lg>.list-group-item.active{margin-top:0}.list-group-horizontal-lg>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-lg>.list-group-item+.list-group-item.active{margin-left:calc(-1 * var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media (min-width: 1200px){.list-group-horizontal-xl{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-xl>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-xl>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-xl>.list-group-item.active{margin-top:0}.list-group-horizontal-xl>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-xl>.list-group-item+.list-group-item.active{margin-left:calc(-1 * var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media (min-width: 1400px){.list-group-horizontal-xxl{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-xxl>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-xxl>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-xxl>.list-group-item.active{margin-top:0}.list-group-horizontal-xxl>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-xxl>.list-group-item+.list-group-item.active{margin-left:calc(-1 * var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}.list-group-flush{border-radius:0}.list-group-flush>.list-group-item{border-width:0 0 var(--bs-list-group-border-width)}.list-group-flush>.list-group-item:last-child{border-bottom-width:0}.list-group-item-default{--bs-list-group-color: var(--bs-default-text-emphasis);--bs-list-group-bg: var(--bs-default-bg-subtle);--bs-list-group-border-color: var(--bs-default-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-default-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-default-border-subtle);--bs-list-group-active-color: var(--bs-default-bg-subtle);--bs-list-group-active-bg: var(--bs-default-text-emphasis);--bs-list-group-active-border-color: var(--bs-default-text-emphasis)}.list-group-item-primary{--bs-list-group-color: var(--bs-primary-text-emphasis);--bs-list-group-bg: var(--bs-primary-bg-subtle);--bs-list-group-border-color: var(--bs-primary-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-primary-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-primary-border-subtle);--bs-list-group-active-color: var(--bs-primary-bg-subtle);--bs-list-group-active-bg: var(--bs-primary-text-emphasis);--bs-list-group-active-border-color: var(--bs-primary-text-emphasis)}.list-group-item-secondary{--bs-list-group-color: var(--bs-secondary-text-emphasis);--bs-list-group-bg: var(--bs-secondary-bg-subtle);--bs-list-group-border-color: var(--bs-secondary-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-secondary-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-secondary-border-subtle);--bs-list-group-active-color: var(--bs-secondary-bg-subtle);--bs-list-group-active-bg: var(--bs-secondary-text-emphasis);--bs-list-group-active-border-color: var(--bs-secondary-text-emphasis)}.list-group-item-success{--bs-list-group-color: var(--bs-success-text-emphasis);--bs-list-group-bg: var(--bs-success-bg-subtle);--bs-list-group-border-color: var(--bs-success-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-success-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-success-border-subtle);--bs-list-group-active-color: var(--bs-success-bg-subtle);--bs-list-group-active-bg: var(--bs-success-text-emphasis);--bs-list-group-active-border-color: var(--bs-success-text-emphasis)}.list-group-item-info{--bs-list-group-color: var(--bs-info-text-emphasis);--bs-list-group-bg: var(--bs-info-bg-subtle);--bs-list-group-border-color: var(--bs-info-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-info-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-info-border-subtle);--bs-list-group-active-color: var(--bs-info-bg-subtle);--bs-list-group-active-bg: var(--bs-info-text-emphasis);--bs-list-group-active-border-color: var(--bs-info-text-emphasis)}.list-group-item-warning{--bs-list-group-color: var(--bs-warning-text-emphasis);--bs-list-group-bg: var(--bs-warning-bg-subtle);--bs-list-group-border-color: var(--bs-warning-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-warning-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-warning-border-subtle);--bs-list-group-active-color: var(--bs-warning-bg-subtle);--bs-list-group-active-bg: var(--bs-warning-text-emphasis);--bs-list-group-active-border-color: var(--bs-warning-text-emphasis)}.list-group-item-danger{--bs-list-group-color: var(--bs-danger-text-emphasis);--bs-list-group-bg: var(--bs-danger-bg-subtle);--bs-list-group-border-color: var(--bs-danger-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-danger-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-danger-border-subtle);--bs-list-group-active-color: var(--bs-danger-bg-subtle);--bs-list-group-active-bg: var(--bs-danger-text-emphasis);--bs-list-group-active-border-color: var(--bs-danger-text-emphasis)}.list-group-item-light{--bs-list-group-color: var(--bs-light-text-emphasis);--bs-list-group-bg: var(--bs-light-bg-subtle);--bs-list-group-border-color: var(--bs-light-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-light-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-light-border-subtle);--bs-list-group-active-color: var(--bs-light-bg-subtle);--bs-list-group-active-bg: var(--bs-light-text-emphasis);--bs-list-group-active-border-color: var(--bs-light-text-emphasis)}.list-group-item-dark{--bs-list-group-color: var(--bs-dark-text-emphasis);--bs-list-group-bg: var(--bs-dark-bg-subtle);--bs-list-group-border-color: var(--bs-dark-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-dark-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-dark-border-subtle);--bs-list-group-active-color: var(--bs-dark-bg-subtle);--bs-list-group-active-bg: var(--bs-dark-text-emphasis);--bs-list-group-active-border-color: var(--bs-dark-text-emphasis)}.btn-close{--bs-btn-close-color: #000;--bs-btn-close-bg: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%23000'%3e%3cpath d='M.293.293a1 1 0 0 1 1.414 0L8 6.586 14.293.293a1 1 0 1 1 1.414 1.414L9.414 8l6.293 6.293a1 1 0 0 1-1.414 1.414L8 9.414l-6.293 6.293a1 1 0 0 1-1.414-1.414L6.586 8 .293 1.707a1 1 0 0 1 0-1.414z'/%3e%3c/svg%3e");--bs-btn-close-opacity: .5;--bs-btn-close-hover-opacity: .75;--bs-btn-close-focus-shadow: 0 0 0 .25rem rgba(13,110,253,0.25);--bs-btn-close-focus-opacity: 1;--bs-btn-close-disabled-opacity: .25;--bs-btn-close-white-filter: invert(1) grayscale(100%) brightness(200%);box-sizing:content-box;width:1em;height:1em;padding:.25em .25em;color:var(--bs-btn-close-color);background:transparent var(--bs-btn-close-bg) center/1em auto 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.offcanvas{position:static;z-index:auto;flex-grow:1;-webkit-flex-grow:1;width:auto !important;height:auto !important;visibility:visible !important;background-color:transparent !important;border:0 !important;transform:none !important;transition:none}.navbar-expand-xxl .offcanvas .offcanvas-header{display:none}.navbar-expand-xxl .offcanvas .offcanvas-body{display:flex;display:-webkit-flex;flex-grow:0;-webkit-flex-grow:0;padding:0;overflow-y:visible}}.navbar-expand{flex-wrap:nowrap;-webkit-flex-wrap:nowrap;justify-content:flex-start;-webkit-justify-content:flex-start}.navbar-expand .navbar-nav{flex-direction:row;-webkit-flex-direction:row}.navbar-expand .navbar-nav .dropdown-menu{position:absolute}.navbar-expand .navbar-nav .nav-link{padding-right:var(--bs-navbar-nav-link-padding-x);padding-left:var(--bs-navbar-nav-link-padding-x)}.navbar-expand .navbar-nav-scroll{overflow:visible}.navbar-expand .navbar-collapse{display:flex !important;display:-webkit-flex !important;flex-basis:auto;-webkit-flex-basis:auto}.navbar-expand .navbar-toggler{display:none}.navbar-expand .offcanvas{position:static;z-index:auto;flex-grow:1;-webkit-flex-grow:1;width:auto !important;height:auto !important;visibility:visible !important;background-color:transparent !important;border:0 !important;transform:none !important;transition:none}.navbar-expand .offcanvas .offcanvas-header{display:none}.navbar-expand .offcanvas .offcanvas-body{display:flex;display:-webkit-flex;flex-grow:0;-webkit-flex-grow:0;padding:0;overflow-y:visible}.navbar-dark,.navbar[data-bs-theme="dark"]{--bs-navbar-color: rgba(var(--bs-emphasis-color-rgb), 0.55);--bs-navbar-hover-color: rgba(var(--bs-emphasis-color-rgb), 0.75);--bs-navbar-disabled-color: rgba(var(--bs-emphasis-color-rgb), 0.25);--bs-navbar-active-color: rgba(var(--bs-emphasis-color-rgb), 1);--bs-navbar-brand-color: rgba(var(--bs-emphasis-color-rgb), 1);--bs-navbar-brand-hover-color: rgba(var(--bs-emphasis-color-rgb), 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(prefers-reduced-motion: reduce){.accordion-button{transition:none}}.accordion-button:not(.collapsed){color:var(--bs-accordion-active-color);background-color:var(--bs-accordion-active-bg);box-shadow:inset 0 calc(-1 * var(--bs-accordion-border-width)) 0 var(--bs-accordion-border-color)}.accordion-button:not(.collapsed)::after{background-image:var(--bs-accordion-btn-active-icon);transform:var(--bs-accordion-btn-icon-transform)}.accordion-button::after{flex-shrink:0;-webkit-flex-shrink:0;width:var(--bs-accordion-btn-icon-width);height:var(--bs-accordion-btn-icon-width);margin-left:auto;content:"";background-image:var(--bs-accordion-btn-icon);background-repeat:no-repeat;background-size:var(--bs-accordion-btn-icon-width);transition:var(--bs-accordion-btn-icon-transition)}@media (prefers-reduced-motion: reduce){.accordion-button::after{transition:none}}.accordion-button:hover{z-index:2}.accordion-button:focus{z-index:3;border-color:var(--bs-accordion-btn-focus-border-color);outline:0;box-shadow:var(--bs-accordion-btn-focus-box-shadow)}.accordion-header{margin-bottom:0}.accordion-item{color:var(--bs-accordion-color);background-color:var(--bs-accordion-bg);border:var(--bs-accordion-border-width) solid var(--bs-accordion-border-color)}.accordion-item:first-of-type{border-top-left-radius:var(--bs-accordion-border-radius);border-top-right-radius:var(--bs-accordion-border-radius)}.accordion-item:first-of-type .accordion-button{border-top-left-radius:var(--bs-accordion-inner-border-radius);border-top-right-radius:var(--bs-accordion-inner-border-radius)}.accordion-item:not(:first-of-type){border-top:0}.accordion-item:last-of-type{border-bottom-right-radius:var(--bs-accordion-border-radius);border-bottom-left-radius:var(--bs-accordion-border-radius)}.accordion-item:last-of-type .accordion-button.collapsed{border-bottom-right-radius:var(--bs-accordion-inner-border-radius);border-bottom-left-radius:var(--bs-accordion-inner-border-radius)}.accordion-item:last-of-type .accordion-collapse{border-bottom-right-radius:var(--bs-accordion-border-radius);border-bottom-left-radius:var(--bs-accordion-border-radius)}.accordion-body{padding:var(--bs-accordion-body-padding-y) var(--bs-accordion-body-padding-x)}.accordion-flush .accordion-collapse{border-width:0}.accordion-flush .accordion-item{border-right:0;border-left:0;border-radius:0}.accordion-flush .accordion-item:first-child{border-top:0}.accordion-flush .accordion-item:last-child{border-bottom:0}.accordion-flush .accordion-item .accordion-button,.accordion-flush .accordion-item .accordion-button.collapsed{border-radius:0}[data-bs-theme="dark"] .accordion-button::after{--bs-accordion-btn-icon: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%236ea8fe'%3e%3cpath fill-rule='evenodd' d='M1.646 4.646a.5.5 0 0 1 .708 0L8 10.293l5.646-5.647a.5.5 0 0 1 .708.708l-6 6a.5.5 0 0 1-.708 0l-6-6a.5.5 0 0 1 0-.708z'/%3e%3c/svg%3e");--bs-accordion-btn-active-icon: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%236ea8fe'%3e%3cpath fill-rule='evenodd' d='M1.646 4.646a.5.5 0 0 1 .708 0L8 10.293l5.646-5.647a.5.5 0 0 1 .708.708l-6 6a.5.5 0 0 1-.708 0l-6-6a.5.5 0 0 1 0-.708z'/%3e%3c/svg%3e")}.breadcrumb{--bs-breadcrumb-padding-x: 0;--bs-breadcrumb-padding-y: 0;--bs-breadcrumb-margin-bottom: 1rem;--bs-breadcrumb-bg: ;--bs-breadcrumb-border-radius: ;--bs-breadcrumb-divider-color: var(--bs-secondary-color);--bs-breadcrumb-item-padding-x: .5rem;--bs-breadcrumb-item-active-color: var(--bs-secondary-color);display:flex;display:-webkit-flex;flex-wrap:wrap;-webkit-flex-wrap:wrap;padding:var(--bs-breadcrumb-padding-y) var(--bs-breadcrumb-padding-x);margin-bottom:var(--bs-breadcrumb-margin-bottom);font-size:var(--bs-breadcrumb-font-size);list-style:none;background-color:var(--bs-breadcrumb-bg);border-radius:var(--bs-breadcrumb-border-radius)}.breadcrumb-item+.breadcrumb-item{padding-left:var(--bs-breadcrumb-item-padding-x)}.breadcrumb-item+.breadcrumb-item::before{float:left;padding-right:var(--bs-breadcrumb-item-padding-x);color:var(--bs-breadcrumb-divider-color);content:var(--bs-breadcrumb-divider, "/") /* rtl: var(--bs-breadcrumb-divider, "/") */}.breadcrumb-item.active{color:var(--bs-breadcrumb-item-active-color)}.pagination{--bs-pagination-padding-x: .75rem;--bs-pagination-padding-y: .375rem;--bs-pagination-font-size:1rem;--bs-pagination-color: var(--bs-link-color);--bs-pagination-bg: var(--bs-body-bg);--bs-pagination-border-width: var(--bs-border-width);--bs-pagination-border-color: var(--bs-border-color);--bs-pagination-border-radius: var(--bs-border-radius);--bs-pagination-hover-color: var(--bs-link-hover-color);--bs-pagination-hover-bg: var(--bs-tertiary-bg);--bs-pagination-hover-border-color: var(--bs-border-color);--bs-pagination-focus-color: var(--bs-link-hover-color);--bs-pagination-focus-bg: var(--bs-secondary-bg);--bs-pagination-focus-box-shadow: 0 0 0 .25rem rgba(13,110,253,0.25);--bs-pagination-active-color: #fff;--bs-pagination-active-bg: #0d6efd;--bs-pagination-active-border-color: #0d6efd;--bs-pagination-disabled-color: var(--bs-secondary-color);--bs-pagination-disabled-bg: var(--bs-secondary-bg);--bs-pagination-disabled-border-color: var(--bs-border-color);display:flex;display:-webkit-flex;padding-left:0;list-style:none}.page-link{position:relative;display:block;padding:var(--bs-pagination-padding-y) var(--bs-pagination-padding-x);font-size:var(--bs-pagination-font-size);color:var(--bs-pagination-color);text-decoration:none;-webkit-text-decoration:none;-moz-text-decoration:none;-ms-text-decoration:none;-o-text-decoration:none;background-color:var(--bs-pagination-bg);border:var(--bs-pagination-border-width) solid var(--bs-pagination-border-color);transition:color 0.15s ease-in-out,background-color 0.15s ease-in-out,border-color 0.15s ease-in-out,box-shadow 0.15s ease-in-out}@media (prefers-reduced-motion: reduce){.page-link{transition:none}}.page-link:hover{z-index:2;color:var(--bs-pagination-hover-color);background-color:var(--bs-pagination-hover-bg);border-color:var(--bs-pagination-hover-border-color)}.page-link:focus{z-index:3;color:var(--bs-pagination-focus-color);background-color:var(--bs-pagination-focus-bg);outline:0;box-shadow:var(--bs-pagination-focus-box-shadow)}.page-link.active,.active>.page-link{z-index:3;color:var(--bs-pagination-active-color);background-color:var(--bs-pagination-active-bg);border-color:var(--bs-pagination-active-border-color)}.page-link.disabled,.disabled>.page-link{color:var(--bs-pagination-disabled-color);pointer-events:none;background-color:var(--bs-pagination-disabled-bg);border-color:var(--bs-pagination-disabled-border-color)}.page-item:not(:first-child) .page-link{margin-left:calc(var(--bs-border-width) * -1)}.page-item:first-child .page-link{border-top-left-radius:var(--bs-pagination-border-radius);border-bottom-left-radius:var(--bs-pagination-border-radius)}.page-item:last-child .page-link{border-top-right-radius:var(--bs-pagination-border-radius);border-bottom-right-radius:var(--bs-pagination-border-radius)}.pagination-lg{--bs-pagination-padding-x: 1.5rem;--bs-pagination-padding-y: .75rem;--bs-pagination-font-size:1.25rem;--bs-pagination-border-radius: var(--bs-border-radius-lg)}.pagination-sm{--bs-pagination-padding-x: .5rem;--bs-pagination-padding-y: .25rem;--bs-pagination-font-size:.875rem;--bs-pagination-border-radius: var(--bs-border-radius-sm)}.badge{--bs-badge-padding-x: .65em;--bs-badge-padding-y: .35em;--bs-badge-font-size:.75em;--bs-badge-font-weight: 700;--bs-badge-color: #fff;--bs-badge-border-radius: var(--bs-border-radius);display:inline-block;padding:var(--bs-badge-padding-y) var(--bs-badge-padding-x);font-size:var(--bs-badge-font-size);font-weight:var(--bs-badge-font-weight);line-height:1;color:var(--bs-badge-color);text-align:center;white-space:nowrap;vertical-align:baseline;border-radius:var(--bs-badge-border-radius)}.badge:empty{display:none}.btn .badge{position:relative;top:-1px}.alert{--bs-alert-bg: transparent;--bs-alert-padding-x: 1rem;--bs-alert-padding-y: 1rem;--bs-alert-margin-bottom: 1rem;--bs-alert-color: inherit;--bs-alert-border-color: transparent;--bs-alert-border: var(--bs-border-width) solid var(--bs-alert-border-color);--bs-alert-border-radius: var(--bs-border-radius);--bs-alert-link-color: inherit;position:relative;padding:var(--bs-alert-padding-y) var(--bs-alert-padding-x);margin-bottom:var(--bs-alert-margin-bottom);color:var(--bs-alert-color);background-color:var(--bs-alert-bg);border:var(--bs-alert-border);border-radius:var(--bs-alert-border-radius)}.alert-heading{color:inherit}.alert-link{font-weight:700;color:var(--bs-alert-link-color)}.alert-dismissible{padding-right:3rem}.alert-dismissible .btn-close{position:absolute;top:0;right:0;z-index:2;padding:1.25rem 1rem}.alert-default{--bs-alert-color: var(--bs-default-text-emphasis);--bs-alert-bg: var(--bs-default-bg-subtle);--bs-alert-border-color: var(--bs-default-border-subtle);--bs-alert-link-color: var(--bs-default-text-emphasis)}.alert-primary{--bs-alert-color: var(--bs-primary-text-emphasis);--bs-alert-bg: var(--bs-primary-bg-subtle);--bs-alert-border-color: var(--bs-primary-border-subtle);--bs-alert-link-color: var(--bs-primary-text-emphasis)}.alert-secondary{--bs-alert-color: var(--bs-secondary-text-emphasis);--bs-alert-bg: var(--bs-secondary-bg-subtle);--bs-alert-border-color: var(--bs-secondary-border-subtle);--bs-alert-link-color: var(--bs-secondary-text-emphasis)}.alert-success{--bs-alert-color: var(--bs-success-text-emphasis);--bs-alert-bg: var(--bs-success-bg-subtle);--bs-alert-border-color: var(--bs-success-border-subtle);--bs-alert-link-color: var(--bs-success-text-emphasis)}.alert-info{--bs-alert-color: var(--bs-info-text-emphasis);--bs-alert-bg: var(--bs-info-bg-subtle);--bs-alert-border-color: var(--bs-info-border-subtle);--bs-alert-link-color: var(--bs-info-text-emphasis)}.alert-warning{--bs-alert-color: var(--bs-warning-text-emphasis);--bs-alert-bg: var(--bs-warning-bg-subtle);--bs-alert-border-color: var(--bs-warning-border-subtle);--bs-alert-link-color: var(--bs-warning-text-emphasis)}.alert-danger{--bs-alert-color: var(--bs-danger-text-emphasis);--bs-alert-bg: var(--bs-danger-bg-subtle);--bs-alert-border-color: var(--bs-danger-border-subtle);--bs-alert-link-color: var(--bs-danger-text-emphasis)}.alert-light{--bs-alert-color: var(--bs-light-text-emphasis);--bs-alert-bg: var(--bs-light-bg-subtle);--bs-alert-border-color: var(--bs-light-border-subtle);--bs-alert-link-color: var(--bs-light-text-emphasis)}.alert-dark{--bs-alert-color: var(--bs-dark-text-emphasis);--bs-alert-bg: var(--bs-dark-bg-subtle);--bs-alert-border-color: var(--bs-dark-border-subtle);--bs-alert-link-color: var(--bs-dark-text-emphasis)}@keyframes progress-bar-stripes{0%{background-position-x:1rem}}.progress,.progress-stacked{--bs-progress-height: 1rem;--bs-progress-font-size:.75rem;--bs-progress-bg: var(--bs-secondary-bg);--bs-progress-border-radius: var(--bs-border-radius);--bs-progress-box-shadow: var(--bs-box-shadow-inset);--bs-progress-bar-color: #fff;--bs-progress-bar-bg: #0d6efd;--bs-progress-bar-transition: width 0.6s ease;display:flex;display:-webkit-flex;height:var(--bs-progress-height);overflow:hidden;font-size:var(--bs-progress-font-size);background-color:var(--bs-progress-bg);border-radius:var(--bs-progress-border-radius)}.progress-bar{display:flex;display:-webkit-flex;flex-direction:column;-webkit-flex-direction:column;justify-content:center;-webkit-justify-content:center;overflow:hidden;color:var(--bs-progress-bar-color);text-align:center;white-space:nowrap;background-color:var(--bs-progress-bar-bg);transition:var(--bs-progress-bar-transition)}@media (prefers-reduced-motion: reduce){.progress-bar{transition:none}}.progress-bar-striped{background-image:linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent);background-size:var(--bs-progress-height) var(--bs-progress-height)}.progress-stacked>.progress{overflow:visible}.progress-stacked>.progress>.progress-bar{width:100%}.progress-bar-animated{animation:1s linear infinite progress-bar-stripes}@media (prefers-reduced-motion: reduce){.progress-bar-animated{animation:none}}.list-group{--bs-list-group-color: var(--bs-body-color);--bs-list-group-bg: var(--bs-body-bg);--bs-list-group-border-color: var(--bs-border-color);--bs-list-group-border-width: var(--bs-border-width);--bs-list-group-border-radius: var(--bs-border-radius);--bs-list-group-item-padding-x: 1rem;--bs-list-group-item-padding-y: .5rem;--bs-list-group-action-color: var(--bs-secondary-color);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-tertiary-bg);--bs-list-group-action-active-color: var(--bs-body-color);--bs-list-group-action-active-bg: var(--bs-secondary-bg);--bs-list-group-disabled-color: var(--bs-secondary-color);--bs-list-group-disabled-bg: var(--bs-body-bg);--bs-list-group-active-color: #fff;--bs-list-group-active-bg: #0d6efd;--bs-list-group-active-border-color: #0d6efd;display:flex;display:-webkit-flex;flex-direction:column;-webkit-flex-direction:column;padding-left:0;margin-bottom:0;border-radius:var(--bs-list-group-border-radius)}.list-group-numbered{list-style-type:none;counter-reset:section}.list-group-numbered>.list-group-item::before{content:counters(section, ".") ". ";counter-increment:section}.list-group-item-action{width:100%;color:var(--bs-list-group-action-color);text-align:inherit}.list-group-item-action:hover,.list-group-item-action:focus{z-index:1;color:var(--bs-list-group-action-hover-color);text-decoration:none;background-color:var(--bs-list-group-action-hover-bg)}.list-group-item-action:active{color:var(--bs-list-group-action-active-color);background-color:var(--bs-list-group-action-active-bg)}.list-group-item{position:relative;display:block;padding:var(--bs-list-group-item-padding-y) var(--bs-list-group-item-padding-x);color:var(--bs-list-group-color);text-decoration:none;-webkit-text-decoration:none;-moz-text-decoration:none;-ms-text-decoration:none;-o-text-decoration:none;background-color:var(--bs-list-group-bg);border:var(--bs-list-group-border-width) solid var(--bs-list-group-border-color)}.list-group-item:first-child{border-top-left-radius:inherit;border-top-right-radius:inherit}.list-group-item:last-child{border-bottom-right-radius:inherit;border-bottom-left-radius:inherit}.list-group-item.disabled,.list-group-item:disabled{color:var(--bs-list-group-disabled-color);pointer-events:none;background-color:var(--bs-list-group-disabled-bg)}.list-group-item.active{z-index:2;color:var(--bs-list-group-active-color);background-color:var(--bs-list-group-active-bg);border-color:var(--bs-list-group-active-border-color)}.list-group-item+.list-group-item{border-top-width:0}.list-group-item+.list-group-item.active{margin-top:calc(-1 * var(--bs-list-group-border-width));border-top-width:var(--bs-list-group-border-width)}.list-group-horizontal{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal>.list-group-item.active{margin-top:0}.list-group-horizontal>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal>.list-group-item+.list-group-item.active{margin-left:calc(-1 * var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}@media (min-width: 576px){.list-group-horizontal-sm{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-sm>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-sm>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-sm>.list-group-item.active{margin-top:0}.list-group-horizontal-sm>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-sm>.list-group-item+.list-group-item.active{margin-left:calc(-1 * var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media (min-width: 768px){.list-group-horizontal-md{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-md>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-md>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-md>.list-group-item.active{margin-top:0}.list-group-horizontal-md>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-md>.list-group-item+.list-group-item.active{margin-left:calc(-1 * var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media (min-width: 992px){.list-group-horizontal-lg{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-lg>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-lg>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-lg>.list-group-item.active{margin-top:0}.list-group-horizontal-lg>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-lg>.list-group-item+.list-group-item.active{margin-left:calc(-1 * var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media (min-width: 1200px){.list-group-horizontal-xl{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-xl>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-xl>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-xl>.list-group-item.active{margin-top:0}.list-group-horizontal-xl>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-xl>.list-group-item+.list-group-item.active{margin-left:calc(-1 * var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media (min-width: 1400px){.list-group-horizontal-xxl{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-xxl>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-xxl>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-xxl>.list-group-item.active{margin-top:0}.list-group-horizontal-xxl>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-xxl>.list-group-item+.list-group-item.active{margin-left:calc(-1 * var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}.list-group-flush{border-radius:0}.list-group-flush>.list-group-item{border-width:0 0 var(--bs-list-group-border-width)}.list-group-flush>.list-group-item:last-child{border-bottom-width:0}.list-group-item-default{--bs-list-group-color: var(--bs-default-text-emphasis);--bs-list-group-bg: var(--bs-default-bg-subtle);--bs-list-group-border-color: var(--bs-default-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-default-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-default-border-subtle);--bs-list-group-active-color: var(--bs-default-bg-subtle);--bs-list-group-active-bg: var(--bs-default-text-emphasis);--bs-list-group-active-border-color: var(--bs-default-text-emphasis)}.list-group-item-primary{--bs-list-group-color: var(--bs-primary-text-emphasis);--bs-list-group-bg: var(--bs-primary-bg-subtle);--bs-list-group-border-color: var(--bs-primary-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-primary-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-primary-border-subtle);--bs-list-group-active-color: var(--bs-primary-bg-subtle);--bs-list-group-active-bg: var(--bs-primary-text-emphasis);--bs-list-group-active-border-color: var(--bs-primary-text-emphasis)}.list-group-item-secondary{--bs-list-group-color: var(--bs-secondary-text-emphasis);--bs-list-group-bg: var(--bs-secondary-bg-subtle);--bs-list-group-border-color: var(--bs-secondary-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-secondary-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-secondary-border-subtle);--bs-list-group-active-color: var(--bs-secondary-bg-subtle);--bs-list-group-active-bg: var(--bs-secondary-text-emphasis);--bs-list-group-active-border-color: var(--bs-secondary-text-emphasis)}.list-group-item-success{--bs-list-group-color: var(--bs-success-text-emphasis);--bs-list-group-bg: var(--bs-success-bg-subtle);--bs-list-group-border-color: var(--bs-success-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-success-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-success-border-subtle);--bs-list-group-active-color: var(--bs-success-bg-subtle);--bs-list-group-active-bg: var(--bs-success-text-emphasis);--bs-list-group-active-border-color: var(--bs-success-text-emphasis)}.list-group-item-info{--bs-list-group-color: var(--bs-info-text-emphasis);--bs-list-group-bg: var(--bs-info-bg-subtle);--bs-list-group-border-color: var(--bs-info-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-info-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-info-border-subtle);--bs-list-group-active-color: var(--bs-info-bg-subtle);--bs-list-group-active-bg: var(--bs-info-text-emphasis);--bs-list-group-active-border-color: var(--bs-info-text-emphasis)}.list-group-item-warning{--bs-list-group-color: var(--bs-warning-text-emphasis);--bs-list-group-bg: var(--bs-warning-bg-subtle);--bs-list-group-border-color: var(--bs-warning-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-warning-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-warning-border-subtle);--bs-list-group-active-color: var(--bs-warning-bg-subtle);--bs-list-group-active-bg: var(--bs-warning-text-emphasis);--bs-list-group-active-border-color: var(--bs-warning-text-emphasis)}.list-group-item-danger{--bs-list-group-color: var(--bs-danger-text-emphasis);--bs-list-group-bg: var(--bs-danger-bg-subtle);--bs-list-group-border-color: var(--bs-danger-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-danger-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-danger-border-subtle);--bs-list-group-active-color: var(--bs-danger-bg-subtle);--bs-list-group-active-bg: var(--bs-danger-text-emphasis);--bs-list-group-active-border-color: var(--bs-danger-text-emphasis)}.list-group-item-light{--bs-list-group-color: var(--bs-light-text-emphasis);--bs-list-group-bg: var(--bs-light-bg-subtle);--bs-list-group-border-color: var(--bs-light-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-light-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-light-border-subtle);--bs-list-group-active-color: var(--bs-light-bg-subtle);--bs-list-group-active-bg: var(--bs-light-text-emphasis);--bs-list-group-active-border-color: var(--bs-light-text-emphasis)}.list-group-item-dark{--bs-list-group-color: var(--bs-dark-text-emphasis);--bs-list-group-bg: var(--bs-dark-bg-subtle);--bs-list-group-border-color: var(--bs-dark-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-dark-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-dark-border-subtle);--bs-list-group-active-color: var(--bs-dark-bg-subtle);--bs-list-group-active-bg: var(--bs-dark-text-emphasis);--bs-list-group-active-border-color: var(--bs-dark-text-emphasis)}.btn-close{--bs-btn-close-color: #000;--bs-btn-close-bg: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%23000'%3e%3cpath d='M.293.293a1 1 0 0 1 1.414 0L8 6.586 14.293.293a1 1 0 1 1 1.414 1.414L9.414 8l6.293 6.293a1 1 0 0 1-1.414 1.414L8 9.414l-6.293 6.293a1 1 0 0 1-1.414-1.414L6.586 8 .293 1.707a1 1 0 0 1 0-1.414z'/%3e%3c/svg%3e");--bs-btn-close-opacity: .5;--bs-btn-close-hover-opacity: .75;--bs-btn-close-focus-shadow: 0 0 0 .25rem rgba(13,110,253,0.25);--bs-btn-close-focus-opacity: 1;--bs-btn-close-disabled-opacity: .25;--bs-btn-close-white-filter: invert(1) grayscale(100%) brightness(200%);box-sizing:content-box;width:1em;height:1em;padding:.25em .25em;color:var(--bs-btn-close-color);background:transparent var(--bs-btn-close-bg) center/1em auto 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diff --git a/index.html b/index.html
index c278e19e..7166aa46 100644
--- a/index.html
+++ b/index.html
@@ -12,7 +12,7 @@
 <link rel="apple-touch-icon" type="image/png" sizes="120x120" href="apple-touch-icon-120x120.png">
 <link rel="apple-touch-icon" type="image/png" sizes="76x76" href="apple-touch-icon-76x76.png">
 <link rel="apple-touch-icon" type="image/png" sizes="60x60" href="apple-touch-icon-60x60.png">
-<script src="deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
+<script src="lightswitch.js"></script><script src="deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
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 <script src="deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet">
 <link href="deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet">
@@ -24,18 +24,25 @@
   window.dataLayer = window.dataLayer || [];
   function gtag(){dataLayer.push(arguments);}
   gtag('js', new Date());
+
   gtag('config', 'G-XZ471458FQ');
 </script>
 </head>
 <body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
-    <nav class="navbar navbar-expand-lg fixed-top bg-dark" data-bs-theme="dark" aria-label="Site navigation"><div class="container">
+
+
+    <nav class="navbar navbar-expand-lg fixed-top " aria-label="Site navigation"><div class="container">
     <a href="https://epiverse-trace.github.io/" class="external-link"><img src="https://epiverse-trace.github.io/blueprints/logo_white.svg" id="logo" alt="Epiverse-TRACE"></a>
     <a class="navbar-brand me-2" href="index.html">epichains</a>
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">0.1.0</small>
+
+    <small class="nav-text text-danger me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Unreleased version">0.1.0.9000</small>
+
+
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
       <span class="navbar-toggler-icon"></span>
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 <li class="nav-item"><a class="nav-link" href="articles/epichains.html">Get started</a></li>
@@ -63,8 +70,18 @@
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="search.json">
 </form></li>
 <li class="nav-item"><a class="external-link nav-link" href="https://github.com/epiverse-trace/epichains/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item dropdown">
+  <button class="nav-link dropdown-toggle" type="button" id="dropdown-lightswitch" data-bs-toggle="dropdown" aria-expanded="false" aria-haspopup="true" aria-label="Light switch"><span class="fa fa-sun"></span></button>
+  <ul class="dropdown-menu dropdown-menu-end" aria-labelledby="dropdown-lightswitch">
+<li><button class="dropdown-item" data-bs-theme-value="light"><span class="fa fa-sun"></span> Light</button></li>
+    <li><button class="dropdown-item" data-bs-theme-value="dark"><span class="fa fa-moon"></span> Dark</button></li>
+    <li><button class="dropdown-item" data-bs-theme-value="auto"><span class="fa fa-adjust"></span> Auto</button></li>
+  </ul>
+</li>
       </ul>
 </div>
+
+
   </div>
 </nav><div class="container template-home">
 <div class="row">
@@ -270,6 +287,7 @@ <h2 data-toc-skip>Links</h2>
 <li><a href="https://github.com/epiverse-trace/epichains/issues" class="external-link">Report a bug</a></li>
 </ul>
 </div>
+
 <div class="license">
 <h2 data-toc-skip>License</h2>
 <ul class="list-unstyled">
@@ -277,6 +295,7 @@ <h2 data-toc-skip>License</h2>
 <li><small><a href="https://opensource.org/licenses/mit-license.php" class="external-link">MIT</a> + file <a href="LICENSE-text.html">LICENSE</a></small></li>
 </ul>
 </div>
+
 <div class="code-of-conduct">
 <h2 data-toc-skip>Code of Conduct</h2>
 <ul class="list-unstyled">
@@ -286,12 +305,15 @@ <h2 data-toc-skip>Code of Conduct</h2>
 </li>
 </ul>
 </div>
+
+
 <div class="citation">
 <h2 data-toc-skip>Citation</h2>
 <ul class="list-unstyled">
 <li><a href="authors.html#citation">Citing epichains</a></li>
 </ul>
 </div>
+
 <div class="developers">
 <h2 data-toc-skip>Developers</h2>
 <ul class="list-unstyled">
@@ -300,17 +322,36 @@ <h2 data-toc-skip>Developers</h2>
 <li>Flavio Finger <br><small class="roles"> Author </small> <a href="https://orcid.org/0000-0002-8613-5170" target="orcid.widget" aria-label="ORCID" class="external-link"><span class="fab fa-orcid orcid" aria-hidden="true"></span></a> </li>
 <li><a href="authors.html">More about authors...</a></li>
 </ul>
+</div>
+
+<div class="dev-status">
+<h2 data-toc-skip>Dev status</h2>
+<ul class="list-unstyled">
+<li><a href="https://opensource.org/licenses/MIT" class="external-link"><img src="https://img.shields.io/badge/License-MIT-yellow.svg" alt="License: MIT"></a></li>
+<li><a href="https://github.com/epiverse-trace/epichains/actions/workflows/R-CMD-check.yaml" class="external-link"><img src="https://github.com/epiverse-trace/epichains/actions/workflows/R-CMD-check.yaml/badge.svg" alt="R-CMD-check"></a></li>
+<li><a href="https://app.codecov.io/gh/epiverse-trace/epichains?branch=main" class="external-link"><img src="https://codecov.io/gh/epiverse-trace/epichains/branch/main/graph/badge.svg" alt="Codecov test coverage"></a></li>
+<li><a href="https://lifecycle.r-lib.org/articles/stages.html#experimental" class="external-link"><img src="https://img.shields.io/badge/lifecycle-experimental-orange.svg" alt="Lifecycle: experimental"></a></li>
+</ul>
 </div>
 
   </aside>
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+
+
     <footer><div class="pkgdown-footer-left">
   <p>Developed by James M. Azam, Sebastian Funk, Flavio Finger.</p>
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+
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-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.9.9000.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
 </div>
+
     </footer>
 </div>
+
+
+
+
+
   </body>
 </html>
diff --git a/news/index.html b/news/index.html
index 2ef27b20..9857b453 100644
--- a/news/index.html
+++ b/news/index.html
@@ -1,18 +1,25 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Changelog • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Changelog"><meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg"><!-- Google tag (gtag.js) --><script async src="https://www.googletagmanager.com/gtag/js?id=G-XZ471458FQ"></script><script>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Changelog • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../lightswitch.js"></script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Changelog"><meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg"><!-- Google tag (gtag.js) --><script async src="https://www.googletagmanager.com/gtag/js?id=G-XZ471458FQ"></script><script>
   window.dataLayer = window.dataLayer || [];
   function gtag(){dataLayer.push(arguments);}
   gtag('js', new Date());
+
   gtag('config', 'G-XZ471458FQ');
 </script></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
-    <nav class="navbar navbar-expand-lg fixed-top bg-dark" data-bs-theme="dark" aria-label="Site navigation"><div class="container">
+
+
+    <nav class="navbar navbar-expand-lg fixed-top " aria-label="Site navigation"><div class="container">
     <a href="https://epiverse-trace.github.io/" class="external-link"><img src="https://epiverse-trace.github.io/blueprints/logo_white.svg" id="logo" alt="Epiverse-TRACE"></a>
     <a class="navbar-brand me-2" href="../index.html">epichains</a>
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">0.1.0</small>
+
+    <small class="nav-text text-danger me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Unreleased version">0.1.0.9000</small>
+
+
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
       <span class="navbar-toggler-icon"></span>
     </button>
+
     <div id="navbar" class="collapse navbar-collapse ms-3">
       <ul class="navbar-nav me-auto"><li class="nav-item"><a class="nav-link" href="../articles/epichains.html">Get started</a></li>
 <li class="nav-item"><a class="nav-link" href="../reference/index.html">Reference</a></li>
@@ -34,14 +41,30 @@
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
 <li class="nav-item"><a class="external-link nav-link" href="https://github.com/epiverse-trace/epichains/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item dropdown">
+  <button class="nav-link dropdown-toggle" type="button" id="dropdown-lightswitch" data-bs-toggle="dropdown" aria-expanded="false" aria-haspopup="true" aria-label="Light switch"><span class="fa fa-sun"></span></button>
+  <ul class="dropdown-menu dropdown-menu-end" aria-labelledby="dropdown-lightswitch"><li><button class="dropdown-item" data-bs-theme-value="light"><span class="fa fa-sun"></span> Light</button></li>
+    <li><button class="dropdown-item" data-bs-theme-value="dark"><span class="fa fa-moon"></span> Dark</button></li>
+    <li><button class="dropdown-item" data-bs-theme-value="auto"><span class="fa fa-adjust"></span> Auto</button></li>
+  </ul></li>
       </ul></div>
+
+
   </div>
 </nav><div class="container template-news">
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.svg" class="logo" alt=""><h1>Changelog</h1>
-      <small>Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/NEWS.md" class="external-link"><code>NEWS.md</code></a></small>
+      <small>Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/NEWS.md" class="external-link"><code>NEWS.md</code></a></small>
     </div>
+
+    <div class="section level2">
+<h2 class="pkg-version" data-toc-text="development version" id="epichains-development-version">epichains (development version)<a class="anchor" aria-label="anchor" href="#epichains-development-version"></a></h2>
+<div class="section level3">
+<h3 id="package-development-version">Package<a class="anchor" aria-label="anchor" href="#package-development-version"></a></h3>
+<ul><li>Removed the <code>as_is = TRUE</code> setting in vignette YAML headers to avoid partial incompatibility with incoming pkgdown versions.</li>
+</ul></div>
+</div>
     <div class="section level2">
 <h2 class="pkg-version" data-toc-text="0.1.0" id="epichains-010">epichains 0.1.0<a class="anchor" aria-label="anchor" href="#epichains-010"></a></h2>
 <p>We are excited to announce the first minor release of <a href="https://github.com/epiverse-trace/epichains" class="external-link">epichains</a>.</p>
@@ -95,12 +118,21 @@ <h4 id="transmission-chain-data-manipulation-0-1-0">Transmission Chain Data Mani
 </div>
   </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
     </nav></aside></div>
+
+
     <footer><div class="pkgdown-footer-left">
   <p>Developed by James M. Azam, Sebastian Funk, Flavio Finger.</p>
 </div>
+
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.9.9000.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
 </div>
+
     </footer></div>
+
+
+
+
+
   </body></html>
 
diff --git a/pkgdown.yml b/pkgdown.yml
index d76e7bd9..7eafc438 100644
--- a/pkgdown.yml
+++ b/pkgdown.yml
@@ -1,6 +1,6 @@
 pandoc: 3.1.11
-pkgdown: 2.0.9.9000
-pkgdown_sha: b683f8acbd41f408f25909e488c07f58ed55c537
+pkgdown: 2.1.0
+pkgdown_sha: ~
 articles:
   branching_process_literature: branching_process_literature.html
   design-principles: design-principles.html
@@ -8,8 +8,7 @@ articles:
   interventions: interventions.html
   projecting_incidence: projecting_incidence.html
   theoretical_background: theoretical_background.html
-last_built: 2024-06-05T17:03Z
+last_built: 2024-07-10T14:47Z
 urls:
   reference: https://epiverse-trace.github.io/epichains/reference
   article: https://epiverse-trace.github.io/epichains/articles
-
diff --git a/reference/aggregate.epichains.html b/reference/aggregate.epichains.html
index 0d9eb507..25dac9a4 100644
--- a/reference/aggregate.epichains.html
+++ b/reference/aggregate.epichains.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Aggregate cases in &lt;epichains&gt; objects by "generation" or "time", if present — aggregate.epichains • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Aggregate cases in &lt;epichains&gt; objects by " generation or if present aggregate.epichains><meta name="description" content="This function provides a quick way to create a time series of cases over
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Aggregate cases in &lt;epichains&gt; objects by "generation" or "time", if present — aggregate.epichains • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../lightswitch.js"></script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Aggregate cases in &lt;epichains&gt; objects by " generation or if present aggregate.epichains><meta name="description" content="This function provides a quick way to create a time series of cases over
 generation or time (if generation_time was specified) from simulated
 &amp;lt;epichains&amp;gt; objects."><meta property="og:description" content="This function provides a quick way to create a time series of cases over
 generation or time (if generation_time was specified) from simulated
@@ -7,16 +7,23 @@
   window.dataLayer = window.dataLayer || [];
   function gtag(){dataLayer.push(arguments);}
   gtag('js', new Date());
+
   gtag('config', 'G-XZ471458FQ');
 </script></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
-    <nav class="navbar navbar-expand-lg fixed-top bg-dark" data-bs-theme="dark" aria-label="Site navigation"><div class="container">
+
+
+    <nav class="navbar navbar-expand-lg fixed-top " aria-label="Site navigation"><div class="container">
     <a href="https://epiverse-trace.github.io/" class="external-link"><img src="https://epiverse-trace.github.io/blueprints/logo_white.svg" id="logo" alt="Epiverse-TRACE"></a>
     <a class="navbar-brand me-2" href="../index.html">epichains</a>
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">0.1.0</small>
+
+    <small class="nav-text text-danger me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Unreleased version">0.1.0.9000</small>
+
+
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
       <span class="navbar-toggler-icon"></span>
     </button>
+
     <div id="navbar" class="collapse navbar-collapse ms-3">
       <ul class="navbar-nav me-auto"><li class="nav-item"><a class="nav-link" href="../articles/epichains.html">Get started</a></li>
 <li class="active nav-item"><a class="nav-link" href="../reference/index.html">Reference</a></li>
@@ -38,34 +45,52 @@
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
 <li class="nav-item"><a class="external-link nav-link" href="https://github.com/epiverse-trace/epichains/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item dropdown">
+  <button class="nav-link dropdown-toggle" type="button" id="dropdown-lightswitch" data-bs-toggle="dropdown" aria-expanded="false" aria-haspopup="true" aria-label="Light switch"><span class="fa fa-sun"></span></button>
+  <ul class="dropdown-menu dropdown-menu-end" aria-labelledby="dropdown-lightswitch"><li><button class="dropdown-item" data-bs-theme-value="light"><span class="fa fa-sun"></span> Light</button></li>
+    <li><button class="dropdown-item" data-bs-theme-value="dark"><span class="fa fa-moon"></span> Dark</button></li>
+    <li><button class="dropdown-item" data-bs-theme-value="auto"><span class="fa fa-adjust"></span> Auto</button></li>
+  </ul></li>
       </ul></div>
+
+
   </div>
 </nav><div class="container template-reference-topic">
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.svg" class="logo" alt=""><h1>Aggregate cases in <code>&lt;epichains&gt;</code> objects by "generation" or "time", if present</h1>
-      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/R/epichains.R" class="external-link"><code>R/epichains.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/R/epichains.R" class="external-link"><code>R/epichains.R</code></a></small>
       <div class="d-none name"><code>aggregate.epichains.Rd</code></div>
     </div>
+
     <div class="ref-description section level2">
     <p>This function provides a quick way to create a time series of cases over
 generation or time (if <code>generation_time</code> was specified) from simulated
 <code>&lt;epichains&gt;</code> objects.</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="co"># S3 method for class 'epichains'</span></span>
 <span><span class="fu"><a href="https://rdrr.io/r/stats/aggregate.html" class="external-link">aggregate</a></span><span class="op">(</span><span class="va">x</span>, by <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"time"</span>, <span class="st">"generation"</span><span class="op">)</span>, <span class="va">...</span><span class="op">)</span></span></code></pre></div>
     </div>
+
     <div class="section level2">
     <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
 <dl><dt id="arg-x">x<a class="anchor" aria-label="anchor" href="#arg-x"></a></dt>
 <dd><p>An <code>&lt;epichains&gt;</code> object.</p></dd>
+
+
 <dt id="arg-by">by<a class="anchor" aria-label="anchor" href="#arg-by"></a></dt>
 <dd><p>The variable to aggregate by; A character string with options
 "time" and "generation".</p></dd>
+
+
 <dt id="arg--">...<a class="anchor" aria-label="anchor" href="#arg--"></a></dt>
 <dd><p>Not used.</p></dd>
+
 </dl></div>
     <div class="section level2">
     <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
@@ -75,6 +100,7 @@ <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2
     <h2 id="author">Author<a class="anchor" aria-label="anchor" href="#author"></a></h2>
     <p>James M. Azam</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/Random.html" class="external-link">set.seed</a></span><span class="op">(</span><span class="fl">32</span><span class="op">)</span></span></span>
@@ -126,12 +152,21 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
     </div>
   </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
     </nav></aside></div>
+
+
     <footer><div class="pkgdown-footer-left">
   <p>Developed by James M. Azam, Sebastian Funk, Flavio Finger.</p>
 </div>
+
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.9.9000.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
 </div>
+
     </footer></div>
+
+
+
+
+
   </body></html>
 
diff --git a/reference/covid19_sa.html b/reference/covid19_sa.html
index 155f38a8..cf3fe2b0 100644
--- a/reference/covid19_sa.html
+++ b/reference/covid19_sa.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>COVID-19 Data Repository for South Africa — covid19_sa • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="COVID-19 Data Repository for South Africa — covid19_sa"><meta name="description" content="An aggregated subset of the COVID-19 Data Repository for South Africa
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>COVID-19 Data Repository for South Africa — covid19_sa • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../lightswitch.js"></script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="COVID-19 Data Repository for South Africa — covid19_sa"><meta name="description" content="An aggregated subset of the COVID-19 Data Repository for South Africa
 created, maintained and hosted by Data Science for Social Impact research
 group, led by Dr. Vukosi Marivate."><meta property="og:description" content="An aggregated subset of the COVID-19 Data Repository for South Africa
 created, maintained and hosted by Data Science for Social Impact research
@@ -7,16 +7,23 @@
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   function gtag(){dataLayer.push(arguments);}
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     <a class="navbar-brand me-2" href="../index.html">epichains</a>
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">0.1.0</small>
+
+    <small class="nav-text text-danger me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Unreleased version">0.1.0.9000</small>
+
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 <li class="active nav-item"><a class="nav-link" href="../reference/index.html">Reference</a></li>
@@ -38,33 +45,51 @@
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
 <li class="nav-item"><a class="external-link nav-link" href="https://github.com/epiverse-trace/epichains/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item dropdown">
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+    <li><button class="dropdown-item" data-bs-theme-value="auto"><span class="fa fa-adjust"></span> Auto</button></li>
+  </ul></li>
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 </nav><div class="container template-reference-topic">
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.svg" class="logo" alt=""><h1>COVID-19 Data Repository for South Africa</h1>
-      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/R/covid19_sa.R" class="external-link"><code>R/covid19_sa.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/R/covid19_sa.R" class="external-link"><code>R/covid19_sa.R</code></a></small>
       <div class="d-none name"><code>covid19_sa.Rd</code></div>
     </div>
+
     <div class="ref-description section level2">
     <p>An aggregated subset of the COVID-19 Data Repository for South Africa
 created, maintained and hosted by Data Science for Social Impact research
 group, led by Dr. Vukosi Marivate.</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="va">covid19_sa</span></span></code></pre></div>
     </div>
+
     <div class="section level2">
     <h2 id="format">Format<a class="anchor" aria-label="anchor" href="#format"></a></h2>
+
 <div class="section">
 <h3 id="covid-sa"><code>covid19_sa</code><a class="anchor" aria-label="anchor" href="#covid-sa"></a></h3>
+
+
 <p>A data frame with 19 rows and 2 columns:</p><dl><dt>date</dt>
 <dd><p>Date case was reported</p></dd>
+
 <dt>cases</dt>
 <dd><p>Number of cases</p></dd>
+
+
 </dl></div>
+
     </div>
     <div class="section level2">
     <h2 id="source">Source<a class="anchor" aria-label="anchor" href="#source"></a></h2>
@@ -76,14 +101,24 @@ <h2 id="details">Details<a class="anchor" aria-label="anchor" href="#details"></
     <p>The data is originally provided as a linelist but has been subsetted and
 cleaned in <code>data-raw/covid19_sa.R</code>.</p>
     </div>
+
   </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
     </nav></aside></div>
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 </div>
+
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+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
 </div>
+
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diff --git a/reference/dborel.html b/reference/dborel.html
index 30a8441b..6e35e5d4 100644
--- a/reference/dborel.html
+++ b/reference/dborel.html
@@ -1,18 +1,25 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Density of the Borel distribution — dborel • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Density of the Borel distribution — dborel"><meta name="description" content="Density of the Borel distribution"><meta property="og:description" content="Density of the Borel distribution"><meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg"><!-- Google tag (gtag.js) --><script async src="https://www.googletagmanager.com/gtag/js?id=G-XZ471458FQ"></script><script>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Density of the Borel distribution — dborel • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../lightswitch.js"></script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Density of the Borel distribution — dborel"><meta name="description" content="Density of the Borel distribution"><meta property="og:description" content="Density of the Borel distribution"><meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg"><!-- Google tag (gtag.js) --><script async src="https://www.googletagmanager.com/gtag/js?id=G-XZ471458FQ"></script><script>
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+
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 </script></head><body>
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-    <nav class="navbar navbar-expand-lg fixed-top bg-dark" data-bs-theme="dark" aria-label="Site navigation"><div class="container">
+
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+    <nav class="navbar navbar-expand-lg fixed-top " aria-label="Site navigation"><div class="container">
     <a href="https://epiverse-trace.github.io/" class="external-link"><img src="https://epiverse-trace.github.io/blueprints/logo_white.svg" id="logo" alt="Epiverse-TRACE"></a>
     <a class="navbar-brand me-2" href="../index.html">epichains</a>
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">0.1.0</small>
+
+    <small class="nav-text text-danger me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Unreleased version">0.1.0.9000</small>
+
+
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
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 <li class="active nav-item"><a class="nav-link" href="../reference/index.html">Reference</a></li>
@@ -34,30 +41,48 @@
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
 <li class="nav-item"><a class="external-link nav-link" href="https://github.com/epiverse-trace/epichains/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item dropdown">
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+    <li><button class="dropdown-item" data-bs-theme-value="auto"><span class="fa fa-adjust"></span> Auto</button></li>
+  </ul></li>
       </ul></div>
+
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   </div>
 </nav><div class="container template-reference-topic">
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.svg" class="logo" alt=""><h1>Density of the Borel distribution</h1>
-      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/R/borel.R" class="external-link"><code>R/borel.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/R/borel.R" class="external-link"><code>R/borel.R</code></a></small>
       <div class="d-none name"><code>dborel.Rd</code></div>
     </div>
+
     <div class="ref-description section level2">
     <p>Density of the Borel distribution</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">dborel</span><span class="op">(</span><span class="va">x</span>, <span class="va">mu</span>, log <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></span></code></pre></div>
     </div>
+
     <div class="section level2">
     <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
 <dl><dt id="arg-x">x<a class="anchor" aria-label="anchor" href="#arg-x"></a></dt>
 <dd><p>A numeric vector of quantiles.</p></dd>
+
+
 <dt id="arg-mu">mu<a class="anchor" aria-label="anchor" href="#arg-mu"></a></dt>
 <dd><p>A non-negative number for the poisson mean.</p></dd>
+
+
 <dt id="arg-log">log<a class="anchor" aria-label="anchor" href="#arg-log"></a></dt>
 <dd><p>Logical; if TRUE, probabilities p are given as log(p).</p></dd>
+
 </dl></div>
     <div class="section level2">
     <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
@@ -67,6 +92,7 @@ <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2
     <h2 id="author">Author<a class="anchor" aria-label="anchor" href="#author"></a></h2>
     <p>Sebastian Funk</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/Random.html" class="external-link">set.seed</a></span><span class="op">(</span><span class="fl">32</span><span class="op">)</span></span></span>
@@ -76,12 +102,21 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
     </div>
   </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
     </nav></aside></div>
+
+
     <footer><div class="pkgdown-footer-left">
   <p>Developed by James M. Azam, Sebastian Funk, Flavio Finger.</p>
 </div>
+
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.9.9000.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
 </div>
+
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+
+
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+
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   </body></html>
 
diff --git a/reference/dot-adjust_next_gen.html b/reference/dot-adjust_next_gen.html
index e7a14cf2..e26e59f9 100644
--- a/reference/dot-adjust_next_gen.html
+++ b/reference/dot-adjust_next_gen.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Adjust new offspring if it exceeds the susceptible population size — .adjust_next_gen • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Adjust new offspring if it exceeds the susceptible population size — .adjust_next_gen"><meta name="description" content="This function is used internally, and input checking is not
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Adjust new offspring if it exceeds the susceptible population size — .adjust_next_gen • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../lightswitch.js"></script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Adjust new offspring if it exceeds the susceptible population size — .adjust_next_gen"><meta name="description" content="This function is used internally, and input checking is not
 performed here, only in the context where it is used. Using it directly
 is not recommended."><meta property="og:description" content="This function is used internally, and input checking is not
 performed here, only in the context where it is used. Using it directly
@@ -7,16 +7,23 @@
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   function gtag(){dataLayer.push(arguments);}
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+    <nav class="navbar navbar-expand-lg fixed-top " aria-label="Site navigation"><div class="container">
     <a href="https://epiverse-trace.github.io/" class="external-link"><img src="https://epiverse-trace.github.io/blueprints/logo_white.svg" id="logo" alt="Epiverse-TRACE"></a>
     <a class="navbar-brand me-2" href="../index.html">epichains</a>
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">0.1.0</small>
+
+    <small class="nav-text text-danger me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Unreleased version">0.1.0.9000</small>
+
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 <li class="active nav-item"><a class="nav-link" href="../reference/index.html">Reference</a></li>
@@ -38,44 +45,70 @@
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
 <li class="nav-item"><a class="external-link nav-link" href="https://github.com/epiverse-trace/epichains/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item dropdown">
+  <button class="nav-link dropdown-toggle" type="button" id="dropdown-lightswitch" data-bs-toggle="dropdown" aria-expanded="false" aria-haspopup="true" aria-label="Light switch"><span class="fa fa-sun"></span></button>
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 </nav><div class="container template-reference-topic">
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.svg" class="logo" alt=""><h1>Adjust new offspring if it exceeds the susceptible population size</h1>
-      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/R/helpers.R" class="external-link"><code>R/helpers.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/R/helpers.R" class="external-link"><code>R/helpers.R</code></a></small>
       <div class="d-none name"><code>dot-adjust_next_gen.Rd</code></div>
     </div>
+
     <div class="ref-description section level2">
     <p>This function is used internally, and input checking is not
 performed here, only in the context where it is used. Using it directly
 is not recommended.</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">.adjust_next_gen</span><span class="op">(</span><span class="va">next_gen</span>, <span class="va">susc_pop</span><span class="op">)</span></span></code></pre></div>
     </div>
+
     <div class="section level2">
     <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
 <dl><dt id="arg-next-gen">next_gen<a class="anchor" aria-label="anchor" href="#arg-next-gen"></a></dt>
 <dd><p>A numeric vector of next generation offspring.</p></dd>
+
+
 <dt id="arg-susc-pop">susc_pop<a class="anchor" aria-label="anchor" href="#arg-susc-pop"></a></dt>
 <dd><p>The susceptible population size; A number coercible to
 integer.</p></dd>
+
 </dl></div>
     <div class="section level2">
     <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
     <p>A numeric vector of the adjusted next generation offspring.</p>
     </div>
+
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     </nav></aside></div>
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+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
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diff --git a/reference/dot-check_generation_time_valid.html b/reference/dot-check_generation_time_valid.html
index 5ec62f72..44cc3ead 100644
--- a/reference/dot-check_generation_time_valid.html
+++ b/reference/dot-check_generation_time_valid.html
@@ -1,18 +1,25 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Check if the generation_time argument is specified as a function — .check_generation_time_valid • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Check if the generation_time argument is specified as a function — .check_generation_time_valid"><meta name="description" content="Check if the generation_time argument is specified as a function"><meta property="og:description" content="Check if the generation_time argument is specified as a function"><meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg"><!-- Google tag (gtag.js) --><script async src="https://www.googletagmanager.com/gtag/js?id=G-XZ471458FQ"></script><script>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Check if the generation_time argument is specified as a function — .check_generation_time_valid • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../lightswitch.js"></script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Check if the generation_time argument is specified as a function — .check_generation_time_valid"><meta name="description" content="Check if the generation_time argument is specified as a function"><meta property="og:description" content="Check if the generation_time argument is specified as a function"><meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg"><!-- Google tag (gtag.js) --><script async src="https://www.googletagmanager.com/gtag/js?id=G-XZ471458FQ"></script><script>
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   function gtag(){dataLayer.push(arguments);}
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+
   gtag('config', 'G-XZ471458FQ');
 </script></head><body>
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-    <nav class="navbar navbar-expand-lg fixed-top bg-dark" data-bs-theme="dark" aria-label="Site navigation"><div class="container">
+
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     <a href="https://epiverse-trace.github.io/" class="external-link"><img src="https://epiverse-trace.github.io/blueprints/logo_white.svg" id="logo" alt="Epiverse-TRACE"></a>
     <a class="navbar-brand me-2" href="../index.html">epichains</a>
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">0.1.0</small>
+
+    <small class="nav-text text-danger me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Unreleased version">0.1.0.9000</small>
+
+
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
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 <li class="active nav-item"><a class="nav-link" href="../reference/index.html">Reference</a></li>
@@ -34,37 +41,61 @@
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
 <li class="nav-item"><a class="external-link nav-link" href="https://github.com/epiverse-trace/epichains/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item dropdown">
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+    <li><button class="dropdown-item" data-bs-theme-value="dark"><span class="fa fa-moon"></span> Dark</button></li>
+    <li><button class="dropdown-item" data-bs-theme-value="auto"><span class="fa fa-adjust"></span> Auto</button></li>
+  </ul></li>
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   </div>
 </nav><div class="container template-reference-topic">
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.svg" class="logo" alt=""><h1>Check if the generation_time argument is specified as a function</h1>
-      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/R/checks.R" class="external-link"><code>R/checks.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/R/checks.R" class="external-link"><code>R/checks.R</code></a></small>
       <div class="d-none name"><code>dot-check_generation_time_valid.Rd</code></div>
     </div>
+
     <div class="ref-description section level2">
     <p>Check if the generation_time argument is specified as a function</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">.check_generation_time_valid</span><span class="op">(</span><span class="va">generation_time</span><span class="op">)</span></span></code></pre></div>
     </div>
+
     <div class="section level2">
     <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
 <dl><dt id="arg-generation-time">generation_time<a class="anchor" aria-label="anchor" href="#arg-generation-time"></a></dt>
 <dd><p>The generation time function; the name
 of a user-defined named or anonymous function with only one argument <code>n</code>,
 representing the number of generation times to sample.</p></dd>
+
 </dl></div>
+
   </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
     </nav></aside></div>
+
+
     <footer><div class="pkgdown-footer-left">
   <p>Developed by James M. Azam, Sebastian Funk, Flavio Finger.</p>
 </div>
+
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.9.9000.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
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diff --git a/reference/dot-check_offspring_func_valid.html b/reference/dot-check_offspring_func_valid.html
index 7d2d0caf..a8491f94 100644
--- a/reference/dot-check_offspring_func_valid.html
+++ b/reference/dot-check_offspring_func_valid.html
@@ -1,20 +1,27 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Check if constructed random number generator for offspring exists and has an n argument. — .check_offspring_func_valid • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Check if constructed random number generator for offspring exists and has an n argument. — .check_offspring_func_valid"><meta name="description" content="Check if constructed random number generator for offspring exists
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-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">0.1.0</small>
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@@ -36,25 +43,38 @@
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       <img src="../logo.svg" class="logo" alt=""><h1>Check if constructed random number generator for offspring exists and has an <code>n</code> argument.</h1>
-      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/R/checks.R" class="external-link"><code>R/checks.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/R/checks.R" class="external-link"><code>R/checks.R</code></a></small>
       <div class="d-none name"><code>dot-check_offspring_func_valid.Rd</code></div>
     </div>
+
     <div class="ref-description section level2">
     <p>Check if constructed random number generator for offspring exists
 and has an <code>n</code> argument.</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">.check_offspring_func_valid</span><span class="op">(</span><span class="va">offspring_dist</span><span class="op">)</span></span></code></pre></div>
     </div>
+
     <div class="section level2">
     <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
 <dl><dt id="arg-offspring-dist">offspring_dist<a class="anchor" aria-label="anchor" href="#arg-offspring-dist"></a></dt>
 <dd><p>Offspring distribution: a <code>&lt;function&gt;</code> like the ones
 provided by R to generate random numbers from given distributions (e.g.,
@@ -64,15 +84,26 @@ <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#argumen
 on to the random number generating functions. Examples that can be provided
 here are <code>rpois</code> for Poisson distributed offspring, <code>rnbinom</code> for negative
 binomial offspring, or custom functions.</p></dd>
+
 </dl></div>
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diff --git a/reference/dot-check_sim_args.html b/reference/dot-check_sim_args.html
index ec388fc2..e6b11ee3 100644
--- a/reference/dot-check_sim_args.html
+++ b/reference/dot-check_sim_args.html
@@ -1,18 +1,25 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Check inputs to simulate_chains() and simulate_summary() — .check_sim_args • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Check inputs to simulate_chains() and simulate_summary() — .check_sim_args"><meta name="description" content="Check inputs to simulate_chains() and simulate_summary()"><meta property="og:description" content="Check inputs to simulate_chains() and simulate_summary()"><meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg"><!-- Google tag (gtag.js) --><script async src="https://www.googletagmanager.com/gtag/js?id=G-XZ471458FQ"></script><script>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Check inputs to simulate_chains() and simulate_summary() — .check_sim_args • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../lightswitch.js"></script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Check inputs to simulate_chains() and simulate_summary() — .check_sim_args"><meta name="description" content="Check inputs to simulate_chains() and simulate_summary()"><meta property="og:description" content="Check inputs to simulate_chains() and simulate_summary()"><meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg"><!-- Google tag (gtag.js) --><script async src="https://www.googletagmanager.com/gtag/js?id=G-XZ471458FQ"></script><script>
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     <a href="https://epiverse-trace.github.io/" class="external-link"><img src="https://epiverse-trace.github.io/blueprints/logo_white.svg" id="logo" alt="Epiverse-TRACE"></a>
     <a class="navbar-brand me-2" href="../index.html">epichains</a>
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">0.1.0</small>
+
+    <small class="nav-text text-danger me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Unreleased version">0.1.0.9000</small>
+
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@@ -34,18 +41,28 @@
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  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
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+<li class="nav-item dropdown">
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 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.svg" class="logo" alt=""><h1>Check inputs to <code>simulate_chains()</code> and <code>simulate_summary()</code></h1>
-      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/R/checks.R" class="external-link"><code>R/checks.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/R/checks.R" class="external-link"><code>R/checks.R</code></a></small>
       <div class="d-none name"><code>dot-check_sim_args.Rd</code></div>
     </div>
+
     <div class="ref-description section level2">
     <p>Check inputs to <code><a href="simulate_chains.html">simulate_chains()</a></code> and <code>simulate_summary()</code></p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">.check_sim_args</span><span class="op">(</span></span>
@@ -57,10 +74,15 @@ <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage">
 <span>  <span class="va">percent_immune</span></span>
 <span><span class="op">)</span></span></code></pre></div>
     </div>
+
     <div class="section level2">
     <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
 <dl><dt id="arg-n-chains">n_chains<a class="anchor" aria-label="anchor" href="#arg-n-chains"></a></dt>
 <dd><p>Number of chains to simulate.</p></dd>
+
+
 <dt id="arg-statistic">statistic<a class="anchor" aria-label="anchor" href="#arg-statistic"></a></dt>
 <dd><p>The chain statistic to track as the
 stopping criteria for each chain being simulated when <code>stat_threshold</code> is not
@@ -69,6 +91,8 @@ <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#argumen
 <li><p>"length": the total number of generations reached by a chain before
 it goes extinct.</p></li>
 </ul></dd>
+
+
 <dt id="arg-offspring-dist">offspring_dist<a class="anchor" aria-label="anchor" href="#arg-offspring-dist"></a></dt>
 <dd><p>Offspring distribution: a <code>&lt;function&gt;</code> like the ones
 provided by R to generate random numbers from given distributions (e.g.,
@@ -78,6 +102,8 @@ <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#argumen
 on to the random number generating functions. Examples that can be provided
 here are <code>rpois</code> for Poisson distributed offspring, <code>rnbinom</code> for negative
 binomial offspring, or custom functions.</p></dd>
+
+
 <dt id="arg-stat-threshold">stat_threshold<a class="anchor" aria-label="anchor" href="#arg-stat-threshold"></a></dt>
 <dd><p>A stopping criterion for individual chain simulations;
 a positive number coercible to integer. When any chain's cumulative statistic
@@ -86,27 +112,42 @@ <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#argumen
 chain that produces 10 or more cases will stop. Note that setting
 <code>stat_threshold</code> does not guarantee that all chains will stop at the same
 value.</p></dd>
+
+
 <dt id="arg-pop">pop<a class="anchor" aria-label="anchor" href="#arg-pop"></a></dt>
 <dd><p>Population size; An <code>&lt;Integer&gt;</code>. Used alongside <code>percent_immune</code>
 to define the susceptible population. Defaults to <code>Inf</code>.</p></dd>
+
+
 <dt id="arg-percent-immune">percent_immune<a class="anchor" aria-label="anchor" href="#arg-percent-immune"></a></dt>
 <dd><p>Percent of the population immune to
 infection at the start of the simulation; A <code>&lt;numeric&gt;</code> between 0 and 1.
 Used alongside <code>pop</code> to initialise the susceptible population. Defaults to
 0.</p></dd>
+
 </dl></div>
     <div class="section level2">
     <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
     <p>NULL; called for side effects</p>
     </div>
+
   </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
     </nav></aside></div>
+
+
     <footer><div class="pkgdown-footer-left">
   <p>Developed by James M. Azam, Sebastian Funk, Flavio Finger.</p>
 </div>
+
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.9.9000.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
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+
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diff --git a/reference/dot-check_statistic_args.html b/reference/dot-check_statistic_args.html
index df7a3a03..1902f486 100644
--- a/reference/dot-check_statistic_args.html
+++ b/reference/dot-check_statistic_args.html
@@ -1,5 +1,5 @@
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+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Check that the statistic and stat_threshold arguments are valid — .check_statistic_args • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../lightswitch.js"></script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Check that the statistic and stat_threshold arguments are valid — .check_statistic_args"><meta name="description" content="The function treats these two arguments as related and checks
 them in one place to remove repeated checks in several places in the
 package."><meta property="og:description" content="The function treats these two arguments as related and checks
 them in one place to remove repeated checks in several places in the
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-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">0.1.0</small>
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@@ -38,26 +45,39 @@
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 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.svg" class="logo" alt=""><h1>Check that the <code>statistic</code> and <code>stat_threshold</code> arguments are valid</h1>
-      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/R/checks.R" class="external-link"><code>R/checks.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/R/checks.R" class="external-link"><code>R/checks.R</code></a></small>
       <div class="d-none name"><code>dot-check_statistic_args.Rd</code></div>
     </div>
+
     <div class="ref-description section level2">
     <p>The function treats these two arguments as related and checks
 them in one place to remove repeated checks in several places in the
 package.</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">.check_statistic_args</span><span class="op">(</span><span class="va">statistic</span>, <span class="va">stat_threshold</span><span class="op">)</span></span></code></pre></div>
     </div>
+
     <div class="section level2">
     <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
 <dl><dt id="arg-statistic">statistic<a class="anchor" aria-label="anchor" href="#arg-statistic"></a></dt>
 <dd><p>The chain statistic to track as the
 stopping criteria for each chain being simulated when <code>stat_threshold</code> is not
@@ -66,6 +86,8 @@ <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#argumen
 <li><p>"length": the total number of generations reached by a chain before
 it goes extinct.</p></li>
 </ul></dd>
+
+
 <dt id="arg-stat-threshold">stat_threshold<a class="anchor" aria-label="anchor" href="#arg-stat-threshold"></a></dt>
 <dd><p>A stopping criterion for individual chain simulations;
 a positive number coercible to integer. When any chain's cumulative statistic
@@ -74,19 +96,30 @@ <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#argumen
 chain that produces 10 or more cases will stop. Note that setting
 <code>stat_threshold</code> does not guarantee that all chains will stop at the same
 value.</p></dd>
+
 </dl></div>
     <div class="section level2">
     <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
     <p>NULL; called for side effects</p>
     </div>
+
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diff --git a/reference/dot-check_time_args.html b/reference/dot-check_time_args.html
index c99c10e7..0d6c43d6 100644
--- a/reference/dot-check_time_args.html
+++ b/reference/dot-check_time_args.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Check inputs that control time events — .check_time_args • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Check inputs that control time events — .check_time_args"><meta name="description" content="This function checks the time-related inputs, i.e., start time of each chain,
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Check inputs that control time events — .check_time_args • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../lightswitch.js"></script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Check inputs that control time events — .check_time_args"><meta name="description" content="This function checks the time-related inputs, i.e., start time of each chain,
 t0, the end time of the simulation, tf, and the generation time,
 generation_time. It also checks that the generation_time argument is
 specified if tf is specified as these go hand-in-hand."><meta property="og:description" content="This function checks the time-related inputs, i.e., start time of each chain,
@@ -9,16 +9,23 @@
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-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">0.1.0</small>
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+    <small class="nav-text text-danger me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Unreleased version">0.1.0.9000</small>
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@@ -40,56 +47,86 @@
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  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
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 </nav><div class="container template-reference-topic">
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.svg" class="logo" alt=""><h1>Check inputs that control time events</h1>
-      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/R/checks.R" class="external-link"><code>R/checks.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/R/checks.R" class="external-link"><code>R/checks.R</code></a></small>
       <div class="d-none name"><code>dot-check_time_args.Rd</code></div>
     </div>
+
     <div class="ref-description section level2">
     <p>This function checks the time-related inputs, i.e., start time of each chain,
 <code>t0</code>, the end time of the simulation, <code>tf</code>, and the generation time,
 generation_time. It also checks that the generation_time argument is
 specified if <code>tf</code> is specified as these go hand-in-hand.</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">.check_time_args</span><span class="op">(</span><span class="va">tf_specified</span>, <span class="va">tf</span>, <span class="va">generation_time</span>, <span class="va">t0</span><span class="op">)</span></span></code></pre></div>
     </div>
+
     <div class="section level2">
     <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
 <dl><dt id="arg-tf-specified">tf_specified<a class="anchor" aria-label="anchor" href="#arg-tf-specified"></a></dt>
 <dd><p><code>&lt;logical&gt;</code>; Whether the <code>tf</code> argument is specified. Only
 makes sense in the context where this function is called, i.e., in
 <code><a href="simulate_chains.html">simulate_chains()</a></code>. If <code>tf</code> is specified, generation_time must be specified.</p></dd>
+
+
 <dt id="arg-tf">tf<a class="anchor" aria-label="anchor" href="#arg-tf"></a></dt>
 <dd><p>A number for the cut-off for the infection times (if generation
 time is given); Defaults to <code>Inf</code>.</p></dd>
+
+
 <dt id="arg-generation-time">generation_time<a class="anchor" aria-label="anchor" href="#arg-generation-time"></a></dt>
 <dd><p>The generation time function; the name
 of a user-defined named or anonymous function with only one argument <code>n</code>,
 representing the number of generation times to sample.</p></dd>
+
+
 <dt id="arg-t-">t0<a class="anchor" aria-label="anchor" href="#arg-t-"></a></dt>
 <dd><p>Start time (if generation time is given); either a single value
 or a vector of same length as <code>n_chains</code> (number of initial cases) with
 corresponding initial times. Defaults to 0, meaning all cases started at
 time 0.</p></dd>
+
 </dl></div>
     <div class="section level2">
     <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
     <p><code>NULL</code>; called for side effects</p>
     </div>
+
   </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
     </nav></aside></div>
+
+
     <footer><div class="pkgdown-footer-left">
   <p>Developed by James M. Azam, Sebastian Funk, Flavio Finger.</p>
 </div>
+
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.9.9000.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
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diff --git a/reference/dot-complementary_logprob.html b/reference/dot-complementary_logprob.html
index 41d68d84..80e2c119 100644
--- a/reference/dot-complementary_logprob.html
+++ b/reference/dot-complementary_logprob.html
@@ -1,18 +1,25 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Calculates the complementary log-probability — .complementary_logprob • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Calculates the complementary log-probability — .complementary_logprob"><meta name="description" content="Given x and norm, this calculates log(1-sum(exp(x)))"><meta property="og:description" content="Given x and norm, this calculates log(1-sum(exp(x)))"><meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg"><!-- Google tag (gtag.js) --><script async src="https://www.googletagmanager.com/gtag/js?id=G-XZ471458FQ"></script><script>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Calculates the complementary log-probability — .complementary_logprob • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../lightswitch.js"></script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Calculates the complementary log-probability — .complementary_logprob"><meta name="description" content="Given x and norm, this calculates log(1-sum(exp(x)))"><meta property="og:description" content="Given x and norm, this calculates log(1-sum(exp(x)))"><meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg"><!-- Google tag (gtag.js) --><script async src="https://www.googletagmanager.com/gtag/js?id=G-XZ471458FQ"></script><script>
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     <a href="https://epiverse-trace.github.io/" class="external-link"><img src="https://epiverse-trace.github.io/blueprints/logo_white.svg" id="logo" alt="Epiverse-TRACE"></a>
     <a class="navbar-brand me-2" href="../index.html">epichains</a>
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">0.1.0</small>
+
+    <small class="nav-text text-danger me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Unreleased version">0.1.0.9000</small>
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 <li class="active nav-item"><a class="nav-link" href="../reference/index.html">Reference</a></li>
@@ -34,26 +41,40 @@
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
 <li class="nav-item"><a class="external-link nav-link" href="https://github.com/epiverse-trace/epichains/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
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 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.svg" class="logo" alt=""><h1>Calculates the complementary log-probability</h1>
-      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/R/utils.R" class="external-link"><code>R/utils.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/R/utils.R" class="external-link"><code>R/utils.R</code></a></small>
       <div class="d-none name"><code>dot-complementary_logprob.Rd</code></div>
     </div>
+
     <div class="ref-description section level2">
     <p>Given x and norm, this calculates log(1-sum(exp(x)))</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">.complementary_logprob</span><span class="op">(</span><span class="va">x</span><span class="op">)</span></span></code></pre></div>
     </div>
+
     <div class="section level2">
     <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
 <dl><dt id="arg-x">x<a class="anchor" aria-label="anchor" href="#arg-x"></a></dt>
 <dd><p>A numeric vector of log-probabilities. Must be negative.</p></dd>
+
 </dl></div>
     <div class="section level2">
     <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
@@ -63,14 +84,24 @@ <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2
     <h2 id="author">Author<a class="anchor" aria-label="anchor" href="#author"></a></h2>
     <p>Sebastian Funk</p>
     </div>
+
   </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
     </nav></aside></div>
+
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     <footer><div class="pkgdown-footer-left">
   <p>Developed by James M. Azam, Sebastian Funk, Flavio Finger.</p>
 </div>
+
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diff --git a/reference/dot-epichains.html b/reference/dot-epichains.html
index b7b5d6f3..4e7d0417 100644
--- a/reference/dot-epichains.html
+++ b/reference/dot-epichains.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Create an &lt;epichains&gt; object — .epichains • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Create an &lt;epichains&gt; object — .epichains"><meta name="description" content="epichains() constructs an &amp;lt;epichains&amp;gt; object, which is
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Create an &lt;epichains&gt; object — .epichains • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../lightswitch.js"></script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Create an &lt;epichains&gt; object — .epichains"><meta name="description" content="epichains() constructs an &amp;lt;epichains&amp;gt; object, which is
 inherently an &amp;lt;data.frame&amp;gt; object that stores some of the inputs
 passed to the simulate_chains() and the
 simulated output. The stored attributes are useful for downstream
@@ -23,16 +23,23 @@
   window.dataLayer = window.dataLayer || [];
   function gtag(){dataLayer.push(arguments);}
   gtag('js', new Date());
+
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 </script></head><body>
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-    <nav class="navbar navbar-expand-lg fixed-top bg-dark" data-bs-theme="dark" aria-label="Site navigation"><div class="container">
+
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+    <nav class="navbar navbar-expand-lg fixed-top " aria-label="Site navigation"><div class="container">
     <a href="https://epiverse-trace.github.io/" class="external-link"><img src="https://epiverse-trace.github.io/blueprints/logo_white.svg" id="logo" alt="Epiverse-TRACE"></a>
     <a class="navbar-brand me-2" href="../index.html">epichains</a>
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">0.1.0</small>
+
+    <small class="nav-text text-danger me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Unreleased version">0.1.0.9000</small>
+
+
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       <ul class="navbar-nav me-auto"><li class="nav-item"><a class="nav-link" href="../articles/epichains.html">Get started</a></li>
 <li class="active nav-item"><a class="nav-link" href="../reference/index.html">Reference</a></li>
@@ -54,15 +61,24 @@
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
 <li class="nav-item"><a class="external-link nav-link" href="https://github.com/epiverse-trace/epichains/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item dropdown">
+  <button class="nav-link dropdown-toggle" type="button" id="dropdown-lightswitch" data-bs-toggle="dropdown" aria-expanded="false" aria-haspopup="true" aria-label="Light switch"><span class="fa fa-sun"></span></button>
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 </nav><div class="container template-reference-topic">
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.svg" class="logo" alt=""><h1>Create an <code>&lt;epichains&gt;</code> object</h1>
-      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/R/epichains.R" class="external-link"><code>R/epichains.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/R/epichains.R" class="external-link"><code>R/epichains.R</code></a></small>
       <div class="d-none name"><code>dot-epichains.Rd</code></div>
     </div>
+
     <div class="ref-description section level2">
     <p><code><a href="epichains-package.html">epichains()</a></code> constructs an <code>&lt;epichains&gt;</code> object, which is
 inherently an <code>&lt;data.frame&gt;</code> object that stores some of the inputs
@@ -76,6 +92,7 @@
 the chain statistic that was tracked, and whether the susceptible
 population was tracked.</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">.epichains</span><span class="op">(</span></span>
@@ -84,17 +101,24 @@ <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage">
 <span>  <span class="va">offspring_dist</span>,</span>
 <span>  <span class="va">track_pop</span>,</span>
 <span>  statistic <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"size"</span>, <span class="st">"length"</span><span class="op">)</span>,</span>
-<span>stat_threshold <span class="op">=</span> <span class="cn">Inf</span></span>
+<span>  stat_threshold <span class="op">=</span> <span class="cn">Inf</span></span>
 <span><span class="op">)</span></span></code></pre></div>
     </div>
+
     <div class="section level2">
     <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
 <dl><dt id="arg-sim-df">sim_df<a class="anchor" aria-label="anchor" href="#arg-sim-df"></a></dt>
 <dd><p>a <code>&lt;data.frame&gt;</code> containing at least columns for
 "infectee_id", "infector_id", and "generation". Also has optional columns
 for "time", and "chain_id".</p></dd>
+
+
 <dt id="arg-n-chains">n_chains<a class="anchor" aria-label="anchor" href="#arg-n-chains"></a></dt>
 <dd><p>Number of chains to simulate.</p></dd>
+
+
 <dt id="arg-offspring-dist">offspring_dist<a class="anchor" aria-label="anchor" href="#arg-offspring-dist"></a></dt>
 <dd><p>Offspring distribution: a <code>&lt;function&gt;</code> like the ones
 provided by R to generate random numbers from given distributions (e.g.,
@@ -104,8 +128,12 @@ <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#argumen
 on to the random number generating functions. Examples that can be provided
 here are <code>rpois</code> for Poisson distributed offspring, <code>rnbinom</code> for negative
 binomial offspring, or custom functions.</p></dd>
+
+
 <dt id="arg-track-pop">track_pop<a class="anchor" aria-label="anchor" href="#arg-track-pop"></a></dt>
 <dd><p>Was the susceptible population tracked? Logical.</p></dd>
+
+
 <dt id="arg-statistic">statistic<a class="anchor" aria-label="anchor" href="#arg-statistic"></a></dt>
 <dd><p>The chain statistic to track as the
 stopping criteria for each chain being simulated when <code>stat_threshold</code> is not
@@ -114,6 +142,8 @@ <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#argumen
 <li><p>"length": the total number of generations reached by a chain before
 it goes extinct.</p></li>
 </ul></dd>
+
+
 <dt id="arg-stat-threshold">stat_threshold<a class="anchor" aria-label="anchor" href="#arg-stat-threshold"></a></dt>
 <dd><p>A stopping criterion for individual chain simulations;
 a positive number coercible to integer. When any chain's cumulative statistic
@@ -122,6 +152,7 @@ <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#argumen
 chain that produces 10 or more cases will stop. Note that setting
 <code>stat_threshold</code> does not guarantee that all chains will stop at the same
 value.</p></dd>
+
 </dl></div>
     <div class="section level2">
     <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
@@ -131,14 +162,24 @@ <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2
     <h2 id="author">Author<a class="anchor" aria-label="anchor" href="#author"></a></h2>
     <p>James M. Azam</p>
     </div>
+
   </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
     </nav></aside></div>
+
+
     <footer><div class="pkgdown-footer-left">
   <p>Developed by James M. Azam, Sebastian Funk, Flavio Finger.</p>
 </div>
+
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.9.9000.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
 </div>
+
     </footer></div>
+
+
+
+
+
   </body></html>
 
diff --git a/reference/dot-epichains_summary.html b/reference/dot-epichains_summary.html
index b85168a9..369a9d88 100644
--- a/reference/dot-epichains_summary.html
+++ b/reference/dot-epichains_summary.html
@@ -1,5 +1,5 @@
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 An &amp;lt;epichains_summary&amp;gt; object is a &amp;lt;vector&amp;gt; of the simulated
 chain sizes or lengths. It also stores information on the number of chains
 simulated, and the statistic that was tracked."><meta property="og:description" content="epichains_summary() constructs an &amp;lt;epichains_summary&amp;gt; object.
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       <img src="../logo.svg" class="logo" alt=""><h1>Create an <code>&lt;epichains_summary&gt;</code> object</h1>
-      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/R/epichains.R" class="external-link"><code>R/epichains.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/R/epichains.R" class="external-link"><code>R/epichains.R</code></a></small>
       <div class="d-none name"><code>dot-epichains_summary.Rd</code></div>
     </div>
+
     <div class="ref-description section level2">
     <p><code>epichains_summary()</code> constructs an <code>&lt;epichains_summary&gt;</code> object.</p>
 <p>An <code>&lt;epichains_summary&gt;</code> object is a <code>&lt;vector&gt;</code> of the simulated
 chain sizes or lengths. It also stores information on the number of chains
 simulated, and the statistic that was tracked.</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">.epichains_summary</span><span class="op">(</span></span>
@@ -62,15 +79,22 @@ <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage">
 <span>  <span class="va">n_chains</span>,</span>
 <span>  <span class="va">offspring_dist</span>,</span>
 <span>  statistic <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"size"</span>, <span class="st">"length"</span><span class="op">)</span>,</span>
-<span>stat_threshold <span class="op">=</span> <span class="cn">Inf</span></span>
+<span>  stat_threshold <span class="op">=</span> <span class="cn">Inf</span></span>
 <span><span class="op">)</span></span></code></pre></div>
     </div>
+
     <div class="section level2">
     <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
 <dl><dt id="arg-chains-summary">chains_summary<a class="anchor" aria-label="anchor" href="#arg-chains-summary"></a></dt>
 <dd><p>A numeric <code>&lt;vector&gt;</code> of chain sizes and lengths.</p></dd>
+
+
 <dt id="arg-n-chains">n_chains<a class="anchor" aria-label="anchor" href="#arg-n-chains"></a></dt>
 <dd><p>Number of chains to simulate.</p></dd>
+
+
 <dt id="arg-offspring-dist">offspring_dist<a class="anchor" aria-label="anchor" href="#arg-offspring-dist"></a></dt>
 <dd><p>Offspring distribution: a <code>&lt;function&gt;</code> like the ones
 provided by R to generate random numbers from given distributions (e.g.,
@@ -80,6 +104,8 @@ <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#argumen
 on to the random number generating functions. Examples that can be provided
 here are <code>rpois</code> for Poisson distributed offspring, <code>rnbinom</code> for negative
 binomial offspring, or custom functions.</p></dd>
+
+
 <dt id="arg-statistic">statistic<a class="anchor" aria-label="anchor" href="#arg-statistic"></a></dt>
 <dd><p>The chain statistic to track as the
 stopping criteria for each chain being simulated when <code>stat_threshold</code> is not
@@ -88,12 +114,15 @@ <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#argumen
 <li><p>"length": the total number of generations reached by a chain before
 it goes extinct.</p></li>
 </ul></dd>
+
+
 <dt id="arg-stat-threshold">stat_threshold<a class="anchor" aria-label="anchor" href="#arg-stat-threshold"></a></dt>
 <dd><p>A stopping criterion for individual chain simulations;
 a positive number coercible to integer. When any chain's cumulative statistic
 reaches or surpasses <code>stat_threshold</code>, that chain ends. It also serves as a
 censoring limit so that results above the specified value, are set to <code>Inf</code>.
 Defaults to <code>Inf</code>.</p></dd>
+
 </dl></div>
     <div class="section level2">
     <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
@@ -103,14 +132,24 @@ <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2
     <h2 id="author">Author<a class="anchor" aria-label="anchor" href="#author"></a></h2>
     <p>James M. Azam</p>
     </div>
+
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     </nav></aside></div>
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diff --git a/reference/dot-gborel_size_ll.html b/reference/dot-gborel_size_ll.html
index 143b8b62..a054d155 100644
--- a/reference/dot-gborel_size_ll.html
+++ b/reference/dot-gborel_size_ll.html
@@ -1,18 +1,25 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Log-likelihood of the size of chains with gamma-Borel offspring distribution — .gborel_size_ll • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Log-likelihood of the size of chains with gamma-Borel offspring distribution — .gborel_size_ll"><meta name="description" content="Log-likelihood of the size of chains with gamma-Borel offspring distribution"><meta property="og:description" content="Log-likelihood of the size of chains with gamma-Borel offspring distribution"><meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg"><!-- Google tag (gtag.js) --><script async src="https://www.googletagmanager.com/gtag/js?id=G-XZ471458FQ"></script><script>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Log-likelihood of the size of chains with gamma-Borel offspring distribution — .gborel_size_ll • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../lightswitch.js"></script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Log-likelihood of the size of chains with gamma-Borel offspring distribution — .gborel_size_ll"><meta name="description" content="Log-likelihood of the size of chains with gamma-Borel offspring distribution"><meta property="og:description" content="Log-likelihood of the size of chains with gamma-Borel offspring distribution"><meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg"><!-- Google tag (gtag.js) --><script async src="https://www.googletagmanager.com/gtag/js?id=G-XZ471458FQ"></script><script>
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@@ -34,35 +41,55 @@
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 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.svg" class="logo" alt=""><h1>Log-likelihood of the size of chains with gamma-Borel offspring distribution</h1>
-      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/R/stat_likelihoods.R" class="external-link"><code>R/stat_likelihoods.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/R/stat_likelihoods.R" class="external-link"><code>R/stat_likelihoods.R</code></a></small>
       <div class="d-none name"><code>dot-gborel_size_ll.Rd</code></div>
     </div>
+
     <div class="ref-description section level2">
     <p>Log-likelihood of the size of chains with gamma-Borel offspring distribution</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">.gborel_size_ll</span><span class="op">(</span><span class="va">x</span>, <span class="va">size</span>, <span class="va">prob</span>, <span class="va">mu</span><span class="op">)</span></span></code></pre></div>
     </div>
+
     <div class="section level2">
     <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
 <dl><dt id="arg-x">x<a class="anchor" aria-label="anchor" href="#arg-x"></a></dt>
 <dd><p>A numeric vector of chain sizes.</p></dd>
+
+
 <dt id="arg-size">size<a class="anchor" aria-label="anchor" href="#arg-size"></a></dt>
 <dd><p>The dispersion parameter (often called <code>k</code> in ecological
 applications); A positive number.</p></dd>
+
+
 <dt id="arg-prob">prob<a class="anchor" aria-label="anchor" href="#arg-prob"></a></dt>
 <dd><p>Probability of success (in the parameterisation with
 <code>prob</code>, see also <code><a href="https://rdrr.io/r/stats/NegBinomial.html" class="external-link">NegBinomial</a></code>); A number between
 0 and 1.</p></dd>
+
+
 <dt id="arg-mu">mu<a class="anchor" aria-label="anchor" href="#arg-mu"></a></dt>
 <dd><p>Mean; A positive number.</p></dd>
+
 </dl></div>
     <div class="section level2">
     <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
@@ -72,14 +99,24 @@ <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2
     <h2 id="author">Author<a class="anchor" aria-label="anchor" href="#author"></a></h2>
     <p>Sebastian Funk</p>
     </div>
+
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diff --git a/reference/dot-geom_length_ll.html b/reference/dot-geom_length_ll.html
index 7fe27fc7..6ea05e2a 100644
--- a/reference/dot-geom_length_ll.html
+++ b/reference/dot-geom_length_ll.html
@@ -1,18 +1,25 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Log-likelihood of the length of chains with geometric offspring distribution — .geom_length_ll • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Log-likelihood of the length of chains with geometric offspring distribution — .geom_length_ll"><meta name="description" content="Log-likelihood of the length of chains with geometric offspring distribution"><meta property="og:description" content="Log-likelihood of the length of chains with geometric offspring distribution"><meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg"><!-- Google tag (gtag.js) --><script async src="https://www.googletagmanager.com/gtag/js?id=G-XZ471458FQ"></script><script>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Log-likelihood of the length of chains with geometric offspring distribution — .geom_length_ll • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../lightswitch.js"></script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Log-likelihood of the length of chains with geometric offspring distribution — .geom_length_ll"><meta name="description" content="Log-likelihood of the length of chains with geometric offspring distribution"><meta property="og:description" content="Log-likelihood of the length of chains with geometric offspring distribution"><meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg"><!-- Google tag (gtag.js) --><script async src="https://www.googletagmanager.com/gtag/js?id=G-XZ471458FQ"></script><script>
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-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">0.1.0</small>
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@@ -34,29 +41,45 @@
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       <img src="../logo.svg" class="logo" alt=""><h1>Log-likelihood of the length of chains with geometric offspring distribution</h1>
-      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/R/stat_likelihoods.R" class="external-link"><code>R/stat_likelihoods.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/R/stat_likelihoods.R" class="external-link"><code>R/stat_likelihoods.R</code></a></small>
       <div class="d-none name"><code>dot-geom_length_ll.Rd</code></div>
     </div>
+
     <div class="ref-description section level2">
     <p>Log-likelihood of the length of chains with geometric offspring distribution</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">.geom_length_ll</span><span class="op">(</span><span class="va">x</span>, <span class="va">prob</span><span class="op">)</span></span></code></pre></div>
     </div>
+
     <div class="section level2">
     <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
 <dl><dt id="arg-x">x<a class="anchor" aria-label="anchor" href="#arg-x"></a></dt>
 <dd><p>A numeric vector of chain lengths.</p></dd>
+
+
 <dt id="arg-prob">prob<a class="anchor" aria-label="anchor" href="#arg-prob"></a></dt>
 <dd><p>The probability of the geometric distribution with mean
 <code>1/prob</code>. A single numeric value between 0 and 1.</p></dd>
+
 </dl></div>
     <div class="section level2">
     <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
@@ -66,14 +89,24 @@ <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2
     <h2 id="author">Author<a class="anchor" aria-label="anchor" href="#author"></a></h2>
     <p>Sebastian Funk</p>
     </div>
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diff --git a/reference/dot-get_statistic_func.html b/reference/dot-get_statistic_func.html
index c4f19b56..2340e6bb 100644
--- a/reference/dot-get_statistic_func.html
+++ b/reference/dot-get_statistic_func.html
@@ -1,18 +1,25 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Return a function for calculating chain statistics — .get_statistic_func • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Return a function for calculating chain statistics — .get_statistic_func"><meta name="description" content="Return a function for calculating chain statistics"><meta property="og:description" content="Return a function for calculating chain statistics"><meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg"><!-- Google tag (gtag.js) --><script async src="https://www.googletagmanager.com/gtag/js?id=G-XZ471458FQ"></script><script>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Return a function for calculating chain statistics — .get_statistic_func • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../lightswitch.js"></script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Return a function for calculating chain statistics — .get_statistic_func"><meta name="description" content="Return a function for calculating chain statistics"><meta property="og:description" content="Return a function for calculating chain statistics"><meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg"><!-- Google tag (gtag.js) --><script async src="https://www.googletagmanager.com/gtag/js?id=G-XZ471458FQ"></script><script>
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-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">0.1.0</small>
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@@ -34,34 +41,55 @@
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       <img src="../logo.svg" class="logo" alt=""><h1>Return a function for calculating chain statistics</h1>
-      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/R/helpers.R" class="external-link"><code>R/helpers.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/R/helpers.R" class="external-link"><code>R/helpers.R</code></a></small>
       <div class="d-none name"><code>dot-get_statistic_func.Rd</code></div>
     </div>
+
     <div class="ref-description section level2">
     <p>Return a function for calculating chain statistics</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">.get_statistic_func</span><span class="op">(</span><span class="va">chain_statistic</span><span class="op">)</span></span></code></pre></div>
     </div>
+
     <div class="section level2">
     <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
     <p>A function for calculating chain statistics.</p>
     </div>
+
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     </nav></aside></div>
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diff --git a/reference/dot-get_susceptible_offspring.html b/reference/dot-get_susceptible_offspring.html
index efa2ef0f..8c0e8b25 100644
--- a/reference/dot-get_susceptible_offspring.html
+++ b/reference/dot-get_susceptible_offspring.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
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+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Sample the number of susceptible offspring from all possible offspring — .get_susceptible_offspring • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../lightswitch.js"></script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Sample the number of susceptible offspring from all possible offspring — .get_susceptible_offspring"><meta name="description" content="Sample susceptible offspring to be infected from all possible offspring.
 This function is used internally, and input checking is not
 performed here, only in the context where it is used. Using it directly
 is not recommended."><meta property="og:description" content="Sample susceptible offspring to be infected from all possible offspring.
@@ -9,16 +9,23 @@
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-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">0.1.0</small>
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@@ -40,47 +47,73 @@
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       <img src="../logo.svg" class="logo" alt=""><h1>Sample the number of susceptible offspring from all possible offspring</h1>
-      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/R/helpers.R" class="external-link"><code>R/helpers.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/R/helpers.R" class="external-link"><code>R/helpers.R</code></a></small>
       <div class="d-none name"><code>dot-get_susceptible_offspring.Rd</code></div>
     </div>
+
     <div class="ref-description section level2">
     <p>Sample susceptible offspring to be infected from all possible offspring.
 This function is used internally, and input checking is not
 performed here, only in the context where it is used. Using it directly
 is not recommended.</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">.get_susceptible_offspring</span><span class="op">(</span><span class="va">new_offspring</span>, <span class="va">susc_pop</span>, <span class="va">pop</span><span class="op">)</span></span></code></pre></div>
     </div>
+
     <div class="section level2">
     <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
 <dl><dt id="arg-new-offspring">new_offspring<a class="anchor" aria-label="anchor" href="#arg-new-offspring"></a></dt>
 <dd><p>A numeric vector of the possible new offspring per
 chain produced by <code><a href="dot-sample_possible_offspring.html">.sample_possible_offspring()</a></code>.</p></dd>
+
+
 <dt id="arg-pop">pop<a class="anchor" aria-label="anchor" href="#arg-pop"></a></dt>
 <dd><p>Population size; An <code>&lt;Integer&gt;</code>. Used alongside <code>percent_immune</code>
 to define the susceptible population. Defaults to <code>Inf</code>.</p></dd>
+
 </dl></div>
     <div class="section level2">
     <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
     <p>A numeric vector of the number of offspring that can be infected
 given the current susceptible population size.</p>
     </div>
+
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+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
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diff --git a/reference/dot-init_susc_pop.html b/reference/dot-init_susc_pop.html
index 3ad9cd73..1f768fb9 100644
--- a/reference/dot-init_susc_pop.html
+++ b/reference/dot-init_susc_pop.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Adjust next generation vector to match susceptible population size — .init_susc_pop • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Adjust next generation vector to match susceptible population size — .init_susc_pop"><meta name="description" content="Calculates the initial susceptible population size given
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Adjust next generation vector to match susceptible population size — .init_susc_pop • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../lightswitch.js"></script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Adjust next generation vector to match susceptible population size — .init_susc_pop"><meta name="description" content="Calculates the initial susceptible population size given
 the total population size, the percent immune, and the number of index
 cases. This function is used internally, and input checking is not
 performed here, only in the context where it is used. Using it directly
@@ -11,16 +11,23 @@
   window.dataLayer = window.dataLayer || [];
   function gtag(){dataLayer.push(arguments);}
   gtag('js', new Date());
+
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 </script></head><body>
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-    <nav class="navbar navbar-expand-lg fixed-top bg-dark" data-bs-theme="dark" aria-label="Site navigation"><div class="container">
+
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     <a href="https://epiverse-trace.github.io/" class="external-link"><img src="https://epiverse-trace.github.io/blueprints/logo_white.svg" id="logo" alt="Epiverse-TRACE"></a>
     <a class="navbar-brand me-2" href="../index.html">epichains</a>
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">0.1.0</small>
+
+    <small class="nav-text text-danger me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Unreleased version">0.1.0.9000</small>
+
+
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 <li class="active nav-item"><a class="nav-link" href="../reference/index.html">Reference</a></li>
@@ -42,15 +49,24 @@
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
 <li class="nav-item"><a class="external-link nav-link" href="https://github.com/epiverse-trace/epichains/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item dropdown">
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+    <li><button class="dropdown-item" data-bs-theme-value="dark"><span class="fa fa-moon"></span> Dark</button></li>
+    <li><button class="dropdown-item" data-bs-theme-value="auto"><span class="fa fa-adjust"></span> Auto</button></li>
+  </ul></li>
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+
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   </div>
 </nav><div class="container template-reference-topic">
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.svg" class="logo" alt=""><h1>Adjust next generation vector to match susceptible population size</h1>
-      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/R/helpers.R" class="external-link"><code>R/helpers.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/R/helpers.R" class="external-link"><code>R/helpers.R</code></a></small>
       <div class="d-none name"><code>dot-init_susc_pop.Rd</code></div>
     </div>
+
     <div class="ref-description section level2">
     <p>Calculates the initial susceptible population size given
 the total population size, the percent immune, and the number of index
@@ -58,33 +74,50 @@
 performed here, only in the context where it is used. Using it directly
 is not recommended.</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">.init_susc_pop</span><span class="op">(</span><span class="va">pop</span>, <span class="va">percent_immune</span>, <span class="va">index_cases</span><span class="op">)</span></span></code></pre></div>
     </div>
+
     <div class="section level2">
     <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
 <dl><dt id="arg-pop">pop<a class="anchor" aria-label="anchor" href="#arg-pop"></a></dt>
 <dd><p>Population size; An <code>&lt;Integer&gt;</code>. Used alongside <code>percent_immune</code>
 to define the susceptible population. Defaults to <code>Inf</code>.</p></dd>
+
+
 <dt id="arg-percent-immune">percent_immune<a class="anchor" aria-label="anchor" href="#arg-percent-immune"></a></dt>
 <dd><p>Percent of the population immune to
 infection at the start of the simulation; A <code>&lt;numeric&gt;</code> between 0 and 1.
 Used alongside <code>pop</code> to initialise the susceptible population. Defaults to
 0.</p></dd>
+
 </dl></div>
     <div class="section level2">
     <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
     <p>Initial susceptible population size; A numeric coercible to integer.</p>
     </div>
+
   </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
     </nav></aside></div>
+
+
     <footer><div class="pkgdown-footer-left">
   <p>Developed by James M. Azam, Sebastian Funk, Flavio Finger.</p>
 </div>
+
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.9.9000.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
 </div>
+
     </footer></div>
+
+
+
+
+
   </body></html>
 
diff --git a/reference/dot-is_epichains.html b/reference/dot-is_epichains.html
index 212e6778..970424eb 100644
--- a/reference/dot-is_epichains.html
+++ b/reference/dot-is_epichains.html
@@ -1,18 +1,25 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Test if x is an epichains object — .is_epichains • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Test if x is an epichains object — .is_epichains"><meta name="description" content="Test if x is an epichains object"><meta property="og:description" content="Test if x is an epichains object"><meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg"><!-- Google tag (gtag.js) --><script async src="https://www.googletagmanager.com/gtag/js?id=G-XZ471458FQ"></script><script>
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@@ -34,26 +41,40 @@
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       <img src="../logo.svg" class="logo" alt=""><h1>Test if x is an <code>epichains</code> object</h1>
-      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/R/epichains.R" class="external-link"><code>R/epichains.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/R/epichains.R" class="external-link"><code>R/epichains.R</code></a></small>
       <div class="d-none name"><code>dot-is_epichains.Rd</code></div>
     </div>
+
     <div class="ref-description section level2">
     <p>Test if x is an <code>epichains</code> object</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">.is_epichains</span><span class="op">(</span><span class="va">x</span><span class="op">)</span></span></code></pre></div>
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+
+
 <dl><dt id="arg-x">x<a class="anchor" aria-label="anchor" href="#arg-x"></a></dt>
 <dd><p>An R object.</p></dd>
+
 </dl></div>
     <div class="section level2">
     <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
@@ -64,14 +85,24 @@ <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2
     <h2 id="author">Author<a class="anchor" aria-label="anchor" href="#author"></a></h2>
     <p>James M. Azam</p>
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diff --git a/reference/dot-is_epichains_summary.html b/reference/dot-is_epichains_summary.html
index 0be925d7..10bc5e48 100644
--- a/reference/dot-is_epichains_summary.html
+++ b/reference/dot-is_epichains_summary.html
@@ -1,18 +1,25 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Test if x is an epichains_summary object — .is_epichains_summary • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Test if x is an epichains_summary object — .is_epichains_summary"><meta name="description" content="Test if x is an epichains_summary object"><meta property="og:description" content="Test if x is an epichains_summary object"><meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg"><!-- Google tag (gtag.js) --><script async src="https://www.googletagmanager.com/gtag/js?id=G-XZ471458FQ"></script><script>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Test if x is an epichains_summary object — .is_epichains_summary • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../lightswitch.js"></script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Test if x is an epichains_summary object — .is_epichains_summary"><meta name="description" content="Test if x is an epichains_summary object"><meta property="og:description" content="Test if x is an epichains_summary object"><meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg"><!-- Google tag (gtag.js) --><script async src="https://www.googletagmanager.com/gtag/js?id=G-XZ471458FQ"></script><script>
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-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">0.1.0</small>
+
+    <small class="nav-text text-danger me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Unreleased version">0.1.0.9000</small>
+
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@@ -34,26 +41,40 @@
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  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
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   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.svg" class="logo" alt=""><h1>Test if x is an <code>epichains_summary</code> object</h1>
-      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/R/epichains.R" class="external-link"><code>R/epichains.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/R/epichains.R" class="external-link"><code>R/epichains.R</code></a></small>
       <div class="d-none name"><code>dot-is_epichains_summary.Rd</code></div>
     </div>
+
     <div class="ref-description section level2">
     <p>Test if x is an <code>epichains_summary</code> object</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">.is_epichains_summary</span><span class="op">(</span><span class="va">x</span><span class="op">)</span></span></code></pre></div>
     </div>
+
     <div class="section level2">
     <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
 <dl><dt id="arg-x">x<a class="anchor" aria-label="anchor" href="#arg-x"></a></dt>
 <dd><p>An R object.</p></dd>
+
 </dl></div>
     <div class="section level2">
     <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
@@ -64,14 +85,24 @@ <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2
     <h2 id="author">Author<a class="anchor" aria-label="anchor" href="#author"></a></h2>
     <p>James M. Azam</p>
     </div>
+
   </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
     </nav></aside></div>
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   <p>Developed by James M. Azam, Sebastian Funk, Flavio Finger.</p>
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+
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+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
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diff --git a/reference/dot-nbinom_size_ll.html b/reference/dot-nbinom_size_ll.html
index aea0ac32..98defe38 100644
--- a/reference/dot-nbinom_size_ll.html
+++ b/reference/dot-nbinom_size_ll.html
@@ -1,20 +1,27 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Log-likelihood of the size of chains with Negative-Binomial offspring distribution — .nbinom_size_ll • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Log-likelihood of the size of chains with Negative-Binomial offspring distribution — .nbinom_size_ll"><meta name="description" content="Log-likelihood of the size of chains with Negative-Binomial offspring
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Log-likelihood of the size of chains with Negative-Binomial offspring distribution — .nbinom_size_ll • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../lightswitch.js"></script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Log-likelihood of the size of chains with Negative-Binomial offspring distribution — .nbinom_size_ll"><meta name="description" content="Log-likelihood of the size of chains with Negative-Binomial offspring
 distribution"><meta property="og:description" content="Log-likelihood of the size of chains with Negative-Binomial offspring
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@@ -36,36 +43,56 @@
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   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.svg" class="logo" alt=""><h1>Log-likelihood of the size of chains with Negative-Binomial offspring distribution</h1>
-      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/R/stat_likelihoods.R" class="external-link"><code>R/stat_likelihoods.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/R/stat_likelihoods.R" class="external-link"><code>R/stat_likelihoods.R</code></a></small>
       <div class="d-none name"><code>dot-nbinom_size_ll.Rd</code></div>
     </div>
+
     <div class="ref-description section level2">
     <p>Log-likelihood of the size of chains with Negative-Binomial offspring
 distribution</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">.nbinom_size_ll</span><span class="op">(</span><span class="va">x</span>, <span class="va">size</span>, <span class="va">prob</span>, <span class="va">mu</span><span class="op">)</span></span></code></pre></div>
     </div>
+
     <div class="section level2">
     <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
 <dl><dt id="arg-x">x<a class="anchor" aria-label="anchor" href="#arg-x"></a></dt>
 <dd><p>A numeric vector of chain sizes.</p></dd>
+
+
 <dt id="arg-size">size<a class="anchor" aria-label="anchor" href="#arg-size"></a></dt>
 <dd><p>The dispersion parameter (often called <code>k</code> in ecological
 applications); A positive number.</p></dd>
+
+
 <dt id="arg-prob">prob<a class="anchor" aria-label="anchor" href="#arg-prob"></a></dt>
 <dd><p>Probability of success (in the parameterisation with
 <code>prob</code>, see also <code><a href="https://rdrr.io/r/stats/NegBinomial.html" class="external-link">NegBinomial</a></code>); A number between
 0 and 1.</p></dd>
+
+
 <dt id="arg-mu">mu<a class="anchor" aria-label="anchor" href="#arg-mu"></a></dt>
 <dd><p>Mean; A positive number.</p></dd>
+
 </dl></div>
     <div class="section level2">
     <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
@@ -75,14 +102,24 @@ <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2
     <h2 id="author">Author<a class="anchor" aria-label="anchor" href="#author"></a></h2>
     <p>Sebastian Funk</p>
     </div>
+
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     </nav></aside></div>
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   <p>Developed by James M. Azam, Sebastian Funk, Flavio Finger.</p>
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diff --git a/reference/dot-new_epichains.html b/reference/dot-new_epichains.html
index d509fe24..bd482a55 100644
--- a/reference/dot-new_epichains.html
+++ b/reference/dot-new_epichains.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Construct an &lt;epichains&gt; object — .new_epichains • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Construct an &lt;epichains&gt; object — .new_epichains"><meta name="description" content="new_epichains() constructs an &amp;lt;epichains&amp;gt; object from a
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Construct an &lt;epichains&gt; object — .new_epichains • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../lightswitch.js"></script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Construct an &lt;epichains&gt; object — .new_epichains"><meta name="description" content="new_epichains() constructs an &amp;lt;epichains&amp;gt; object from a
 supplied &amp;lt;data.frame&amp;gt; and extra attributes passed as individual arguments.
 It is meant to be lazy and performant, by creating the object without
 checking the arguments for correctness. It is not safe to call
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-    <nav class="navbar navbar-expand-lg fixed-top bg-dark" data-bs-theme="dark" aria-label="Site navigation"><div class="container">
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     <a href="https://epiverse-trace.github.io/" class="external-link"><img src="https://epiverse-trace.github.io/blueprints/logo_white.svg" id="logo" alt="Epiverse-TRACE"></a>
     <a class="navbar-brand me-2" href="../index.html">epichains</a>
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">0.1.0</small>
+
+    <small class="nav-text text-danger me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Unreleased version">0.1.0.9000</small>
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@@ -46,15 +53,24 @@
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 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.svg" class="logo" alt=""><h1>Construct an <code>&lt;epichains&gt;</code> object</h1>
-      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/R/epichains.R" class="external-link"><code>R/epichains.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/R/epichains.R" class="external-link"><code>R/epichains.R</code></a></small>
       <div class="d-none name"><code>dot-new_epichains.Rd</code></div>
     </div>
+
     <div class="ref-description section level2">
     <p><code>new_epichains()</code> constructs an <code>&lt;epichains&gt;</code> object from a
 supplied <code>&lt;data.frame&gt;</code> and extra attributes passed as individual arguments.
@@ -64,6 +80,7 @@
 after the arguments have been checked. To create an <code>&lt;epichains&gt;</code>
 object, use <code><a href="epichains-package.html">epichains()</a></code>.</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">.new_epichains</span><span class="op">(</span></span>
@@ -75,14 +92,21 @@ <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage">
 <span>  <span class="va">track_pop</span></span>
 <span><span class="op">)</span></span></code></pre></div>
     </div>
+
     <div class="section level2">
     <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
 <dl><dt id="arg-sim-df">sim_df<a class="anchor" aria-label="anchor" href="#arg-sim-df"></a></dt>
 <dd><p>a <code>&lt;data.frame&gt;</code> containing at least columns for
 "infectee_id", "infector_id", and "generation". Also has optional columns
 for "time", and "chain_id".</p></dd>
+
+
 <dt id="arg-n-chains">n_chains<a class="anchor" aria-label="anchor" href="#arg-n-chains"></a></dt>
 <dd><p>Number of chains to simulate.</p></dd>
+
+
 <dt id="arg-statistic">statistic<a class="anchor" aria-label="anchor" href="#arg-statistic"></a></dt>
 <dd><p>The chain statistic to track as the
 stopping criteria for each chain being simulated when <code>stat_threshold</code> is not
@@ -91,6 +115,8 @@ <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#argumen
 <li><p>"length": the total number of generations reached by a chain before
 it goes extinct.</p></li>
 </ul></dd>
+
+
 <dt id="arg-offspring-dist">offspring_dist<a class="anchor" aria-label="anchor" href="#arg-offspring-dist"></a></dt>
 <dd><p>Offspring distribution: a <code>&lt;function&gt;</code> like the ones
 provided by R to generate random numbers from given distributions (e.g.,
@@ -100,6 +126,8 @@ <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#argumen
 on to the random number generating functions. Examples that can be provided
 here are <code>rpois</code> for Poisson distributed offspring, <code>rnbinom</code> for negative
 binomial offspring, or custom functions.</p></dd>
+
+
 <dt id="arg-stat-threshold">stat_threshold<a class="anchor" aria-label="anchor" href="#arg-stat-threshold"></a></dt>
 <dd><p>A stopping criterion for individual chain simulations;
 a positive number coercible to integer. When any chain's cumulative statistic
@@ -108,21 +136,34 @@ <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#argumen
 chain that produces 10 or more cases will stop. Note that setting
 <code>stat_threshold</code> does not guarantee that all chains will stop at the same
 value.</p></dd>
+
+
 <dt id="arg-track-pop">track_pop<a class="anchor" aria-label="anchor" href="#arg-track-pop"></a></dt>
 <dd><p>Was the susceptible population tracked? Logical.</p></dd>
+
 </dl></div>
     <div class="section level2">
     <h2 id="author">Author<a class="anchor" aria-label="anchor" href="#author"></a></h2>
     <p>James M. Azam</p>
     </div>
+
   </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
     </nav></aside></div>
+
+
     <footer><div class="pkgdown-footer-left">
   <p>Developed by James M. Azam, Sebastian Funk, Flavio Finger.</p>
 </div>
+
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.9.9000.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
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+
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+
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diff --git a/reference/dot-new_epichains_summary.html b/reference/dot-new_epichains_summary.html
index 8c2653ac..229d5466 100644
--- a/reference/dot-new_epichains_summary.html
+++ b/reference/dot-new_epichains_summary.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Construct a &lt;epichains_summary&gt; object — .new_epichains_summary • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Construct a &lt;epichains_summary&gt; object — .new_epichains_summary"><meta name="description" content="new_epichains_summary() constructs an &amp;lt;epichains_summary&amp;gt; object from a
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Construct a &lt;epichains_summary&gt; object — .new_epichains_summary • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../lightswitch.js"></script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Construct a &lt;epichains_summary&gt; object — .new_epichains_summary"><meta name="description" content="new_epichains_summary() constructs an &amp;lt;epichains_summary&amp;gt; object from a
 supplied &amp;lt;vector&amp;gt; of chain sizes or lengths. It also stores extra
 attributes passed as individual arguments.
 new_epichains_summary() is meant to be lazy and performant, by creating
@@ -17,16 +17,23 @@
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-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">0.1.0</small>
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@@ -48,15 +55,24 @@
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 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.svg" class="logo" alt=""><h1>Construct a <code>&lt;epichains_summary&gt;</code> object</h1>
-      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/R/epichains.R" class="external-link"><code>R/epichains.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/R/epichains.R" class="external-link"><code>R/epichains.R</code></a></small>
       <div class="d-none name"><code>dot-new_epichains_summary.Rd</code></div>
     </div>
+
     <div class="ref-description section level2">
     <p><code>new_epichains_summary()</code> constructs an <code>&lt;epichains_summary&gt;</code> object from a
 supplied <code>&lt;vector&gt;</code> of chain sizes or lengths. It also stores extra
@@ -67,6 +83,7 @@
 <code>epichains_summary()</code> after the arguments have been checked. To create a
 new <code>&lt;epichains_summary&gt;</code> object safely, use <code>epichains_summary()</code>.</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">.new_epichains_summary</span><span class="op">(</span></span>
@@ -77,12 +94,19 @@ <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage">
 <span>  <span class="va">stat_threshold</span></span>
 <span><span class="op">)</span></span></code></pre></div>
     </div>
+
     <div class="section level2">
     <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
 <dl><dt id="arg-chains-summary">chains_summary<a class="anchor" aria-label="anchor" href="#arg-chains-summary"></a></dt>
 <dd><p>A numeric <code>&lt;vector&gt;</code> of chain sizes and lengths.</p></dd>
+
+
 <dt id="arg-n-chains">n_chains<a class="anchor" aria-label="anchor" href="#arg-n-chains"></a></dt>
 <dd><p>Number of chains to simulate.</p></dd>
+
+
 <dt id="arg-statistic">statistic<a class="anchor" aria-label="anchor" href="#arg-statistic"></a></dt>
 <dd><p>The chain statistic to track as the
 stopping criteria for each chain being simulated when <code>stat_threshold</code> is not
@@ -91,6 +115,8 @@ <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#argumen
 <li><p>"length": the total number of generations reached by a chain before
 it goes extinct.</p></li>
 </ul></dd>
+
+
 <dt id="arg-offspring-dist">offspring_dist<a class="anchor" aria-label="anchor" href="#arg-offspring-dist"></a></dt>
 <dd><p>Offspring distribution: a <code>&lt;function&gt;</code> like the ones
 provided by R to generate random numbers from given distributions (e.g.,
@@ -100,25 +126,38 @@ <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#argumen
 on to the random number generating functions. Examples that can be provided
 here are <code>rpois</code> for Poisson distributed offspring, <code>rnbinom</code> for negative
 binomial offspring, or custom functions.</p></dd>
+
+
 <dt id="arg-stat-threshold">stat_threshold<a class="anchor" aria-label="anchor" href="#arg-stat-threshold"></a></dt>
 <dd><p>A stopping criterion for individual chain simulations;
 a positive number coercible to integer. When any chain's cumulative statistic
 reaches or surpasses <code>stat_threshold</code>, that chain ends. It also serves as a
 censoring limit so that results above the specified value, are set to <code>Inf</code>.
 Defaults to <code>Inf</code>.</p></dd>
+
 </dl></div>
     <div class="section level2">
     <h2 id="author">Author<a class="anchor" aria-label="anchor" href="#author"></a></h2>
     <p>James M. Azam</p>
     </div>
+
   </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
     </nav></aside></div>
+
+
     <footer><div class="pkgdown-footer-left">
   <p>Developed by James M. Azam, Sebastian Funk, Flavio Finger.</p>
 </div>
+
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-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.9.9000.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
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diff --git a/reference/dot-offspring_ll.html b/reference/dot-offspring_ll.html
index ee3113d0..5afc707d 100644
--- a/reference/dot-offspring_ll.html
+++ b/reference/dot-offspring_ll.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Log-likelihood of the summary (size/length) of chains with generic offspring distribution — .offspring_ll • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Log-likelihood of the summary (size/length) of chains with generic offspring distribution — .offspring_ll"><meta name="description" content="The log-likelihoods are calculated with a crude approximation using simulated
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Log-likelihood of the summary (size/length) of chains with generic offspring distribution — .offspring_ll • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../lightswitch.js"></script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Log-likelihood of the summary (size/length) of chains with generic offspring distribution — .offspring_ll"><meta name="description" content="The log-likelihoods are calculated with a crude approximation using simulated
 chain summaries by linearly approximating any missing values in the empirical
 cumulative distribution function (ecdf)."><meta property="og:description" content="The log-likelihoods are calculated with a crude approximation using simulated
 chain summaries by linearly approximating any missing values in the empirical
@@ -7,16 +7,23 @@
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   function gtag(){dataLayer.push(arguments);}
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+
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 </script></head><body>
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-    <nav class="navbar navbar-expand-lg fixed-top bg-dark" data-bs-theme="dark" aria-label="Site navigation"><div class="container">
+
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     <a href="https://epiverse-trace.github.io/" class="external-link"><img src="https://epiverse-trace.github.io/blueprints/logo_white.svg" id="logo" alt="Epiverse-TRACE"></a>
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-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">0.1.0</small>
+
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@@ -38,28 +45,43 @@
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
 <li class="nav-item"><a class="external-link nav-link" href="https://github.com/epiverse-trace/epichains/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item dropdown">
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 </nav><div class="container template-reference-topic">
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.svg" class="logo" alt=""><h1>Log-likelihood of the summary (size/length) of chains with generic offspring distribution</h1>
-      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/R/stat_likelihoods.R" class="external-link"><code>R/stat_likelihoods.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/R/stat_likelihoods.R" class="external-link"><code>R/stat_likelihoods.R</code></a></small>
       <div class="d-none name"><code>dot-offspring_ll.Rd</code></div>
     </div>
+
     <div class="ref-description section level2">
     <p>The log-likelihoods are calculated with a crude approximation using simulated
 chain summaries by linearly approximating any missing values in the empirical
 cumulative distribution function (ecdf).</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">.offspring_ll</span><span class="op">(</span><span class="va">x</span>, <span class="va">offspring_dist</span>, <span class="va">statistic</span>, nsim_offspring <span class="op">=</span> <span class="fl">100</span>, <span class="va">...</span><span class="op">)</span></span></code></pre></div>
     </div>
+
     <div class="section level2">
     <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
 <dl><dt id="arg-x">x<a class="anchor" aria-label="anchor" href="#arg-x"></a></dt>
 <dd><p>A numeric vector of chain summaries (sizes/lengths).</p></dd>
+
+
 <dt id="arg-offspring-dist">offspring_dist<a class="anchor" aria-label="anchor" href="#arg-offspring-dist"></a></dt>
 <dd><p>Offspring distribution: a <code>&lt;function&gt;</code> like the ones
 provided by R to generate random numbers from given distributions (e.g.,
@@ -69,6 +91,8 @@ <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#argumen
 on to the random number generating functions. Examples that can be provided
 here are <code>rpois</code> for Poisson distributed offspring, <code>rnbinom</code> for negative
 binomial offspring, or custom functions.</p></dd>
+
+
 <dt id="arg-statistic">statistic<a class="anchor" aria-label="anchor" href="#arg-statistic"></a></dt>
 <dd><p>The chain statistic to track as the
 stopping criteria for each chain being simulated when <code>stat_threshold</code> is not
@@ -77,12 +101,17 @@ <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#argumen
 <li><p>"length": the total number of generations reached by a chain before
 it goes extinct.</p></li>
 </ul></dd>
+
+
 <dt id="arg-nsim-offspring">nsim_offspring<a class="anchor" aria-label="anchor" href="#arg-nsim-offspring"></a></dt>
 <dd><p>Number of simulations of the offspring distribution
 for approximating the distribution of the chain statistic summary
 (size/length)</p></dd>
+
+
 <dt id="arg--">...<a class="anchor" aria-label="anchor" href="#arg--"></a></dt>
 <dd><p>any parameters to pass to <code><a href="simulate_chain_stats.html">simulate_chain_stats</a></code></p></dd>
+
 </dl></div>
     <div class="section level2">
     <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
@@ -92,14 +121,24 @@ <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2
     <h2 id="author">Author<a class="anchor" aria-label="anchor" href="#author"></a></h2>
     <p>Sebastian Funk</p>
     </div>
+
   </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
     </nav></aside></div>
+
+
     <footer><div class="pkgdown-footer-left">
   <p>Developed by James M. Azam, Sebastian Funk, Flavio Finger.</p>
 </div>
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diff --git a/reference/dot-pois_length_ll.html b/reference/dot-pois_length_ll.html
index 0a4104f7..b1cdc534 100644
--- a/reference/dot-pois_length_ll.html
+++ b/reference/dot-pois_length_ll.html
@@ -1,18 +1,25 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Log-likelihood of the length of chains with Poisson offspring distribution — .pois_length_ll • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Log-likelihood of the length of chains with Poisson offspring distribution — .pois_length_ll"><meta name="description" content="Log-likelihood of the length of chains with Poisson offspring distribution"><meta property="og:description" content="Log-likelihood of the length of chains with Poisson offspring distribution"><meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg"><!-- Google tag (gtag.js) --><script async src="https://www.googletagmanager.com/gtag/js?id=G-XZ471458FQ"></script><script>
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-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">0.1.0</small>
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       <img src="../logo.svg" class="logo" alt=""><h1>Log-likelihood of the length of chains with Poisson offspring distribution</h1>
-      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/R/stat_likelihoods.R" class="external-link"><code>R/stat_likelihoods.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/R/stat_likelihoods.R" class="external-link"><code>R/stat_likelihoods.R</code></a></small>
       <div class="d-none name"><code>dot-pois_length_ll.Rd</code></div>
     </div>
+
     <div class="ref-description section level2">
     <p>Log-likelihood of the length of chains with Poisson offspring distribution</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">.pois_length_ll</span><span class="op">(</span><span class="va">x</span>, <span class="va">lambda</span><span class="op">)</span></span></code></pre></div>
     </div>
+
     <div class="section level2">
     <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
 <dl><dt id="arg-x">x<a class="anchor" aria-label="anchor" href="#arg-x"></a></dt>
 <dd><p>A numeric vector of chain lengths.</p></dd>
+
+
 <dt id="arg-lambda">lambda<a class="anchor" aria-label="anchor" href="#arg-lambda"></a></dt>
 <dd><p>The rate of the Poisson distribution. A single numeric value.
 Must be positive.</p></dd>
+
 </dl></div>
     <div class="section level2">
     <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
@@ -66,14 +89,24 @@ <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2
     <h2 id="author">Author<a class="anchor" aria-label="anchor" href="#author"></a></h2>
     <p>Sebastian Funk</p>
     </div>
+
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+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
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diff --git a/reference/dot-pois_size_ll.html b/reference/dot-pois_size_ll.html
index aeb54864..c166793c 100644
--- a/reference/dot-pois_size_ll.html
+++ b/reference/dot-pois_size_ll.html
@@ -1,18 +1,25 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Log-likelihood of the size of chains with Poisson offspring distribution — .pois_size_ll • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Log-likelihood of the size of chains with Poisson offspring distribution — .pois_size_ll"><meta name="description" content="Log-likelihood of the size of chains with Poisson offspring distribution"><meta property="og:description" content="Log-likelihood of the size of chains with Poisson offspring distribution"><meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg"><!-- Google tag (gtag.js) --><script async src="https://www.googletagmanager.com/gtag/js?id=G-XZ471458FQ"></script><script>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Log-likelihood of the size of chains with Poisson offspring distribution — .pois_size_ll • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../lightswitch.js"></script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Log-likelihood of the size of chains with Poisson offspring distribution — .pois_size_ll"><meta name="description" content="Log-likelihood of the size of chains with Poisson offspring distribution"><meta property="og:description" content="Log-likelihood of the size of chains with Poisson offspring distribution"><meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg"><!-- Google tag (gtag.js) --><script async src="https://www.googletagmanager.com/gtag/js?id=G-XZ471458FQ"></script><script>
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     <a class="navbar-brand me-2" href="../index.html">epichains</a>
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">0.1.0</small>
+
+    <small class="nav-text text-danger me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Unreleased version">0.1.0.9000</small>
+
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@@ -34,28 +41,44 @@
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
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 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.svg" class="logo" alt=""><h1>Log-likelihood of the size of chains with Poisson offspring distribution</h1>
-      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/R/stat_likelihoods.R" class="external-link"><code>R/stat_likelihoods.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/R/stat_likelihoods.R" class="external-link"><code>R/stat_likelihoods.R</code></a></small>
       <div class="d-none name"><code>dot-pois_size_ll.Rd</code></div>
     </div>
+
     <div class="ref-description section level2">
     <p>Log-likelihood of the size of chains with Poisson offspring distribution</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">.pois_size_ll</span><span class="op">(</span><span class="va">x</span>, <span class="va">lambda</span><span class="op">)</span></span></code></pre></div>
     </div>
+
     <div class="section level2">
     <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
 <dl><dt id="arg-x">x<a class="anchor" aria-label="anchor" href="#arg-x"></a></dt>
 <dd><p>A numeric vector of sizes</p></dd>
+
+
 <dt id="arg-lambda">lambda<a class="anchor" aria-label="anchor" href="#arg-lambda"></a></dt>
 <dd><p>The rate of the Poisson distribution; A single numeric value.</p></dd>
+
 </dl></div>
     <div class="section level2">
     <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
@@ -65,14 +88,24 @@ <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2
     <h2 id="author">Author<a class="anchor" aria-label="anchor" href="#author"></a></h2>
     <p>Sebastian Funk</p>
     </div>
+
   </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
     </nav></aside></div>
+
+
     <footer><div class="pkgdown-footer-left">
   <p>Developed by James M. Azam, Sebastian Funk, Flavio Finger.</p>
 </div>
+
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.9.9000.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
 </div>
+
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+
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+
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   </body></html>
 
diff --git a/reference/dot-rbinom_size.html b/reference/dot-rbinom_size.html
index 4b034561..7ac2bded 100644
--- a/reference/dot-rbinom_size.html
+++ b/reference/dot-rbinom_size.html
@@ -1,20 +1,27 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Samples size (the number of trials) of a binomial distribution — .rbinom_size • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Samples size (the number of trials) of a binomial distribution — .rbinom_size"><meta name="description" content="Samples the size parameter from the binomial distribution with fixed x
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Samples size (the number of trials) of a binomial distribution — .rbinom_size • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../lightswitch.js"></script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Samples size (the number of trials) of a binomial distribution — .rbinom_size"><meta name="description" content="Samples the size parameter from the binomial distribution with fixed x
 (number of successes) and p (success probability)"><meta property="og:description" content="Samples the size parameter from the binomial distribution with fixed x
 (number of successes) and p (success probability)"><meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg"><!-- Google tag (gtag.js) --><script async src="https://www.googletagmanager.com/gtag/js?id=G-XZ471458FQ"></script><script>
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     <a class="navbar-brand me-2" href="../index.html">epichains</a>
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">0.1.0</small>
+
+    <small class="nav-text text-danger me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Unreleased version">0.1.0.9000</small>
+
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@@ -36,31 +43,49 @@
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  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
 <li class="nav-item"><a class="external-link nav-link" href="https://github.com/epiverse-trace/epichains/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item dropdown">
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+  <ul class="dropdown-menu dropdown-menu-end" aria-labelledby="dropdown-lightswitch"><li><button class="dropdown-item" data-bs-theme-value="light"><span class="fa fa-sun"></span> Light</button></li>
+    <li><button class="dropdown-item" data-bs-theme-value="dark"><span class="fa fa-moon"></span> Dark</button></li>
+    <li><button class="dropdown-item" data-bs-theme-value="auto"><span class="fa fa-adjust"></span> Auto</button></li>
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 </nav><div class="container template-reference-topic">
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.svg" class="logo" alt=""><h1>Samples size (the number of trials) of a binomial distribution</h1>
-      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/R/utils.R" class="external-link"><code>R/utils.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/R/utils.R" class="external-link"><code>R/utils.R</code></a></small>
       <div class="d-none name"><code>dot-rbinom_size.Rd</code></div>
     </div>
+
     <div class="ref-description section level2">
     <p>Samples the size parameter from the binomial distribution with fixed x
 (number of successes) and p (success probability)</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">.rbinom_size</span><span class="op">(</span><span class="va">n</span>, <span class="va">x</span>, <span class="va">prob</span><span class="op">)</span></span></code></pre></div>
     </div>
+
     <div class="section level2">
     <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
 <dl><dt id="arg-n">n<a class="anchor" aria-label="anchor" href="#arg-n"></a></dt>
 <dd><p>The number of samples to generate. Must be a positive integer.</p></dd>
+
+
 <dt id="arg-x">x<a class="anchor" aria-label="anchor" href="#arg-x"></a></dt>
 <dd><p>The number of successes. Must be a positive integer.</p></dd>
+
+
 <dt id="arg-prob">prob<a class="anchor" aria-label="anchor" href="#arg-prob"></a></dt>
 <dd><p>The probability of success. A numeric between 0 and 1.</p></dd>
+
 </dl></div>
     <div class="section level2">
     <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
@@ -70,14 +95,24 @@ <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2
     <h2 id="author">Author<a class="anchor" aria-label="anchor" href="#author"></a></h2>
     <p>Sebastian Funk</p>
     </div>
+
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     </nav></aside></div>
+
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   <p>Developed by James M. Azam, Sebastian Funk, Flavio Finger.</p>
 </div>
+
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+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
 </div>
+
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   </body></html>
 
diff --git a/reference/dot-rgen_length.html b/reference/dot-rgen_length.html
index 351af537..314d817f 100644
--- a/reference/dot-rgen_length.html
+++ b/reference/dot-rgen_length.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Samples chain lengths with given observation probabilities — .rgen_length • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Samples chain lengths with given observation probabilities — .rgen_length"><meta name="description" content="Samples the length of a transmission chain where each individual element is
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Samples chain lengths with given observation probabilities — .rgen_length • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../lightswitch.js"></script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Samples chain lengths with given observation probabilities — .rgen_length"><meta name="description" content="Samples the length of a transmission chain where each individual element is
 observed with binomial probability with parameters n (number of successes)
 and p (success probability)"><meta property="og:description" content="Samples the length of a transmission chain where each individual element is
 observed with binomial probability with parameters n (number of successes)
@@ -7,16 +7,23 @@
   window.dataLayer = window.dataLayer || [];
   function gtag(){dataLayer.push(arguments);}
   gtag('js', new Date());
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 </script></head><body>
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-    <nav class="navbar navbar-expand-lg fixed-top bg-dark" data-bs-theme="dark" aria-label="Site navigation"><div class="container">
+
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+    <nav class="navbar navbar-expand-lg fixed-top " aria-label="Site navigation"><div class="container">
     <a href="https://epiverse-trace.github.io/" class="external-link"><img src="https://epiverse-trace.github.io/blueprints/logo_white.svg" id="logo" alt="Epiverse-TRACE"></a>
     <a class="navbar-brand me-2" href="../index.html">epichains</a>
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">0.1.0</small>
+
+    <small class="nav-text text-danger me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Unreleased version">0.1.0.9000</small>
+
+
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
       <span class="navbar-toggler-icon"></span>
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+
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       <ul class="navbar-nav me-auto"><li class="nav-item"><a class="nav-link" href="../articles/epichains.html">Get started</a></li>
 <li class="active nav-item"><a class="nav-link" href="../reference/index.html">Reference</a></li>
@@ -38,32 +45,50 @@
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
 <li class="nav-item"><a class="external-link nav-link" href="https://github.com/epiverse-trace/epichains/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item dropdown">
+  <button class="nav-link dropdown-toggle" type="button" id="dropdown-lightswitch" data-bs-toggle="dropdown" aria-expanded="false" aria-haspopup="true" aria-label="Light switch"><span class="fa fa-sun"></span></button>
+  <ul class="dropdown-menu dropdown-menu-end" aria-labelledby="dropdown-lightswitch"><li><button class="dropdown-item" data-bs-theme-value="light"><span class="fa fa-sun"></span> Light</button></li>
+    <li><button class="dropdown-item" data-bs-theme-value="dark"><span class="fa fa-moon"></span> Dark</button></li>
+    <li><button class="dropdown-item" data-bs-theme-value="auto"><span class="fa fa-adjust"></span> Auto</button></li>
+  </ul></li>
       </ul></div>
+
+
   </div>
 </nav><div class="container template-reference-topic">
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.svg" class="logo" alt=""><h1>Samples chain lengths with given observation probabilities</h1>
-      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/R/utils.R" class="external-link"><code>R/utils.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/R/utils.R" class="external-link"><code>R/utils.R</code></a></small>
       <div class="d-none name"><code>dot-rgen_length.Rd</code></div>
     </div>
+
     <div class="ref-description section level2">
     <p>Samples the length of a transmission chain where each individual element is
 observed with binomial probability with parameters n (number of successes)
 and p (success probability)</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">.rgen_length</span><span class="op">(</span><span class="va">n</span>, <span class="va">x</span>, <span class="va">prob</span><span class="op">)</span></span></code></pre></div>
     </div>
+
     <div class="section level2">
     <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
 <dl><dt id="arg-n">n<a class="anchor" aria-label="anchor" href="#arg-n"></a></dt>
 <dd><p>The number of samples to generate. Must be a positive integer.</p></dd>
+
+
 <dt id="arg-x">x<a class="anchor" aria-label="anchor" href="#arg-x"></a></dt>
 <dd><p>A numeric vector of the observed chain lengths.</p></dd>
+
+
 <dt id="arg-prob">prob<a class="anchor" aria-label="anchor" href="#arg-prob"></a></dt>
 <dd><p>The probability of observation. A numeric between 0 and 1.</p></dd>
+
 </dl></div>
     <div class="section level2">
     <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
@@ -73,14 +98,24 @@ <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2
     <h2 id="author">Author<a class="anchor" aria-label="anchor" href="#author"></a></h2>
     <p>Sebastian Funk</p>
     </div>
+
   </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
     </nav></aside></div>
+
+
     <footer><div class="pkgdown-footer-left">
   <p>Developed by James M. Azam, Sebastian Funk, Flavio Finger.</p>
 </div>
+
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.9.9000.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
 </div>
+
     </footer></div>
+
+
+
+
+
   </body></html>
 
diff --git a/reference/dot-sample_possible_offspring.html b/reference/dot-sample_possible_offspring.html
index e160827c..06f6d9a0 100644
--- a/reference/dot-sample_possible_offspring.html
+++ b/reference/dot-sample_possible_offspring.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Sample all possible offspring for the next generation — .sample_possible_offspring • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Sample all possible offspring for the next generation — .sample_possible_offspring"><meta name="description" content="Sample next generation of offspring using offspring distribution and
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Sample all possible offspring for the next generation — .sample_possible_offspring • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../lightswitch.js"></script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Sample all possible offspring for the next generation — .sample_possible_offspring"><meta name="description" content="Sample next generation of offspring using offspring distribution and
 associated parameters. This function is used internally, and input
 checking is not performed here, only in the context where it is used.
 Using it directly is not recommended."><meta property="og:description" content="Sample next generation of offspring using offspring distribution and
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-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">0.1.0</small>
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@@ -40,21 +47,31 @@
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       <img src="../logo.svg" class="logo" alt=""><h1>Sample all possible offspring for the next generation</h1>
-      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/R/helpers.R" class="external-link"><code>R/helpers.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/R/helpers.R" class="external-link"><code>R/helpers.R</code></a></small>
       <div class="d-none name"><code>dot-sample_possible_offspring.Rd</code></div>
     </div>
+
     <div class="ref-description section level2">
     <p>Sample next generation of offspring using offspring distribution and
 associated parameters. This function is used internally, and input
 checking is not performed here, only in the context where it is used.
 Using it directly is not recommended.</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">.sample_possible_offspring</span><span class="op">(</span></span>
@@ -64,29 +81,49 @@ <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage">
 <span>  <span class="va">chains</span></span>
 <span><span class="op">)</span></span></code></pre></div>
     </div>
+
     <div class="section level2">
     <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
 <dl><dt id="arg-offspring-func">offspring_func<a class="anchor" aria-label="anchor" href="#arg-offspring-func"></a></dt>
 <dd><p>A function to sample offspring.</p></dd>
+
+
 <dt id="arg-offspring-func-pars">offspring_func_pars<a class="anchor" aria-label="anchor" href="#arg-offspring-func-pars"></a></dt>
 <dd><p>A list of parameters for the offspring function.</p></dd>
+
+
 <dt id="arg-n-offspring">n_offspring<a class="anchor" aria-label="anchor" href="#arg-n-offspring"></a></dt>
 <dd><p>A numeric vector of the number of offspring per chain.</p></dd>
+
+
 <dt id="arg-chains">chains<a class="anchor" aria-label="anchor" href="#arg-chains"></a></dt>
 <dd><p>Numeric indices of chains/infectors being simulated</p></dd>
+
 </dl></div>
     <div class="section level2">
     <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
     <p>A numeric vector of the number of offspring per chain.</p>
     </div>
+
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diff --git a/reference/dot-update_chain_stat.html b/reference/dot-update_chain_stat.html
index 50dfeb5d..1d04eab6 100644
--- a/reference/dot-update_chain_stat.html
+++ b/reference/dot-update_chain_stat.html
@@ -1,18 +1,25 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Determine and update the chain statistic being tracked — .update_chain_stat • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Determine and update the chain statistic being tracked — .update_chain_stat"><meta name="description" content="Determine and update the chain statistic being tracked"><meta property="og:description" content="Determine and update the chain statistic being tracked"><meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg"><!-- Google tag (gtag.js) --><script async src="https://www.googletagmanager.com/gtag/js?id=G-XZ471458FQ"></script><script>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Determine and update the chain statistic being tracked — .update_chain_stat • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../lightswitch.js"></script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Determine and update the chain statistic being tracked — .update_chain_stat"><meta name="description" content="Determine and update the chain statistic being tracked"><meta property="og:description" content="Determine and update the chain statistic being tracked"><meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg"><!-- Google tag (gtag.js) --><script async src="https://www.googletagmanager.com/gtag/js?id=G-XZ471458FQ"></script><script>
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-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">0.1.0</small>
+
+    <small class="nav-text text-danger me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Unreleased version">0.1.0.9000</small>
+
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@@ -34,46 +41,74 @@
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   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.svg" class="logo" alt=""><h1>Determine and update the chain statistic being tracked</h1>
-      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/R/helpers.R" class="external-link"><code>R/helpers.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/R/helpers.R" class="external-link"><code>R/helpers.R</code></a></small>
       <div class="d-none name"><code>dot-update_chain_stat.Rd</code></div>
     </div>
+
     <div class="ref-description section level2">
     <p>Determine and update the chain statistic being tracked</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">.update_chain_stat</span><span class="op">(</span><span class="va">stat_type</span>, <span class="va">stat_latest</span>, <span class="va">n_offspring</span><span class="op">)</span></span></code></pre></div>
     </div>
+
     <div class="section level2">
     <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
 <dl><dt id="arg-stat-type">stat_type<a class="anchor" aria-label="anchor" href="#arg-stat-type"></a></dt>
 <dd><p>Chain statistic (size/length) to update; A character string.
 Must be one of 'size' or 'length'.</p></dd>
+
+
 <dt id="arg-stat-latest">stat_latest<a class="anchor" aria-label="anchor" href="#arg-stat-latest"></a></dt>
 <dd><p>The latest chain statistic numeric vector to be updated.</p></dd>
+
+
 <dt id="arg-n-offspring">n_offspring<a class="anchor" aria-label="anchor" href="#arg-n-offspring"></a></dt>
 <dd><p>A vector of offspring per chain. A numeric vector
 (coercible to integer).</p></dd>
+
 </dl></div>
     <div class="section level2">
     <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
     <p>A vector of chain statistics (size/length). A numeric vector
 coercible to integer.</p>
     </div>
+
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     </nav></aside></div>
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   <p>Developed by James M. Azam, Sebastian Funk, Flavio Finger.</p>
 </div>
+
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+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
 </div>
+
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+
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diff --git a/reference/dot-validate_epichains.html b/reference/dot-validate_epichains.html
index b21ebf76..cac688c4 100644
--- a/reference/dot-validate_epichains.html
+++ b/reference/dot-validate_epichains.html
@@ -1,18 +1,25 @@
 <!DOCTYPE html>
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+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Validate an &lt;epichains&gt; object — .validate_epichains • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../lightswitch.js"></script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Validate an &lt;epichains&gt; object — .validate_epichains"><meta name="description" content="Validate an &amp;lt;epichains&amp;gt; object"><meta property="og:description" content="Validate an &amp;lt;epichains&amp;gt; object"><meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg"><!-- Google tag (gtag.js) --><script async src="https://www.googletagmanager.com/gtag/js?id=G-XZ471458FQ"></script><script>
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-    <nav class="navbar navbar-expand-lg fixed-top bg-dark" data-bs-theme="dark" aria-label="Site navigation"><div class="container">
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+    <nav class="navbar navbar-expand-lg fixed-top " aria-label="Site navigation"><div class="container">
     <a href="https://epiverse-trace.github.io/" class="external-link"><img src="https://epiverse-trace.github.io/blueprints/logo_white.svg" id="logo" alt="Epiverse-TRACE"></a>
     <a class="navbar-brand me-2" href="../index.html">epichains</a>
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">0.1.0</small>
+
+    <small class="nav-text text-danger me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Unreleased version">0.1.0.9000</small>
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@@ -34,26 +41,40 @@
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
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+    <li><button class="dropdown-item" data-bs-theme-value="auto"><span class="fa fa-adjust"></span> Auto</button></li>
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   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.svg" class="logo" alt=""><h1>Validate an <code>&lt;epichains&gt;</code> object</h1>
-      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/R/epichains.R" class="external-link"><code>R/epichains.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/R/epichains.R" class="external-link"><code>R/epichains.R</code></a></small>
       <div class="d-none name"><code>dot-validate_epichains.Rd</code></div>
     </div>
+
     <div class="ref-description section level2">
     <p>Validate an <code>&lt;epichains&gt;</code> object</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">.validate_epichains</span><span class="op">(</span><span class="va">x</span><span class="op">)</span></span></code></pre></div>
     </div>
+
     <div class="section level2">
     <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
 <dl><dt id="arg-x">x<a class="anchor" aria-label="anchor" href="#arg-x"></a></dt>
 <dd><p>An <code>&lt;epichains&gt;</code> object.</p></dd>
+
 </dl></div>
     <div class="section level2">
     <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
@@ -63,14 +84,24 @@ <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2
     <h2 id="author">Author<a class="anchor" aria-label="anchor" href="#author"></a></h2>
     <p>James M. Azam</p>
     </div>
+
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   <p>Developed by James M. Azam, Sebastian Funk, Flavio Finger.</p>
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 </div>
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diff --git a/reference/dot-validate_epichains_summary.html b/reference/dot-validate_epichains_summary.html
index 900bbb23..eedcc773 100644
--- a/reference/dot-validate_epichains_summary.html
+++ b/reference/dot-validate_epichains_summary.html
@@ -1,18 +1,25 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Validate an &lt;epichains_summary&gt; object — .validate_epichains_summary • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Validate an &lt;epichains_summary&gt; object — .validate_epichains_summary"><meta name="description" content="Validate an &amp;lt;epichains_summary&amp;gt; object"><meta property="og:description" content="Validate an &amp;lt;epichains_summary&amp;gt; object"><meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg"><!-- Google tag (gtag.js) --><script async src="https://www.googletagmanager.com/gtag/js?id=G-XZ471458FQ"></script><script>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Validate an &lt;epichains_summary&gt; object — .validate_epichains_summary • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../lightswitch.js"></script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Validate an &lt;epichains_summary&gt; object — .validate_epichains_summary"><meta name="description" content="Validate an &amp;lt;epichains_summary&amp;gt; object"><meta property="og:description" content="Validate an &amp;lt;epichains_summary&amp;gt; object"><meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg"><!-- Google tag (gtag.js) --><script async src="https://www.googletagmanager.com/gtag/js?id=G-XZ471458FQ"></script><script>
   window.dataLayer = window.dataLayer || [];
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   gtag('config', 'G-XZ471458FQ');
 </script></head><body>
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-    <nav class="navbar navbar-expand-lg fixed-top bg-dark" data-bs-theme="dark" aria-label="Site navigation"><div class="container">
+
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+    <nav class="navbar navbar-expand-lg fixed-top " aria-label="Site navigation"><div class="container">
     <a href="https://epiverse-trace.github.io/" class="external-link"><img src="https://epiverse-trace.github.io/blueprints/logo_white.svg" id="logo" alt="Epiverse-TRACE"></a>
     <a class="navbar-brand me-2" href="../index.html">epichains</a>
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">0.1.0</small>
+
+    <small class="nav-text text-danger me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Unreleased version">0.1.0.9000</small>
+
+
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
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 <li class="active nav-item"><a class="nav-link" href="../reference/index.html">Reference</a></li>
@@ -34,26 +41,40 @@
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
 <li class="nav-item"><a class="external-link nav-link" href="https://github.com/epiverse-trace/epichains/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item dropdown">
+  <button class="nav-link dropdown-toggle" type="button" id="dropdown-lightswitch" data-bs-toggle="dropdown" aria-expanded="false" aria-haspopup="true" aria-label="Light switch"><span class="fa fa-sun"></span></button>
+  <ul class="dropdown-menu dropdown-menu-end" aria-labelledby="dropdown-lightswitch"><li><button class="dropdown-item" data-bs-theme-value="light"><span class="fa fa-sun"></span> Light</button></li>
+    <li><button class="dropdown-item" data-bs-theme-value="dark"><span class="fa fa-moon"></span> Dark</button></li>
+    <li><button class="dropdown-item" data-bs-theme-value="auto"><span class="fa fa-adjust"></span> Auto</button></li>
+  </ul></li>
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   </div>
 </nav><div class="container template-reference-topic">
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.svg" class="logo" alt=""><h1>Validate an <code>&lt;epichains_summary&gt;</code> object</h1>
-      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/R/epichains.R" class="external-link"><code>R/epichains.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/R/epichains.R" class="external-link"><code>R/epichains.R</code></a></small>
       <div class="d-none name"><code>dot-validate_epichains_summary.Rd</code></div>
     </div>
+
     <div class="ref-description section level2">
     <p>Validate an <code>&lt;epichains_summary&gt;</code> object</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">.validate_epichains_summary</span><span class="op">(</span><span class="va">x</span><span class="op">)</span></span></code></pre></div>
     </div>
+
     <div class="section level2">
     <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
 <dl><dt id="arg-x">x<a class="anchor" aria-label="anchor" href="#arg-x"></a></dt>
 <dd><p>An <code>&lt;epichains_summary&gt;</code> object.</p></dd>
+
 </dl></div>
     <div class="section level2">
     <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
@@ -63,14 +84,24 @@ <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2
     <h2 id="author">Author<a class="anchor" aria-label="anchor" href="#author"></a></h2>
     <p>James M. Azam</p>
     </div>
+
   </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
     </nav></aside></div>
+
+
     <footer><div class="pkgdown-footer-left">
   <p>Developed by James M. Azam, Sebastian Funk, Flavio Finger.</p>
 </div>
+
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.9.9000.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
 </div>
+
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+
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+
+
+
   </body></html>
 
diff --git a/reference/epichains-package.html b/reference/epichains-package.html
index 6a486661..7f986d10 100644
--- a/reference/epichains-package.html
+++ b/reference/epichains-package.html
@@ -1,20 +1,27 @@
 <!DOCTYPE html>
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+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>epichains: Simulating and Analysing Transmission Chain Statistics Using Branching Process Models — epichains-package • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../lightswitch.js"></script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="epichains: Simulating and Analysing Transmission Chain Statistics Using Branching Process Models — epichains-package"><meta name="description" content="Provides methods to simulate and analyse the size and length of branching processes with an arbitrary offspring distribution. These can be used, for example, to analyse the distribution of chain sizes or length of infectious disease outbreaks, as discussed in Farrington et al. (2003) doi:10.1093/biostatistics/4.2.279
 ."><meta property="og:description" content="Provides methods to simulate and analyse the size and length of branching processes with an arbitrary offspring distribution. These can be used, for example, to analyse the distribution of chain sizes or length of infectious disease outbreaks, as discussed in Farrington et al. (2003) doi:10.1093/biostatistics/4.2.279
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       <img src="../logo.svg" class="logo" alt=""><h1>epichains: Simulating and Analysing Transmission Chain Statistics Using Branching Process Models</h1>
-      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/R/epichains-package.R" class="external-link"><code>R/epichains-package.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/R/epichains-package.R" class="external-link"><code>R/epichains-package.R</code></a></small>
       <div class="d-none name"><code>epichains-package.Rd</code></div>
     </div>
+
     <div class="ref-description section level2">
     <p>Provides methods to simulate and analyse the size and length of branching processes with an arbitrary offspring distribution. These can be used, for example, to analyse the distribution of chain sizes or length of infectious disease outbreaks, as discussed in Farrington et al. (2003) <a href="https://doi.org/10.1093/biostatistics/4.2.279" class="external-link">doi:10.1093/biostatistics/4.2.279</a>
 .</p>
     </div>
+
+
     <div class="section level2">
     <h2 id="see-also">See also<a class="anchor" aria-label="anchor" href="#see-also"></a></h2>
     <div class="dont-index"><p>Useful links:</p><ul><li><p><a href="https://github.com/epiverse-trace/epichains" class="external-link">https://github.com/epiverse-trace/epichains</a></p></li>
@@ -67,14 +85,24 @@ <h2 id="author">Author<a class="anchor" aria-label="anchor" href="#author"></a><
 <li><p>Pratik Gupte <a href="mailto:pratik.gupte@lshtm.ac.uk">pratik.gupte@lshtm.ac.uk</a> (<a href="https://orcid.org/0000-0001-5294-7819" class="external-link">ORCID</a>) [reviewer]</p></li>
 <li><p>Joshua W. Lambert <a href="mailto:joshua.lambert@lshtm.ac.uk">joshua.lambert@lshtm.ac.uk</a> (<a href="https://orcid.org/0000-0001-5218-3046" class="external-link">ORCID</a>) [reviewer]</p></li>
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diff --git a/reference/head.epichains.html b/reference/head.epichains.html
index 55bd2017..20b250f4 100644
--- a/reference/head.epichains.html
+++ b/reference/head.epichains.html
@@ -1,18 +1,25 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>head and tail method for &lt;epichains&gt; class — head.epichains • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="head and tail method for &lt;epichains&gt; class — head.epichains"><meta name="description" content="head and tail method for &amp;lt;epichains&amp;gt; class"><meta property="og:description" content="head and tail method for &amp;lt;epichains&amp;gt; class"><meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg"><!-- Google tag (gtag.js) --><script async src="https://www.googletagmanager.com/gtag/js?id=G-XZ471458FQ"></script><script>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>head and tail method for &lt;epichains&gt; class — head.epichains • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../lightswitch.js"></script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="head and tail method for &lt;epichains&gt; class — head.epichains"><meta name="description" content="head and tail method for &amp;lt;epichains&amp;gt; class"><meta property="og:description" content="head and tail method for &amp;lt;epichains&amp;gt; class"><meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg"><!-- Google tag (gtag.js) --><script async src="https://www.googletagmanager.com/gtag/js?id=G-XZ471458FQ"></script><script>
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-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">0.1.0</small>
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+    <small class="nav-text text-danger me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Unreleased version">0.1.0.9000</small>
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@@ -34,18 +41,28 @@
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 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.svg" class="logo" alt=""><h1><code>head</code> and <code>tail</code> method for <code>&lt;epichains&gt;</code> class</h1>
-      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/R/epichains.R" class="external-link"><code>R/epichains.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/R/epichains.R" class="external-link"><code>R/epichains.R</code></a></small>
       <div class="d-none name"><code>head.epichains.Rd</code></div>
     </div>
+
     <div class="ref-description section level2">
     <p><code>head</code> and <code>tail</code> method for <code>&lt;epichains&gt;</code> class</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="co"># S3 method for class 'epichains'</span></span>
@@ -54,12 +71,18 @@ <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage">
 <span><span class="co"># S3 method for class 'epichains'</span></span>
 <span><span class="fu"><a href="https://rdrr.io/r/utils/head.html" class="external-link">tail</a></span><span class="op">(</span><span class="va">x</span>, <span class="va">...</span><span class="op">)</span></span></code></pre></div>
     </div>
+
     <div class="section level2">
     <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
 <dl><dt id="arg-x">x<a class="anchor" aria-label="anchor" href="#arg-x"></a></dt>
 <dd><p>An <code>&lt;epichains&gt;</code> object.</p></dd>
+
+
 <dt id="arg--">...<a class="anchor" aria-label="anchor" href="#arg--"></a></dt>
 <dd><p>Further arguments passed to or from other methods.</p></dd>
+
 </dl></div>
     <div class="section level2">
     <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
@@ -75,6 +98,7 @@ <h2 id="details">Details<a class="anchor" aria-label="anchor" href="#details"></
     <h2 id="author">Author<a class="anchor" aria-label="anchor" href="#author"></a></h2>
     <p>James M. Azam</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/Random.html" class="external-link">set.seed</a></span><span class="op">(</span><span class="fl">32</span><span class="op">)</span></span></span>
@@ -115,12 +139,21 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
     </div>
   </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
     </nav></aside></div>
+
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   <p>Developed by James M. Azam, Sebastian Funk, Flavio Finger.</p>
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+
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+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
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diff --git a/reference/index.html b/reference/index.html
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-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">0.1.0</small>
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@@ -34,97 +41,196 @@
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       <img src="../logo.svg" class="logo" alt=""><h1>Package index</h1>
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+
     <div class="section level2">
       <h2 id="simulate-branching-processes">Simulate branching processes<a class="anchor" aria-label="anchor" href="#simulate-branching-processes"></a></h2>
+
+
+
+
     </div><div class="section level2">
+
+
+
+
       <dl><dt>
+
           <code><a href="simulate_chain_stats.html">simulate_chain_stats()</a></code>
+
         </dt>
         <dd>Simulate a vector of transmission chains statistics (sizes/lengths)</dd>
       </dl><dl><dt>
+
           <code><a href="simulate_chains.html">simulate_chains()</a></code>
+
         </dt>
         <dd>Simulate transmission chains</dd>
       </dl></div><div class="section level2">
       <h2 id="calculate-log-likelihoods">Calculate (log)likelihoods<a class="anchor" aria-label="anchor" href="#calculate-log-likelihoods"></a></h2>
+
+
+
+
     </div><div class="section level2">
+
+
+
+
       <dl><dt>
+
           <code><a href="likelihood.html">likelihood()</a></code>
+
         </dt>
         <dd>Estimate the log-likelihood/likelihood for observed branching processes</dd>
       </dl></div><div class="section level2">
       <h2 id="methods-for-internal-classes">Methods for internal classes<a class="anchor" aria-label="anchor" href="#methods-for-internal-classes"></a></h2>
+
+
+
+
     </div><div class="section level2">
+
       <h3 id="epichains-class">epichains class<a class="anchor" aria-label="anchor" href="#epichains-class"></a></h3>
+
+
+
     </div><div class="section level2">
+
+
+
+
       <dl><dt>
+
           <code><a href="aggregate.epichains.html">aggregate(<i>&lt;epichains&gt;</i>)</a></code>
+
         </dt>
         <dd>Aggregate cases in <code>&lt;epichains&gt;</code> objects by "generation" or "time", if present</dd>
       </dl><dl><dt>
+
           <code><a href="summary.epichains.html">summary(<i>&lt;epichains&gt;</i>)</a></code>
+
         </dt>
         <dd>Summary method for <code>&lt;epichains&gt;</code> class</dd>
       </dl><dl><dt>
+
           <code><a href="print.epichains.html">print(<i>&lt;epichains&gt;</i>)</a></code>
+
         </dt>
         <dd>Print an <code>&lt;epichains&gt;</code> object</dd>
       </dl><dl><dt>
+
           <code><a href="head.epichains.html">head(<i>&lt;epichains&gt;</i>)</a></code> <code><a href="head.epichains.html">tail(<i>&lt;epichains&gt;</i>)</a></code>
+
         </dt>
         <dd><code>head</code> and <code>tail</code> method for <code>&lt;epichains&gt;</code> class</dd>
       </dl></div><div class="section level2">
+
       <h3 id="epichains-summary">epichains_summary<a class="anchor" aria-label="anchor" href="#epichains-summary"></a></h3>
+
+
+
     </div><div class="section level2">
+
+
+
+
       <dl><dt>
+
           <code><a href="summary.epichains_summary.html">summary(<i>&lt;epichains_summary&gt;</i>)</a></code>
+
         </dt>
         <dd>Summary method for <code>&lt;epichains_summary&gt;</code> class</dd>
       </dl><dl><dt>
+
           <code><a href="print.epichains_summary.html">print(<i>&lt;epichains_summary&gt;</i>)</a></code>
+
         </dt>
         <dd>Print an <code>&lt;epichains_summary&gt;</code> object</dd>
       </dl></div><div class="section level2">
       <h2 id="special-distributions">Special distributions<a class="anchor" aria-label="anchor" href="#special-distributions"></a></h2>
+
+
+
+
     </div><div class="section level2">
+
+
+
+
       <dl><dt>
+
           <code><a href="dborel.html">dborel()</a></code>
+
         </dt>
         <dd>Density of the Borel distribution</dd>
       </dl><dl><dt>
+
           <code><a href="rborel.html">rborel()</a></code>
+
         </dt>
         <dd>Generate random numbers from the Borel distribution</dd>
       </dl><dl><dt>
+
           <code><a href="rgborel.html">rgborel()</a></code>
+
         </dt>
         <dd>Generate random numbers from a Gamma-Borel mixture distribution</dd>
       </dl></div><div class="section level2">
       <h2 id="miscellaneous">Miscellaneous<a class="anchor" aria-label="anchor" href="#miscellaneous"></a></h2>
+
+
+
+
     </div><div class="section level2">
+
       <h3 id="data">Data<a class="anchor" aria-label="anchor" href="#data"></a></h3>
       <div class="section-desc"><p>Data stored in the package</p></div>
+
+
     </div><div class="section level2">
+
+
+
+
       <dl><dt>
+
           <code><a href="covid19_sa.html">covid19_sa</a></code>
+
         </dt>
         <dd>COVID-19 Data Repository for South Africa</dd>
       </dl></div>
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diff --git a/reference/likelihood.html b/reference/likelihood.html
index 8dfbc1d6..3f5c220a 100644
--- a/reference/likelihood.html
+++ b/reference/likelihood.html
@@ -1,18 +1,25 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Estimate the log-likelihood/likelihood for observed branching processes — likelihood • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Estimate the log-likelihood/likelihood for observed branching processes — likelihood"><meta name="description" content="Estimate the log-likelihood/likelihood for observed branching processes"><meta property="og:description" content="Estimate the log-likelihood/likelihood for observed branching processes"><meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg"><!-- Google tag (gtag.js) --><script async src="https://www.googletagmanager.com/gtag/js?id=G-XZ471458FQ"></script><script>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Estimate the log-likelihood/likelihood for observed branching processes — likelihood • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../lightswitch.js"></script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Estimate the log-likelihood/likelihood for observed branching processes — likelihood"><meta name="description" content="Estimate the log-likelihood/likelihood for observed branching processes"><meta property="og:description" content="Estimate the log-likelihood/likelihood for observed branching processes"><meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg"><!-- Google tag (gtag.js) --><script async src="https://www.googletagmanager.com/gtag/js?id=G-XZ471458FQ"></script><script>
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-    <nav class="navbar navbar-expand-lg fixed-top bg-dark" data-bs-theme="dark" aria-label="Site navigation"><div class="container">
+
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     <a href="https://epiverse-trace.github.io/" class="external-link"><img src="https://epiverse-trace.github.io/blueprints/logo_white.svg" id="logo" alt="Epiverse-TRACE"></a>
     <a class="navbar-brand me-2" href="../index.html">epichains</a>
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">0.1.0</small>
+
+    <small class="nav-text text-danger me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Unreleased version">0.1.0.9000</small>
+
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@@ -34,18 +41,28 @@
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
 <li class="nav-item"><a class="external-link nav-link" href="https://github.com/epiverse-trace/epichains/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item dropdown">
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 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.svg" class="logo" alt=""><h1>Estimate the log-likelihood/likelihood for observed branching processes</h1>
-      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/R/likelihood.R" class="external-link"><code>R/likelihood.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/R/likelihood.R" class="external-link"><code>R/likelihood.R</code></a></small>
       <div class="d-none name"><code>likelihood.Rd</code></div>
     </div>
+
     <div class="ref-description section level2">
     <p>Estimate the log-likelihood/likelihood for observed branching processes</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">likelihood</span><span class="op">(</span></span>
@@ -61,13 +78,18 @@ <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage">
 <span>  <span class="va">...</span></span>
 <span><span class="op">)</span></span></code></pre></div>
     </div>
+
     <div class="section level2">
     <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
 <dl><dt id="arg-chains">chains<a class="anchor" aria-label="anchor" href="#arg-chains"></a></dt>
 <dd><p>Vector of chain summaries (sizes/lengths). Can be a
 <code>&lt;numeric&gt;</code> vector or an object of class <code>&lt;epichains&gt;</code> or
 <code>&lt;epichains_summary&gt;</code> (obtained from <code><a href="simulate_chains.html">simulate_chains()</a></code> or
 <code><a href="simulate_chain_stats.html">simulate_chain_stats()</a></code>). See examples below.</p></dd>
+
+
 <dt id="arg-statistic">statistic<a class="anchor" aria-label="anchor" href="#arg-statistic"></a></dt>
 <dd><p>The chain statistic to track as the
 stopping criteria for each chain being simulated when <code>stat_threshold</code> is not
@@ -76,6 +98,8 @@ <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#argumen
 <li><p>"length": the total number of generations reached by a chain before
 it goes extinct.</p></li>
 </ul></dd>
+
+
 <dt id="arg-offspring-dist">offspring_dist<a class="anchor" aria-label="anchor" href="#arg-offspring-dist"></a></dt>
 <dd><p>Offspring distribution: a <code>&lt;function&gt;</code> like the ones
 provided by R to generate random numbers from given distributions (e.g.,
@@ -85,16 +109,22 @@ <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#argumen
 on to the random number generating functions. Examples that can be provided
 here are <code>rpois</code> for Poisson distributed offspring, <code>rnbinom</code> for negative
 binomial offspring, or custom functions.</p></dd>
+
+
 <dt id="arg-nsim-obs">nsim_obs<a class="anchor" aria-label="anchor" href="#arg-nsim-obs"></a></dt>
 <dd><p>Number of simulations to be used to approximate the
 log-likelihood/likelihood if <code>obs_prob &lt; 1</code> (imperfect observation). If
 <code>obs_prob == 1</code>, this argument is ignored.</p></dd>
+
+
 <dt id="arg-obs-prob">obs_prob<a class="anchor" aria-label="anchor" href="#arg-obs-prob"></a></dt>
 <dd><p>Observation probability. A number (probability) between 0
 and 1. A value greater than 0 but less 1 implies imperfect observation and
 simulations will be used to approximate the (log)likelihood. This will
 also require specifying <code>nsim_obs</code>. In the simulation, the observation
 process is assumed to be constant.</p></dd>
+
+
 <dt id="arg-stat-threshold">stat_threshold<a class="anchor" aria-label="anchor" href="#arg-stat-threshold"></a></dt>
 <dd><p>A stopping criterion for individual chain simulations;
 a positive number coercible to integer. When any chain's cumulative statistic
@@ -104,18 +134,27 @@ <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#argumen
 <code>&lt;epichains_summary&gt;</code>, the <code>stat_threshold</code> used in the simulation is
 extracted and used here so if this argument is specified, it is ignored and
 a warning is thrown.</p></dd>
+
+
 <dt id="arg-log">log<a class="anchor" aria-label="anchor" href="#arg-log"></a></dt>
 <dd><p>Should the log-likelihoods be transformed to
 likelihoods? Logical. Defaults to <code>TRUE</code>.</p></dd>
+
+
 <dt id="arg-exclude">exclude<a class="anchor" aria-label="anchor" href="#arg-exclude"></a></dt>
 <dd><p>A vector of indices of the sizes/lengths to exclude from the
 log-likelihood calculation.</p></dd>
+
+
 <dt id="arg-individual">individual<a class="anchor" aria-label="anchor" href="#arg-individual"></a></dt>
 <dd><p>Logical; If TRUE, a vector of individual
 log-likelihood/likelihood contributions will be returned rather than the
 sum/product.</p></dd>
+
+
 <dt id="arg--">...<a class="anchor" aria-label="anchor" href="#arg--"></a></dt>
 <dd><p>any parameters to pass to <code><a href="simulate_chain_stats.html">simulate_chain_stats</a></code></p></dd>
+
 </dl></div>
     <div class="section level2">
     <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
@@ -136,6 +175,7 @@ <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2
     <h2 id="author">Author<a class="anchor" aria-label="anchor" href="#author"></a></h2>
     <p>Sebastian Funk, James M. Azam</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="co"># example of observed chain sizes</span></span></span>
@@ -201,12 +241,21 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
     </div>
   </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
     </nav></aside></div>
+
+
     <footer><div class="pkgdown-footer-left">
   <p>Developed by James M. Azam, Sebastian Funk, Flavio Finger.</p>
 </div>
+
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.9.9000.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
 </div>
+
     </footer></div>
+
+
+
+
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   </body></html>
 
diff --git a/reference/print.epichains.html b/reference/print.epichains.html
index 0834de6e..10310eb1 100644
--- a/reference/print.epichains.html
+++ b/reference/print.epichains.html
@@ -1,18 +1,25 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Print an &lt;epichains&gt; object — print.epichains • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Print an &lt;epichains&gt; object — print.epichains"><meta name="description" content="Print an &amp;lt;epichains&amp;gt; object"><meta property="og:description" content="Print an &amp;lt;epichains&amp;gt; object"><meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg"><!-- Google tag (gtag.js) --><script async src="https://www.googletagmanager.com/gtag/js?id=G-XZ471458FQ"></script><script>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Print an &lt;epichains&gt; object — print.epichains • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../lightswitch.js"></script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Print an &lt;epichains&gt; object — print.epichains"><meta name="description" content="Print an &amp;lt;epichains&amp;gt; object"><meta property="og:description" content="Print an &amp;lt;epichains&amp;gt; object"><meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg"><!-- Google tag (gtag.js) --><script async src="https://www.googletagmanager.com/gtag/js?id=G-XZ471458FQ"></script><script>
   window.dataLayer = window.dataLayer || [];
   function gtag(){dataLayer.push(arguments);}
   gtag('js', new Date());
+
   gtag('config', 'G-XZ471458FQ');
 </script></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
-    <nav class="navbar navbar-expand-lg fixed-top bg-dark" data-bs-theme="dark" aria-label="Site navigation"><div class="container">
+
+
+    <nav class="navbar navbar-expand-lg fixed-top " aria-label="Site navigation"><div class="container">
     <a href="https://epiverse-trace.github.io/" class="external-link"><img src="https://epiverse-trace.github.io/blueprints/logo_white.svg" id="logo" alt="Epiverse-TRACE"></a>
     <a class="navbar-brand me-2" href="../index.html">epichains</a>
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">0.1.0</small>
+
+    <small class="nav-text text-danger me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Unreleased version">0.1.0.9000</small>
+
+
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
       <span class="navbar-toggler-icon"></span>
     </button>
+
     <div id="navbar" class="collapse navbar-collapse ms-3">
       <ul class="navbar-nav me-auto"><li class="nav-item"><a class="nav-link" href="../articles/epichains.html">Get started</a></li>
 <li class="active nav-item"><a class="nav-link" href="../reference/index.html">Reference</a></li>
@@ -34,29 +41,45 @@
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
 <li class="nav-item"><a class="external-link nav-link" href="https://github.com/epiverse-trace/epichains/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item dropdown">
+  <button class="nav-link dropdown-toggle" type="button" id="dropdown-lightswitch" data-bs-toggle="dropdown" aria-expanded="false" aria-haspopup="true" aria-label="Light switch"><span class="fa fa-sun"></span></button>
+  <ul class="dropdown-menu dropdown-menu-end" aria-labelledby="dropdown-lightswitch"><li><button class="dropdown-item" data-bs-theme-value="light"><span class="fa fa-sun"></span> Light</button></li>
+    <li><button class="dropdown-item" data-bs-theme-value="dark"><span class="fa fa-moon"></span> Dark</button></li>
+    <li><button class="dropdown-item" data-bs-theme-value="auto"><span class="fa fa-adjust"></span> Auto</button></li>
+  </ul></li>
       </ul></div>
+
+
   </div>
 </nav><div class="container template-reference-topic">
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.svg" class="logo" alt=""><h1>Print an <code>&lt;epichains&gt;</code> object</h1>
-      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/R/epichains.R" class="external-link"><code>R/epichains.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/R/epichains.R" class="external-link"><code>R/epichains.R</code></a></small>
       <div class="d-none name"><code>print.epichains.Rd</code></div>
     </div>
+
     <div class="ref-description section level2">
     <p>Print an <code>&lt;epichains&gt;</code> object</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="co"># S3 method for class 'epichains'</span></span>
 <span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">x</span>, <span class="va">...</span><span class="op">)</span></span></code></pre></div>
     </div>
+
     <div class="section level2">
     <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
 <dl><dt id="arg-x">x<a class="anchor" aria-label="anchor" href="#arg-x"></a></dt>
 <dd><p>An <code>&lt;epichains&gt;</code> object.</p></dd>
+
+
 <dt id="arg--">...<a class="anchor" aria-label="anchor" href="#arg--"></a></dt>
 <dd><p>Other parameters passed to <code><a href="https://rdrr.io/r/base/print.html" class="external-link">print()</a></code>.</p></dd>
+
 </dl></div>
     <div class="section level2">
     <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
@@ -67,6 +90,7 @@ <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2
     <h2 id="author">Author<a class="anchor" aria-label="anchor" href="#author"></a></h2>
     <p>James M. Azam</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="co"># Using a Poisson offspring distribution and simulating from an infinite</span></span></span>
@@ -102,12 +126,21 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
     </div>
   </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
     </nav></aside></div>
+
+
     <footer><div class="pkgdown-footer-left">
   <p>Developed by James M. Azam, Sebastian Funk, Flavio Finger.</p>
 </div>
+
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.9.9000.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
 </div>
+
     </footer></div>
+
+
+
+
+
   </body></html>
 
diff --git a/reference/print.epichains_summary.html b/reference/print.epichains_summary.html
index 9410c91c..435f208d 100644
--- a/reference/print.epichains_summary.html
+++ b/reference/print.epichains_summary.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Print an &lt;epichains_summary&gt; object — print.epichains_summary • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Print an &lt;epichains_summary&gt; object — print.epichains_summary"><meta name="description" content="Prints a summary of the &amp;lt;epichains_summary&amp;gt; object. In particular, it
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Print an &lt;epichains_summary&gt; object — print.epichains_summary • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../lightswitch.js"></script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Print an &lt;epichains_summary&gt; object — print.epichains_summary"><meta name="description" content="Prints a summary of the &amp;lt;epichains_summary&amp;gt; object. In particular, it
 prints the number of chains simulated, and the range of
 the statistic, represented as the maximum (max_stat) and minimum
 (min_stat). If the minimum or maximum is infinite, it is represented as
@@ -13,16 +13,23 @@
   window.dataLayer = window.dataLayer || [];
   function gtag(){dataLayer.push(arguments);}
   gtag('js', new Date());
+
   gtag('config', 'G-XZ471458FQ');
 </script></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
-    <nav class="navbar navbar-expand-lg fixed-top bg-dark" data-bs-theme="dark" aria-label="Site navigation"><div class="container">
+
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+    <nav class="navbar navbar-expand-lg fixed-top " aria-label="Site navigation"><div class="container">
     <a href="https://epiverse-trace.github.io/" class="external-link"><img src="https://epiverse-trace.github.io/blueprints/logo_white.svg" id="logo" alt="Epiverse-TRACE"></a>
     <a class="navbar-brand me-2" href="../index.html">epichains</a>
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">0.1.0</small>
+
+    <small class="nav-text text-danger me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Unreleased version">0.1.0.9000</small>
+
+
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
       <span class="navbar-toggler-icon"></span>
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+
     <div id="navbar" class="collapse navbar-collapse ms-3">
       <ul class="navbar-nav me-auto"><li class="nav-item"><a class="nav-link" href="../articles/epichains.html">Get started</a></li>
 <li class="active nav-item"><a class="nav-link" href="../reference/index.html">Reference</a></li>
@@ -44,15 +51,24 @@
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
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+<li class="nav-item dropdown">
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+    <li><button class="dropdown-item" data-bs-theme-value="dark"><span class="fa fa-moon"></span> Dark</button></li>
+    <li><button class="dropdown-item" data-bs-theme-value="auto"><span class="fa fa-adjust"></span> Auto</button></li>
+  </ul></li>
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   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.svg" class="logo" alt=""><h1>Print an <code>&lt;epichains_summary&gt;</code> object</h1>
-      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/R/epichains.R" class="external-link"><code>R/epichains.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/R/epichains.R" class="external-link"><code>R/epichains.R</code></a></small>
       <div class="d-none name"><code>print.epichains_summary.Rd</code></div>
     </div>
+
     <div class="ref-description section level2">
     <p>Prints a summary of the <code>&lt;epichains_summary&gt;</code> object. In particular, it
 prints the number of chains simulated, and the range of
@@ -61,17 +77,24 @@
 <code>&gt;= stat_threshold</code> where <code>stat_threshold</code> is the value of the censoring
 limit. See <code>?epichains_summary()</code> for the definition of <code>stat_threshold</code>.</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="co"># S3 method for class 'epichains_summary'</span></span>
 <span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">x</span>, <span class="va">...</span><span class="op">)</span></span></code></pre></div>
     </div>
+
     <div class="section level2">
     <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
 <dl><dt id="arg-x">x<a class="anchor" aria-label="anchor" href="#arg-x"></a></dt>
 <dd><p>An <code>&lt;epichains_summary&gt;</code> object.</p></dd>
+
+
 <dt id="arg--">...<a class="anchor" aria-label="anchor" href="#arg--"></a></dt>
 <dd><p>Not used.</p></dd>
+
 </dl></div>
     <div class="section level2">
     <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
@@ -82,6 +105,7 @@ <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2
     <h2 id="author">Author<a class="anchor" aria-label="anchor" href="#author"></a></h2>
     <p>James M. Azam</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="co"># Using a Poisson offspring distribution and simulating from an infinite</span></span></span>
@@ -107,12 +131,21 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
     </div>
   </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
     </nav></aside></div>
+
+
     <footer><div class="pkgdown-footer-left">
   <p>Developed by James M. Azam, Sebastian Funk, Flavio Finger.</p>
 </div>
+
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.9.9000.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
 </div>
+
     </footer></div>
+
+
+
+
+
   </body></html>
 
diff --git a/reference/rborel.html b/reference/rborel.html
index ba66f26c..4dd76dc1 100644
--- a/reference/rborel.html
+++ b/reference/rborel.html
@@ -1,18 +1,25 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Generate random numbers from the Borel distribution — rborel • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Generate random numbers from the Borel distribution — rborel"><meta name="description" content="Random numbers are generated by simulating from a Poisson branching process"><meta property="og:description" content="Random numbers are generated by simulating from a Poisson branching process"><meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg"><!-- Google tag (gtag.js) --><script async src="https://www.googletagmanager.com/gtag/js?id=G-XZ471458FQ"></script><script>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Generate random numbers from the Borel distribution — rborel • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../lightswitch.js"></script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Generate random numbers from the Borel distribution — rborel"><meta name="description" content="Random numbers are generated by simulating from a Poisson branching process"><meta property="og:description" content="Random numbers are generated by simulating from a Poisson branching process"><meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg"><!-- Google tag (gtag.js) --><script async src="https://www.googletagmanager.com/gtag/js?id=G-XZ471458FQ"></script><script>
   window.dataLayer = window.dataLayer || [];
   function gtag(){dataLayer.push(arguments);}
   gtag('js', new Date());
+
   gtag('config', 'G-XZ471458FQ');
 </script></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
-    <nav class="navbar navbar-expand-lg fixed-top bg-dark" data-bs-theme="dark" aria-label="Site navigation"><div class="container">
+
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+    <nav class="navbar navbar-expand-lg fixed-top " aria-label="Site navigation"><div class="container">
     <a href="https://epiverse-trace.github.io/" class="external-link"><img src="https://epiverse-trace.github.io/blueprints/logo_white.svg" id="logo" alt="Epiverse-TRACE"></a>
     <a class="navbar-brand me-2" href="../index.html">epichains</a>
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">0.1.0</small>
+
+    <small class="nav-text text-danger me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Unreleased version">0.1.0.9000</small>
+
+
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
       <span class="navbar-toggler-icon"></span>
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+
     <div id="navbar" class="collapse navbar-collapse ms-3">
       <ul class="navbar-nav me-auto"><li class="nav-item"><a class="nav-link" href="../articles/epichains.html">Get started</a></li>
 <li class="active nav-item"><a class="nav-link" href="../reference/index.html">Reference</a></li>
@@ -34,28 +41,45 @@
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
 <li class="nav-item"><a class="external-link nav-link" href="https://github.com/epiverse-trace/epichains/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item dropdown">
+  <button class="nav-link dropdown-toggle" type="button" id="dropdown-lightswitch" data-bs-toggle="dropdown" aria-expanded="false" aria-haspopup="true" aria-label="Light switch"><span class="fa fa-sun"></span></button>
+  <ul class="dropdown-menu dropdown-menu-end" aria-labelledby="dropdown-lightswitch"><li><button class="dropdown-item" data-bs-theme-value="light"><span class="fa fa-sun"></span> Light</button></li>
+    <li><button class="dropdown-item" data-bs-theme-value="dark"><span class="fa fa-moon"></span> Dark</button></li>
+    <li><button class="dropdown-item" data-bs-theme-value="auto"><span class="fa fa-adjust"></span> Auto</button></li>
+  </ul></li>
       </ul></div>
+
+
   </div>
 </nav><div class="container template-reference-topic">
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.svg" class="logo" alt=""><h1>Generate random numbers from the Borel distribution</h1>
-      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/R/borel.R" class="external-link"><code>R/borel.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/R/borel.R" class="external-link"><code>R/borel.R</code></a></small>
       <div class="d-none name"><code>rborel.Rd</code></div>
     </div>
+
     <div class="ref-description section level2">
     <p>Random numbers are generated by simulating from a Poisson branching process</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">rborel</span><span class="op">(</span><span class="va">n</span>, <span class="va">mu</span>, censor_at <span class="op">=</span> <span class="cn">Inf</span><span class="op">)</span></span></code></pre></div>
     </div>
+
     <div class="section level2">
     <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
 <dl><dt id="arg-n">n<a class="anchor" aria-label="anchor" href="#arg-n"></a></dt>
 <dd><p>Number of random variates to generate.</p></dd>
+
+
 <dt id="arg-mu">mu<a class="anchor" aria-label="anchor" href="#arg-mu"></a></dt>
 <dd><p>A non-negative number for the poisson mean.</p></dd>
+
+
 <dt id="arg-censor-at">censor_at<a class="anchor" aria-label="anchor" href="#arg-censor-at"></a></dt>
 <dd><p>A stopping criterion; <code>&lt;numeric&gt;</code>. Defaults to <code>Inf</code>. A
 value above which the simulation ends and the random number is set to
@@ -63,6 +87,7 @@ <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#argumen
 <code><a href="simulate_chain_stats.html">simulate_chain_stats()</a></code> with a Poisson offspring distribution, so if
 <code>mu &gt;= 1</code>, the simulation could proceed unendingly. This parameter is used
 to prevent this.</p></dd>
+
 </dl></div>
     <div class="section level2">
     <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
@@ -72,6 +97,7 @@ <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2
     <h2 id="author">Author<a class="anchor" aria-label="anchor" href="#author"></a></h2>
     <p>Sebastian Funk</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/Random.html" class="external-link">set.seed</a></span><span class="op">(</span><span class="fl">32</span><span class="op">)</span></span></span>
@@ -81,12 +107,21 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
     </div>
   </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
     </nav></aside></div>
+
+
     <footer><div class="pkgdown-footer-left">
   <p>Developed by James M. Azam, Sebastian Funk, Flavio Finger.</p>
 </div>
+
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.9.9000.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
 </div>
+
     </footer></div>
+
+
+
+
+
   </body></html>
 
diff --git a/reference/rgborel.html b/reference/rgborel.html
index dcd61032..50db7754 100644
--- a/reference/rgborel.html
+++ b/reference/rgborel.html
@@ -1,18 +1,25 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Generate random numbers from a Gamma-Borel mixture distribution — rgborel • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Generate random numbers from a Gamma-Borel mixture distribution — rgborel"><meta name="description" content="Generate random numbers from a Gamma-Borel mixture distribution"><meta property="og:description" content="Generate random numbers from a Gamma-Borel mixture distribution"><meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg"><!-- Google tag (gtag.js) --><script async src="https://www.googletagmanager.com/gtag/js?id=G-XZ471458FQ"></script><script>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Generate random numbers from a Gamma-Borel mixture distribution — rgborel • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../lightswitch.js"></script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Generate random numbers from a Gamma-Borel mixture distribution — rgborel"><meta name="description" content="Generate random numbers from a Gamma-Borel mixture distribution"><meta property="og:description" content="Generate random numbers from a Gamma-Borel mixture distribution"><meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg"><!-- Google tag (gtag.js) --><script async src="https://www.googletagmanager.com/gtag/js?id=G-XZ471458FQ"></script><script>
   window.dataLayer = window.dataLayer || [];
   function gtag(){dataLayer.push(arguments);}
   gtag('js', new Date());
+
   gtag('config', 'G-XZ471458FQ');
 </script></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
-    <nav class="navbar navbar-expand-lg fixed-top bg-dark" data-bs-theme="dark" aria-label="Site navigation"><div class="container">
+
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+    <nav class="navbar navbar-expand-lg fixed-top " aria-label="Site navigation"><div class="container">
     <a href="https://epiverse-trace.github.io/" class="external-link"><img src="https://epiverse-trace.github.io/blueprints/logo_white.svg" id="logo" alt="Epiverse-TRACE"></a>
     <a class="navbar-brand me-2" href="../index.html">epichains</a>
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">0.1.0</small>
+
+    <small class="nav-text text-danger me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Unreleased version">0.1.0.9000</small>
+
+
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@@ -34,35 +41,56 @@
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
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+    <li><button class="dropdown-item" data-bs-theme-value="auto"><span class="fa fa-adjust"></span> Auto</button></li>
+  </ul></li>
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   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.svg" class="logo" alt=""><h1>Generate random numbers from a Gamma-Borel mixture distribution</h1>
-      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/R/borel.R" class="external-link"><code>R/borel.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/R/borel.R" class="external-link"><code>R/borel.R</code></a></small>
       <div class="d-none name"><code>rgborel.Rd</code></div>
     </div>
+
     <div class="ref-description section level2">
     <p>Generate random numbers from a Gamma-Borel mixture distribution</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">rgborel</span><span class="op">(</span><span class="va">n</span>, <span class="va">size</span>, <span class="va">prob</span>, <span class="va">mu</span>, censor_at <span class="op">=</span> <span class="cn">Inf</span><span class="op">)</span></span></code></pre></div>
     </div>
+
     <div class="section level2">
     <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
 <dl><dt id="arg-n">n<a class="anchor" aria-label="anchor" href="#arg-n"></a></dt>
 <dd><p>Number of random variates to generate.</p></dd>
+
+
 <dt id="arg-size">size<a class="anchor" aria-label="anchor" href="#arg-size"></a></dt>
 <dd><p>The dispersion parameter (often called <code>k</code> in ecological
 applications); A positive number.</p></dd>
+
+
 <dt id="arg-prob">prob<a class="anchor" aria-label="anchor" href="#arg-prob"></a></dt>
 <dd><p>Probability of success (in the parameterisation with
 <code>prob</code>, see also <code><a href="https://rdrr.io/r/stats/NegBinomial.html" class="external-link">NegBinomial</a></code>); A number between
 0 and 1.</p></dd>
+
+
 <dt id="arg-mu">mu<a class="anchor" aria-label="anchor" href="#arg-mu"></a></dt>
 <dd><p>Mean; A positive number.</p></dd>
+
+
 <dt id="arg-censor-at">censor_at<a class="anchor" aria-label="anchor" href="#arg-censor-at"></a></dt>
 <dd><p>A stopping criterion; <code>&lt;numeric&gt;</code>. Defaults to <code>Inf</code>. A
 value above which the simulation ends and the random number is set to
@@ -70,6 +98,7 @@ <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#argumen
 <code><a href="simulate_chain_stats.html">simulate_chain_stats()</a></code> with a Poisson offspring distribution, so if
 <code>mu &gt;= 1</code>, the simulation could proceed unendingly. This parameter is used
 to prevent this.</p></dd>
+
 </dl></div>
     <div class="section level2">
     <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
@@ -79,6 +108,7 @@ <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2
     <h2 id="author">Author<a class="anchor" aria-label="anchor" href="#author"></a></h2>
     <p>Sebastian Funk</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/Random.html" class="external-link">set.seed</a></span><span class="op">(</span><span class="fl">32</span><span class="op">)</span></span></span>
@@ -88,12 +118,21 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
     </div>
   </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
     </nav></aside></div>
+
+
     <footer><div class="pkgdown-footer-left">
   <p>Developed by James M. Azam, Sebastian Funk, Flavio Finger.</p>
 </div>
+
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.9.9000.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
 </div>
+
     </footer></div>
+
+
+
+
+
   </body></html>
 
diff --git a/reference/simulate_chain_stats.html b/reference/simulate_chain_stats.html
index 14aeb82d..ce93c231 100644
--- a/reference/simulate_chain_stats.html
+++ b/reference/simulate_chain_stats.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Simulate a vector of transmission chains statistics (sizes/lengths) — simulate_chain_stats • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Simulate a vector of transmission chains statistics (sizes/lengths) — simulate_chain_stats"><meta name="description" content="It generates a vector of transmission chain sizes or lengths using the
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Simulate a vector of transmission chains statistics (sizes/lengths) — simulate_chain_stats • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../lightswitch.js"></script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Simulate a vector of transmission chains statistics (sizes/lengths) — simulate_chain_stats"><meta name="description" content="It generates a vector of transmission chain sizes or lengths using the
 same model as simulate_chains() but without tracking details of the
 individual chains. This function is useful when only the chain sizes or
 lengths are of interest.
@@ -21,16 +21,23 @@
   window.dataLayer = window.dataLayer || [];
   function gtag(){dataLayer.push(arguments);}
   gtag('js', new Date());
+
   gtag('config', 'G-XZ471458FQ');
 </script></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
-    <nav class="navbar navbar-expand-lg fixed-top bg-dark" data-bs-theme="dark" aria-label="Site navigation"><div class="container">
+
+
+    <nav class="navbar navbar-expand-lg fixed-top " aria-label="Site navigation"><div class="container">
     <a href="https://epiverse-trace.github.io/" class="external-link"><img src="https://epiverse-trace.github.io/blueprints/logo_white.svg" id="logo" alt="Epiverse-TRACE"></a>
     <a class="navbar-brand me-2" href="../index.html">epichains</a>
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">0.1.0</small>
+
+    <small class="nav-text text-danger me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Unreleased version">0.1.0.9000</small>
+
+
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
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 <li class="active nav-item"><a class="nav-link" href="../reference/index.html">Reference</a></li>
@@ -52,15 +59,24 @@
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
 <li class="nav-item"><a class="external-link nav-link" href="https://github.com/epiverse-trace/epichains/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
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+
+
   </div>
 </nav><div class="container template-reference-topic">
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.svg" class="logo" alt=""><h1>Simulate a vector of transmission chains statistics (sizes/lengths)</h1>
-      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/R/simulate.R" class="external-link"><code>R/simulate.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/R/simulate.R" class="external-link"><code>R/simulate.R</code></a></small>
       <div class="d-none name"><code>simulate_chain_stats.Rd</code></div>
     </div>
+
     <div class="ref-description section level2">
     <p>It generates a vector of transmission chain sizes or lengths using the
 same model as <code><a href="simulate_chains.html">simulate_chains()</a></code> but without tracking details of the
@@ -73,6 +89,7 @@
 accepts population related inputs such as the population size (defaults
 to Inf) and percentage of the population initially immune (defaults to 0).</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">simulate_chain_stats</span><span class="op">(</span></span>
@@ -82,13 +99,18 @@ <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage">
 <span>  <span class="va">...</span>,</span>
 <span>  stat_threshold <span class="op">=</span> <span class="cn">Inf</span>,</span>
 <span>  pop <span class="op">=</span> <span class="cn">Inf</span>,</span>
-<span>percent_immune <span class="op">=</span> <span class="fl">0</span></span>
+<span>  percent_immune <span class="op">=</span> <span class="fl">0</span></span>
 <span><span class="op">)</span></span></code></pre></div>
     </div>
+
     <div class="section level2">
     <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
 <dl><dt id="arg-n-chains">n_chains<a class="anchor" aria-label="anchor" href="#arg-n-chains"></a></dt>
 <dd><p>Number of chains to simulate.</p></dd>
+
+
 <dt id="arg-statistic">statistic<a class="anchor" aria-label="anchor" href="#arg-statistic"></a></dt>
 <dd><p>The chain statistic to track as the
 stopping criteria for each chain being simulated when <code>stat_threshold</code> is not
@@ -97,6 +119,8 @@ <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#argumen
 <li><p>"length": the total number of generations reached by a chain before
 it goes extinct.</p></li>
 </ul></dd>
+
+
 <dt id="arg-offspring-dist">offspring_dist<a class="anchor" aria-label="anchor" href="#arg-offspring-dist"></a></dt>
 <dd><p>Offspring distribution: a <code>&lt;function&gt;</code> like the ones
 provided by R to generate random numbers from given distributions (e.g.,
@@ -106,22 +130,31 @@ <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#argumen
 on to the random number generating functions. Examples that can be provided
 here are <code>rpois</code> for Poisson distributed offspring, <code>rnbinom</code> for negative
 binomial offspring, or custom functions.</p></dd>
+
+
 <dt id="arg--">...<a class="anchor" aria-label="anchor" href="#arg--"></a></dt>
 <dd><p>Parameters of the offspring distribution as required by R.</p></dd>
+
+
 <dt id="arg-stat-threshold">stat_threshold<a class="anchor" aria-label="anchor" href="#arg-stat-threshold"></a></dt>
 <dd><p>A stopping criterion for individual chain simulations;
 a positive number coercible to integer. When any chain's cumulative statistic
 reaches or surpasses <code>stat_threshold</code>, that chain ends. It also serves as a
 censoring limit so that results above the specified value, are set to <code>Inf</code>.
 Defaults to <code>Inf</code>.</p></dd>
+
+
 <dt id="arg-pop">pop<a class="anchor" aria-label="anchor" href="#arg-pop"></a></dt>
 <dd><p>Population size; An <code>&lt;Integer&gt;</code>. Used alongside <code>percent_immune</code>
 to define the susceptible population. Defaults to <code>Inf</code>.</p></dd>
+
+
 <dt id="arg-percent-immune">percent_immune<a class="anchor" aria-label="anchor" href="#arg-percent-immune"></a></dt>
 <dd><p>Percent of the population immune to
 infection at the start of the simulation; A <code>&lt;numeric&gt;</code> between 0 and 1.
 Used alongside <code>pop</code> to initialise the susceptible population. Defaults to
 0.</p></dd>
+
 </dl></div>
     <div class="section level2">
     <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
@@ -186,6 +219,7 @@ <h2 id="references">References<a class="anchor" aria-label="anchor" href="#refer
     <h2 id="author">Author<a class="anchor" aria-label="anchor" href="#author"></a></h2>
     <p>James M. Azam, Sebastian Funk</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="co"># Simulate chain sizes with a poisson offspring distribution, assuming an</span></span></span>
@@ -232,12 +266,21 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
     </div>
   </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
     </nav></aside></div>
+
+
     <footer><div class="pkgdown-footer-left">
   <p>Developed by James M. Azam, Sebastian Funk, Flavio Finger.</p>
 </div>
+
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.9.9000.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
 </div>
+
     </footer></div>
+
+
+
+
+
   </body></html>
 
diff --git a/reference/simulate_chains.html b/reference/simulate_chains.html
index f018f737..3b0c087f 100644
--- a/reference/simulate_chains.html
+++ b/reference/simulate_chains.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Simulate transmission chains — simulate_chains • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Simulate transmission chains — simulate_chains"><meta name="description" content='It generates independent transmission chains starting with a single case
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Simulate transmission chains — simulate_chains • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../lightswitch.js"></script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Simulate transmission chains — simulate_chains"><meta name="description" content='It generates independent transmission chains starting with a single case
 per chain, using a simple branching process model (See details for
 definition of "chains" and assumptions). Offspring for each
 chain are generated with an offspring distribution, and an optional
@@ -21,16 +21,23 @@
   window.dataLayer = window.dataLayer || [];
   function gtag(){dataLayer.push(arguments);}
   gtag('js', new Date());
+
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-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">0.1.0</small>
+
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       <span class="navbar-toggler-icon"></span>
     </button>
+
     <div id="navbar" class="collapse navbar-collapse ms-3">
       <ul class="navbar-nav me-auto"><li class="nav-item"><a class="nav-link" href="../articles/epichains.html">Get started</a></li>
 <li class="active nav-item"><a class="nav-link" href="../reference/index.html">Reference</a></li>
@@ -52,15 +59,24 @@
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
 <li class="nav-item"><a class="external-link nav-link" href="https://github.com/epiverse-trace/epichains/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item dropdown">
+  <button class="nav-link dropdown-toggle" type="button" id="dropdown-lightswitch" data-bs-toggle="dropdown" aria-expanded="false" aria-haspopup="true" aria-label="Light switch"><span class="fa fa-sun"></span></button>
+  <ul class="dropdown-menu dropdown-menu-end" aria-labelledby="dropdown-lightswitch"><li><button class="dropdown-item" data-bs-theme-value="light"><span class="fa fa-sun"></span> Light</button></li>
+    <li><button class="dropdown-item" data-bs-theme-value="dark"><span class="fa fa-moon"></span> Dark</button></li>
+    <li><button class="dropdown-item" data-bs-theme-value="auto"><span class="fa fa-adjust"></span> Auto</button></li>
+  </ul></li>
       </ul></div>
+
+
   </div>
 </nav><div class="container template-reference-topic">
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.svg" class="logo" alt=""><h1>Simulate transmission chains</h1>
-      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/R/simulate.R" class="external-link"><code>R/simulate.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/R/simulate.R" class="external-link"><code>R/simulate.R</code></a></small>
       <div class="d-none name"><code>simulate_chains.Rd</code></div>
     </div>
+
     <div class="ref-description section level2">
     <p>It generates independent transmission chains starting with a single case
 per chain, using a simple branching process model (See details for
@@ -73,6 +89,7 @@
 such as the population size (defaults to Inf) and percentage of the
 population initially immune (defaults to 0).</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">simulate_chains</span><span class="op">(</span></span>
@@ -85,13 +102,18 @@ <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage">
 <span>  percent_immune <span class="op">=</span> <span class="fl">0</span>,</span>
 <span>  generation_time <span class="op">=</span> <span class="cn">NULL</span>,</span>
 <span>  t0 <span class="op">=</span> <span class="fl">0</span>,</span>
-<span>tf <span class="op">=</span> <span class="cn">Inf</span></span>
+<span>  tf <span class="op">=</span> <span class="cn">Inf</span></span>
 <span><span class="op">)</span></span></code></pre></div>
     </div>
+
     <div class="section level2">
     <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
 <dl><dt id="arg-n-chains">n_chains<a class="anchor" aria-label="anchor" href="#arg-n-chains"></a></dt>
 <dd><p>Number of chains to simulate.</p></dd>
+
+
 <dt id="arg-statistic">statistic<a class="anchor" aria-label="anchor" href="#arg-statistic"></a></dt>
 <dd><p>The chain statistic to track as the
 stopping criteria for each chain being simulated when <code>stat_threshold</code> is not
@@ -100,6 +122,8 @@ <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#argumen
 <li><p>"length": the total number of generations reached by a chain before
 it goes extinct.</p></li>
 </ul></dd>
+
+
 <dt id="arg-offspring-dist">offspring_dist<a class="anchor" aria-label="anchor" href="#arg-offspring-dist"></a></dt>
 <dd><p>Offspring distribution: a <code>&lt;function&gt;</code> like the ones
 provided by R to generate random numbers from given distributions (e.g.,
@@ -109,8 +133,12 @@ <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#argumen
 on to the random number generating functions. Examples that can be provided
 here are <code>rpois</code> for Poisson distributed offspring, <code>rnbinom</code> for negative
 binomial offspring, or custom functions.</p></dd>
+
+
 <dt id="arg--">...<a class="anchor" aria-label="anchor" href="#arg--"></a></dt>
 <dd><p>Parameters of the offspring distribution as required by R.</p></dd>
+
+
 <dt id="arg-stat-threshold">stat_threshold<a class="anchor" aria-label="anchor" href="#arg-stat-threshold"></a></dt>
 <dd><p>A stopping criterion for individual chain simulations;
 a positive number coercible to integer. When any chain's cumulative statistic
@@ -119,26 +147,37 @@ <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#argumen
 chain that produces 10 or more cases will stop. Note that setting
 <code>stat_threshold</code> does not guarantee that all chains will stop at the same
 value.</p></dd>
+
+
 <dt id="arg-pop">pop<a class="anchor" aria-label="anchor" href="#arg-pop"></a></dt>
 <dd><p>Population size; An <code>&lt;Integer&gt;</code>. Used alongside <code>percent_immune</code>
 to define the susceptible population. Defaults to <code>Inf</code>.</p></dd>
+
+
 <dt id="arg-percent-immune">percent_immune<a class="anchor" aria-label="anchor" href="#arg-percent-immune"></a></dt>
 <dd><p>Percent of the population immune to
 infection at the start of the simulation; A <code>&lt;numeric&gt;</code> between 0 and 1.
 Used alongside <code>pop</code> to initialise the susceptible population. Defaults to
 0.</p></dd>
+
+
 <dt id="arg-generation-time">generation_time<a class="anchor" aria-label="anchor" href="#arg-generation-time"></a></dt>
 <dd><p>The generation time function; the name
 of a user-defined named or anonymous function with only one argument <code>n</code>,
 representing the number of generation times to sample.</p></dd>
+
+
 <dt id="arg-t-">t0<a class="anchor" aria-label="anchor" href="#arg-t-"></a></dt>
 <dd><p>Start time (if generation time is given); either a single value
 or a vector of same length as <code>n_chains</code> (number of initial cases) with
 corresponding initial times. Defaults to 0, meaning all cases started at
 time 0.</p></dd>
+
+
 <dt id="arg-tf">tf<a class="anchor" aria-label="anchor" href="#arg-tf"></a></dt>
 <dd><p>A number for the cut-off for the infection times (if generation
 time is given); Defaults to <code>Inf</code>.</p></dd>
+
 </dl></div>
     <div class="section level2">
     <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
@@ -211,6 +250,7 @@ <h2 id="references">References<a class="anchor" aria-label="anchor" href="#refer
     <h2 id="author">Author<a class="anchor" aria-label="anchor" href="#author"></a></h2>
     <p>James M. Azam, Sebastian Funk</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="co"># Using a Poisson offspring distribution and simulating from an infinite</span></span></span>
@@ -279,12 +319,21 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
     </div>
   </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
     </nav></aside></div>
+
+
     <footer><div class="pkgdown-footer-left">
   <p>Developed by James M. Azam, Sebastian Funk, Flavio Finger.</p>
 </div>
+
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.9.9000.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
 </div>
+
     </footer></div>
+
+
+
+
+
   </body></html>
 
diff --git a/reference/summary.epichains.html b/reference/summary.epichains.html
index f0c9af19..59169886 100644
--- a/reference/summary.epichains.html
+++ b/reference/summary.epichains.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Summary method for &lt;epichains&gt; class — summary.epichains • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Summary method for &lt;epichains&gt; class — summary.epichains"><meta name="description" content="This calculates the chain statistic (size/length) for the simulated
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Summary method for &lt;epichains&gt; class — summary.epichains • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../lightswitch.js"></script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Summary method for &lt;epichains&gt; class — summary.epichains"><meta name="description" content="This calculates the chain statistic (size/length) for the simulated
 chains and returns an object with the same information as that returned
 by an equivalent simulate_chain_stats() call."><meta property="og:description" content="This calculates the chain statistic (size/length) for the simulated
 chains and returns an object with the same information as that returned
@@ -7,16 +7,23 @@
   window.dataLayer = window.dataLayer || [];
   function gtag(){dataLayer.push(arguments);}
   gtag('js', new Date());
+
   gtag('config', 'G-XZ471458FQ');
 </script></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
-    <nav class="navbar navbar-expand-lg fixed-top bg-dark" data-bs-theme="dark" aria-label="Site navigation"><div class="container">
+
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+    <nav class="navbar navbar-expand-lg fixed-top " aria-label="Site navigation"><div class="container">
     <a href="https://epiverse-trace.github.io/" class="external-link"><img src="https://epiverse-trace.github.io/blueprints/logo_white.svg" id="logo" alt="Epiverse-TRACE"></a>
     <a class="navbar-brand me-2" href="../index.html">epichains</a>
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">0.1.0</small>
+
+    <small class="nav-text text-danger me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Unreleased version">0.1.0.9000</small>
+
+
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
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+
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       <ul class="navbar-nav me-auto"><li class="nav-item"><a class="nav-link" href="../articles/epichains.html">Get started</a></li>
 <li class="active nav-item"><a class="nav-link" href="../reference/index.html">Reference</a></li>
@@ -38,31 +45,47 @@
       </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
  <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
 <li class="nav-item"><a class="external-link nav-link" href="https://github.com/epiverse-trace/epichains/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li>
+<li class="nav-item dropdown">
+  <button class="nav-link dropdown-toggle" type="button" id="dropdown-lightswitch" data-bs-toggle="dropdown" aria-expanded="false" aria-haspopup="true" aria-label="Light switch"><span class="fa fa-sun"></span></button>
+  <ul class="dropdown-menu dropdown-menu-end" aria-labelledby="dropdown-lightswitch"><li><button class="dropdown-item" data-bs-theme-value="light"><span class="fa fa-sun"></span> Light</button></li>
+    <li><button class="dropdown-item" data-bs-theme-value="dark"><span class="fa fa-moon"></span> Dark</button></li>
+    <li><button class="dropdown-item" data-bs-theme-value="auto"><span class="fa fa-adjust"></span> Auto</button></li>
+  </ul></li>
       </ul></div>
+
+
   </div>
 </nav><div class="container template-reference-topic">
 <div class="row">
   <main id="main" class="col-md-9"><div class="page-header">
       <img src="../logo.svg" class="logo" alt=""><h1>Summary method for <code>&lt;epichains&gt;</code> class</h1>
-      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/R/epichains.R" class="external-link"><code>R/epichains.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/R/epichains.R" class="external-link"><code>R/epichains.R</code></a></small>
       <div class="d-none name"><code>summary.epichains.Rd</code></div>
     </div>
+
     <div class="ref-description section level2">
     <p>This calculates the chain statistic (size/length) for the simulated
 chains and returns an object with the same information as that returned
 by an equivalent <code><a href="simulate_chain_stats.html">simulate_chain_stats()</a></code> call.</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="co"># S3 method for class 'epichains'</span></span>
 <span><span class="fu"><a href="https://rdrr.io/r/base/summary.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">object</span>, <span class="va">...</span><span class="op">)</span></span></code></pre></div>
     </div>
+
     <div class="section level2">
     <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
 <dl><dt id="arg-object">object<a class="anchor" aria-label="anchor" href="#arg-object"></a></dt>
 <dd><p>An <code>&lt;epichains&gt;</code> object.</p></dd>
+
+
 <dt id="arg--">...<a class="anchor" aria-label="anchor" href="#arg--"></a></dt>
 <dd><p>Not used.</p></dd>
+
 </dl></div>
     <div class="section level2">
     <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
@@ -76,6 +99,7 @@ <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2
     <h2 id="author">Author<a class="anchor" aria-label="anchor" href="#author"></a></h2>
     <p>James M. Azam</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="co"># Using a negative binomial offspring distribution and simulating from a</span></span></span>
@@ -132,12 +156,21 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
     </div>
   </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
     </nav></aside></div>
+
+
     <footer><div class="pkgdown-footer-left">
   <p>Developed by James M. Azam, Sebastian Funk, Flavio Finger.</p>
 </div>
+
 <div class="pkgdown-footer-right">
-  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.9.9000.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.0.</p>
 </div>
+
     </footer></div>
+
+
+
+
+
   </body></html>
 
diff --git a/reference/summary.epichains_summary.html b/reference/summary.epichains_summary.html
index dc0905ab..79e26ea4 100644
--- a/reference/summary.epichains_summary.html
+++ b/reference/summary.epichains_summary.html
@@ -1,18 +1,25 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Summary method for &lt;epichains_summary&gt; class — summary.epichains_summary • epichains</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Summary method for &lt;epichains_summary&gt; class — summary.epichains_summary"><meta name="description" content="Summary method for &amp;lt;epichains_summary&amp;gt; class"><meta property="og:description" content="Summary method for &amp;lt;epichains_summary&amp;gt; class"><meta property="og:image" content="https://epiverse-trace.github.io/epichains/logo.svg"><!-- Google tag (gtag.js) --><script async src="https://www.googletagmanager.com/gtag/js?id=G-XZ471458FQ"></script><script>
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       <img src="../logo.svg" class="logo" alt=""><h1>Summary method for <code>&lt;epichains_summary&gt;</code> class</h1>
-      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/v0.1.0/R/epichains.R" class="external-link"><code>R/epichains.R</code></a></small>
+      <small class="dont-index">Source: <a href="https://github.com/epiverse-trace/epichains/blob/main/R/epichains.R" class="external-link"><code>R/epichains.R</code></a></small>
       <div class="d-none name"><code>summary.epichains_summary.Rd</code></div>
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+
     <div class="ref-description section level2">
     <p>Summary method for <code>&lt;epichains_summary&gt;</code> class</p>
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     <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="co"># S3 method for class 'epichains_summary'</span></span>
 <span><span class="fu"><a href="https://rdrr.io/r/base/summary.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">object</span>, <span class="va">...</span><span class="op">)</span></span></code></pre></div>
     </div>
+
     <div class="section level2">
     <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
 <dl><dt id="arg-object">object<a class="anchor" aria-label="anchor" href="#arg-object"></a></dt>
 <dd><p>An <code>&lt;epichains_summary&gt;</code> object.</p></dd>
+
+
 <dt id="arg--">...<a class="anchor" aria-label="anchor" href="#arg--"></a></dt>
 <dd><p>Not used.</p></dd>
+
 </dl></div>
     <div class="section level2">
     <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
@@ -71,6 +94,7 @@ <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2
     <h2 id="author">Author<a class="anchor" aria-label="anchor" href="#author"></a></h2>
     <p>James M. Azam</p>
     </div>
+
     <div class="section level2">
     <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="co"># Using a Poisson offspring distribution and simulating from an infinite</span></span></span>
@@ -97,12 +121,21 @@ <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-e
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diff --git a/search.json b/search.json
index a47bb989..734f788d 100644
--- a/search.json
+++ b/search.json
@@ -1 +1 @@
-[{"path":"https://epiverse-trace.github.io/epichains/LICENSE.html","id":null,"dir":"","previous_headings":"","what":"MIT License","title":"MIT License","text":"Copyright (c) 2024 epichains authors Permission hereby granted, free charge, person obtaining copy software associated documentation files (“Software”), deal Software without restriction, including without limitation rights use, copy, modify, merge, publish, distribute, sublicense, /sell copies Software, permit persons Software furnished , subject following conditions: copyright notice permission notice shall included copies substantial portions Software. SOFTWARE PROVIDED “”, WITHOUT WARRANTY KIND, EXPRESS IMPLIED, INCLUDING LIMITED WARRANTIES MERCHANTABILITY, FITNESS PARTICULAR PURPOSE NONINFRINGEMENT. EVENT SHALL AUTHORS COPYRIGHT HOLDERS LIABLE CLAIM, DAMAGES LIABILITY, WHETHER ACTION CONTRACT, TORT OTHERWISE, ARISING , CONNECTION SOFTWARE USE DEALINGS SOFTWARE.","code":""},{"path":[]},{"path":"https://epiverse-trace.github.io/epichains/articles/design-principles.html","id":"scope","dir":"Articles","previous_headings":"","what":"Scope","title":"Design Principles for {epichains}","text":"{epichains} aims facilitate: Simulation transmission chains using branching processes methods, Handling transmission chains using objected-orientated design, Analytical/closed-form likelihoods take form <distribution>_<chain_statistic_type>_ll>, example, gborel_size_ll() pois_length_ll(). Numerical likelihood simulation using offspring_ll(). Additionally, package provides mixture probability distributions generating offspring distributions, example, rborel().","code":""},{"path":[]},{"path":"https://epiverse-trace.github.io/epichains/articles/design-principles.html","id":"simulation-functions","dir":"Articles","previous_headings":"Design decisions","what":"Simulation functions","title":"Design Principles for {epichains}","text":"Simulation branching processes achieved simulate_chains() simulate_chain_stats(). details underlying methods, see theory vignette. simulations stochastic, meaning one set inputs can produce varied results. models can also use explore scenario analyses varying inputs. Often, cases need one run model /one set parameter values, inputs outputs stored separate data structures. However, approach can limiting performing scenario analyses, user manually manipulate two objects reshaping joining operations. potential lead errors loss information. Hence, simulate_chains() simulate_chain_stats() return objects dedicated classes <epichains> <epichains_summary> respectively store input parameters output simulation single object. <epichains> class extends <data.frame>, using columns store information simulated transmission chains parameter values attributes. <data.frame> chosen tabular structure allows us store information rows columns, widely used data structure R. Similarly, <epichains_summary> class superclass (extension) R’s <numeric> class stores parameter values attributes. <epichains> object contains information whole outbreak, key summaries easily deduced quick glance object. Hence, class dedicated format()/print() method print simulated transmission chains manner similar <dataframe>, accompanied extra summary information including number chains simulated, number generations reached, number infectors created. summaries useful quickly assessing output simulation. Importantly, <epichains> class summary() method returns <epichains_summary> object. design decision taken allow easy coercion <epichains> object obtained simulate_chains() summaries <epichains> object otherwise attainable separate run simulate_chain_stats() parameter values passed simulate_chains(). Lastly, <epichains> objects aggregate() method aggregates simulated outbreak cases “generation” “time”. syntactic sugar dplyr::group_by() dplyr::summarise() style aggregation added benefit taking dplyr dependency achieve goal. summary, <epichains> object following structure: chain (<integer>) infector (<integer>) infectee (<integer>) generation (<integer>), optionally, time (<numeric>), generation_time specified n_chains, statistic, stat_threshold, offspring_dist, track_pop (pop finite, .e., specified).","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/design-principles.html","id":"likelihood-estimation","dir":"Articles","previous_headings":"Design decisions","what":"likelihood estimation","title":"Design Principles for {epichains}","text":"Likelihoods estimated using likelihood() function. function designed flexible two inputs: data can supplied vector chain summaries, <epichains> object, <epichains_summary> object, offspring distribution can supplied function, allowing user use custom offspring distributions. likelihood() uses either analytical numerical methods estimate likelihood observing input chain summaries. analytical methods closed-form likelihoods take form .<offspring_dist>_<statistic>_ll(), example, .gborel_size_ll() .pois_length_ll() shipped package. user supplies offspring distribution statistic solution exists, internally, used. , simulations used estimate likelihood. numerical likelihood simulation achieved using .offspring_ll(), internal wrapper around simulate_chain_stats(). output type likelihood() depends combination arguments individual, obs_prob, nsim_obs summarised table :","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/design-principles.html","id":"naming-and-documentation-style","dir":"Articles","previous_headings":"","what":"Naming and documentation style","title":"Design Principles for {epichains}","text":"package uses following naming conventions: Functions arguments named using snake_case, example, simulate_chains(). Internal functions prefixed period, example, .offspring_ll(). visual cue technical implications. documentation: Classes objects enclosed angle brackets, example, <epichains>. Packages enclosed curly braces, example, epichains. function arguments defined sentence case punctuated (especially full stops). Function titles imperative form. Functions referred function_name()","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/design-principles.html","id":"dependencies","dir":"Articles","previous_headings":"","what":"Dependencies","title":"Design Principles for {epichains}","text":"checkmate: exports many test_*(), check_*() assert_*() functions available CRAN.","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/design-principles.html","id":"development-journey","dir":"Articles","previous_headings":"","what":"Development journey","title":"Design Principles for {epichains}","text":"{epichains} successor bpmodels package, retired {epichains} released. {epichains} born need refactor {bpmodels}, led name change subsequent changes design required significant disruptive changes {bpmodels}. {epichains} major refactoring {bpmodels} provide simulation function accounts susceptible depletion population immunity without restrictions offspring distributions, better function long form documentation, object-oriented approach simulating handling transmission chains R. Future plans include simulation contacts infectees, incorporation network effects, object-oriented approach estimating chain size length likelihoods, interoperability {epiparameter} package ease setting various epidemiological delays.","code":""},{"path":[]},{"path":"https://epiverse-trace.github.io/epichains/articles/epichains.html","id":"use-case","dir":"Articles","previous_headings":"Transmission chains likelihoods","what":"Use case","title":"Getting started with epichains","text":"Suppose observed number transmission chains, arising separate index case. likely transmission properties (reproduction number /superspreading coefficient) generated chains (assuming parameters across chains)? first step answering question calculate likelihood observing observed chain summaries given transmission properties. likelihood() function comes . returned estimate can used infer transmission properties using estimation frameworks maximum likelihood Bayesian inference. epichains provide estimation frameworks.","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/epichains.html","id":"what-we-have","dir":"Articles","previous_headings":"Transmission chains likelihoods","what":"What we have","title":"Getting started with epichains","text":"Data observed transmission chains summaries (sizes lengths).","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/epichains.html","id":"what-we-assume","dir":"Articles","previous_headings":"Transmission chains likelihoods","what":"What we assume","title":"Getting started with epichains","text":"offspring distribution governs number secondary cases produced case. Parameters offspring distribution (example, mean overdispersion using negative binomial; can interpreted reproduction number superspreading coefficient, respectively) (optional) observation process/probability generates observed chain summaries. (optional) threshold chain summaries considered large consistent reproduction number R<1R<1 (e.g., NN cases TT generations total).","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/epichains.html","id":"likelihood","dir":"Articles","previous_headings":"Transmission chains likelihoods","what":"likelihood()","title":"Getting started with epichains","text":"function calculates likelihood/loglikelihood observing vector outbreak summaries obtained transmission chains. “Outbreak summaries” refer transmission chain sizes lengths/durations. likelihood() requires vector chain summaries (sizes lengths), chains, corresponding statistic use, statistic, offspring distribution, offspring_dist associated parameters. offspring_dist specified R function used generate random numbers, .e. rpois Poisson, rnbinom negative binomial, custom function. default, result log-likelihood log = FALSE, likelihoods returned (See ?likelihood details). understand likelihood() works see section likelihood() works. Let’s look following example estimate log-likelihood observing chain_sizes.","code":"set.seed(121) # example of observed chain sizes # randomly generate 20 chains of size between 1 to 10 chain_sizes <- sample(1:10, 20, replace = TRUE) chain_sizes #>  [1]  4  7  4  9  1  3  7  5  1  8 10  2  1  2  4  5 10  6  8  7 # estimate loglikelihood of the observed chain sizes for given lambda likelihood_eg <- likelihood(   chains = chain_sizes,   statistic = \"size\",   offspring_dist = rpois,   nsim_obs = 100,   lambda = 0.5 ) # Print the estimate likelihood_eg #> [1] -67.82879"},{"path":"https://epiverse-trace.github.io/epichains/articles/epichains.html","id":"joint-and-individual-log-likelihoods","dir":"Articles","previous_headings":"Transmission chains likelihoods","what":"Joint and individual log-likelihoods","title":"Getting started with epichains","text":"likelihood(), default, returns joint log-likelihood, given sum log-likelihoods observed chain. instead individual log-likelihoods desired (example calculating Watanabe–Akaike information criterion values, individual argument must set TRUE. return likelihoods instead, set log = FALSE.","code":"set.seed(121) # example of observed chain sizes # randomly generate 20 chains of size between 1 to 10 chain_sizes <- sample(1:10, 20, replace = TRUE) chain_sizes #>  [1]  4  7  4  9  1  3  7  5  1  8 10  2  1  2  4  5 10  6  8  7 # estimate loglikelihood of the observed chain sizes likelihood_ind_eg <- likelihood(   chains = chain_sizes,   statistic = \"size\",   offspring_dist = rpois,   nsim_obs = 100,   lambda = 0.5,   individual = TRUE ) # Print the estimate likelihood_ind_eg #> [[1]] #>  [1] -3.098612 -4.508584 -3.098612 -5.269208 -0.500000 -2.480829 -4.508584 #>  [8] -3.622329 -0.500000 -4.900542 -5.619471 -1.693147 -0.500000 -1.693147 #> [15] -3.098612 -3.622329 -5.619471 -4.086190 -4.900542 -4.508584"},{"path":"https://epiverse-trace.github.io/epichains/articles/epichains.html","id":"observation-probability","dir":"Articles","previous_headings":"Transmission chains likelihoods","what":"Observation probability","title":"Getting started with epichains","text":"likelihood() uses argument obs_prob model observation probability. default, assumes perfect observation, obs_prob = 1 (See ?likelihood), meaning transmission events observed recorded data. observations imperfect, obs_prob must less 1. case imperfect observation, “true” chain sizes lengths simulated nsim_obs times, likelihood calculated simulations. example, probability observing case obs_prob = 0.30, use returns 10 likelihood values (nsim_obs = 10), can averaged come overall likelihood estimate.","code":"set.seed(121) # example of observed chain sizes; randomly generate 20 chains of size 1 to 10 chain_sizes <- sample(1:10, 20, replace = TRUE) # get their likelihood liks <- likelihood(   chains = chain_sizes,   statistic = \"size\",   offspring_dist = rpois,   obs_prob = 0.3,   lambda = 0.5,   nsim_obs = 10 ) liks #>  [1] -183.8670 -162.1382 -166.6720 -170.1077 -152.9557 -157.9814 -166.0587 #>  [8] -174.8488 -156.4197 -160.0229"},{"path":"https://epiverse-trace.github.io/epichains/articles/epichains.html","id":"how-likelihood-works","dir":"Articles","previous_headings":"Transmission chains likelihoods","what":"How likelihood() works","title":"Getting started with epichains","text":"likelihood() first checks analytical solution likelihood exists given offspring distribution chain statistic specified. ’s none, simulations used estimate likelihoods. epichains package includes closed-form (analytical) solutions calculating likelihoods associated certain summaries transmission chains (“size” “length”) specific offspring distributions. size distributions, package provides Poisson, negative binomial, gamma-borel mixture. provide gamma-Borel size likelihood, Borel distribution needed. However, base R provide distribution natively like poisson gamma, epichains provides density random generator. length distribution, ’s Poisson geometric distributions. can used likelihood() based specified offspring_dist statistic. analytical solution exist, internal simulation function, .offspring_ll() employed. uses simulations approximate probability distributions (using linear approximation cumulative distribution unobserved sizes/lengths). simulation used, extra argument nsim_offspring must passed likelihood() specify number simulations used approximation. Approximate values likelihood vary every call simulation (simulations used estimation vary), may worth calling likelihood() multiple times case see error may introduce. example, let’s look example chain_sizes observed want calculate likelihood drawn binomial distribution probability prob = 0.9.","code":"set.seed(121) # example of observed chain sizes; randomly generate 20 chains of size 1 to 10 chain_sizes <- sample(1:10, 20, replace = TRUE) # get their likelihood liks <- likelihood(   chains = chain_sizes,   offspring_dist = rbinom,   statistic = \"size\",   size = 1,   prob = 0.9,   nsim_offspring = 250 ) liks #> [1] -56.76805"},{"path":"https://epiverse-trace.github.io/epichains/articles/epichains.html","id":"transmission-chain-simulation","dir":"Articles","previous_headings":"","what":"Transmission chain simulation","title":"Getting started with epichains","text":"two simulation functions, herein referred collectively simulate_*() functions can help us achieve .","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/epichains.html","id":"use-case-1","dir":"Articles","previous_headings":"Transmission chain simulation","what":"Use case","title":"Getting started with epichains","text":"want simulate scenario number chains produced separate index case. want simulate chains transmission result cases, given specific offspring distribution reproduction number.","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/epichains.html","id":"what-we-have-1","dir":"Articles","previous_headings":"Transmission chain simulation","what":"What we have","title":"Getting started with epichains","text":"initial number cases seed outbreak.","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/epichains.html","id":"what-we-assume-1","dir":"Articles","previous_headings":"Transmission chain simulation","what":"What we assume","title":"Getting started with epichains","text":"offspring distribution governs number secondary cases produced case. Parameters offspring distribution (example, mean overdispersion using negative binomial; can interpreted reproduction number superspreading coefficient, respectively) (optional) threshold chain summaries considered large consistent reproduction number R<1R<1 (e.g., NN cases TT generations total). (optional) generation time distribution governs time successive cases.","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/epichains.html","id":"simulate_chains","dir":"Articles","previous_headings":"Transmission chain simulation","what":"simulate_chains()","title":"Getting started with epichains","text":"simulate_chains() simulates outbreak given number infections offspring distribution. default, assumes population infinite pre-existing immunity. function tracks returns information infectors (ancestors), infectees, generation infection, time, generation time function specified. Let’s look example simulate transmission tree 1010 index cases. assume poisson offspring distribution mean, lambda=0.9\\text{lambda} = 0.9, generation time 33 days: default, simulate_chains() assumes infinite population can account susceptible depletion finite pop specified. Pre-existing immunity levels can also specified, applied pop simulation initialised. quick example simulate outbreak population size 10001000 1010 index cases 10/10/% pre-existing immunity. assume individuals poisson offspring distribution mean, lambda=1\\text{lambda} = 1, fixed generation time 33:","code":"set.seed(32) # Define generation time generation_time_fn <- function(n) {   gt <- rep(3, n)   return(gt) }  sim_chains <- simulate_chains(   n_chains = 10,   statistic = \"size\",   offspring_dist = rpois,   stat_threshold = 10,   generation_time = generation_time_fn,   lambda = 0.9 )  head(sim_chains) #>    chain infector infectee generation time #> 11     1        1        2          2    3 #> 12     2        1        2          2    3 #> 13     3        1        2          2    3 #> 14     3        1        3          2    3 #> 15     4        1        2          2    3 #> 16     6        1        2          2    3 set.seed(32) # Define generation time generation_time_fn <- function(n) {   gt <- rep(3, n)   return(gt) }  sim_chains_with_pop <- simulate_chains(   pop = 1000,   n_chains = 10,   percent_immune = 0.1,   offspring_dist = rpois,   statistic = \"size\",   lambda = 1,   generation_time = generation_time_fn )  head(sim_chains_with_pop) #>    chain infector infectee generation time #> 11     1        1        2          2    3 #> 12     2        1        2          2    3 #> 13     3        1        2          2    3 #> 14     3        1        3          2    3 #> 15     4        1        2          2    3 #> 16     6        1        2          2    3"},{"path":"https://epiverse-trace.github.io/epichains/articles/epichains.html","id":"simulate_chain_stats","dir":"Articles","previous_headings":"Transmission chain simulation","what":"simulate_chain_stats()","title":"Getting started with epichains","text":"simulate_chain_stats() performant version simulate_chains() track information infector infectee. returns eventual size length/duration transmission chain. function especially useful calculating numerical likelihoods likelihood(). example simulate previous examples without intervention, returning size 1010 chains. assumes Poisson offspring distribution distribution mean 0.90.9.","code":"set.seed(123)  simulate_chain_stats_eg <- simulate_chain_stats(   n_chains = 10,   statistic = \"size\",   offspring_dist = rpois,   stat_threshold = 10,   lambda = 0.9 )  # Print the results simulate_chain_stats_eg #> `epichains_summary` object  #>  #>  [1]   1 Inf   4   4 Inf   1   2 Inf   5   3 #>  #>  Simulated sizes:  #>  #> Max: >=10 #> Min: 1"},{"path":"https://epiverse-trace.github.io/epichains/articles/epichains.html","id":"s3-methods","dir":"Articles","previous_headings":"","what":"S3 Methods","title":"Getting started with epichains","text":"Let’s subset one chains biggest size sim_chains object created . Now, can plot chain using epicontacts package. Aggregated <epichains_tree> objects can also plotted using base R ggplot2 little data manipulation. end--end example simulation aggregation plotting.","code":"# Get the biggest chain longest_chain <- sim_chains[sim_chains$chain == which.max(   unname(table(sim_chains$chain)) ), ]  # Convert to data.frame to view the whole data as.data.frame(longest_chain) #>    chain infector infectee generation time #> 6      6       NA        1          1    0 #> 16     6        1        2          2    3 #> 17     6        1        3          2    3 #> 18     6        1        4          2    3 #> 27     6        2        5          3    6 #> 28     6        3        6          3    6 #> 29     6        3        7          3    6 #> 30     6        4        8          3    6 #> 42     6        5        9          4    9 #> 43     6        6       10          4    9 #> 44     6        7       11          4    9 #> 45     6        8       12          4    9 # Create an `<epicontacts>` object epc <- make_epicontacts(   linelist = longest_chain,   contacts = longest_chain,   id = \"infectee\",   from = \"infector\",   to = \"infectee\",   directed = TRUE )  # Plot the chain plot(epc) # Run simulation with simulate_chains() set.seed(32) # Define generation time generation_time_fn <- function(n) {   gt <- rep(3, n)   return(gt) }  sim_chains <- simulate_chains(   n_chains = 10,   statistic = \"size\",   offspring_dist = rpois,   stat_threshold = 1000,   generation_time = generation_time_fn,   lambda = 2 )  # Aggregate cases over time sim_chains_aggreg <- aggregate(sim_chains, by = \"time\")  # Plot cases over time plot(   sim_chains_aggreg,   type = \"b\",   col = \"red\",   lwd = 2,   xlab = \"Time\",   ylab = \"Cases\" )"},{"path":"https://epiverse-trace.github.io/epichains/articles/epichains.html","id":"summarising","dir":"Articles","previous_headings":"S3 Methods","what":"Summarising","title":"Getting started with epichains","text":"can run summary() object returned simulate_chains() obtain chain summaries per index case. summary output simulate_chain_stats() inputs used. simulate_chain_stats() performant version simulate_chains(), hence, can use instead, interested summary simulated chains without details infection tree. ::: can confirm two outputs using base::setequal(), checks two objects equal returns TRUE/FALSE.","code":"set.seed(32) # Define generation time generation_time_fn <- function(n) {   gt <- rep(3, n)   return(gt) }  sim_chains <- simulate_chains(   n_chains = 10,   statistic = \"size\",   offspring_dist = rpois,   stat_threshold = 10,   generation_time = generation_time_fn,   lambda = 0.9 )  summary(sim_chains) #> `epichains_summary` object  #>  #>  [1] Inf   2 Inf   2   1 Inf   3 Inf   9   1 #>  #>  Simulated sizes:  #>  #> Max: >=10 #> Min: 1 # Example with simulate_chain_stats() set.seed(32)  simulate_chain_stats_eg <- simulate_chain_stats(   n_chains = 10,   statistic = \"size\",   offspring_dist = rpois,   stat_threshold = 10,   lambda = 0.9 )  # Get summaries summary(simulate_chain_stats_eg) #> $n_chains #> [1] 10 #>  #> $max_stat #> [1] Inf #>  #> $min_stat #> [1] 1 setequal(   # summary of output from simulate_chains()   summary(sim_chains),   # results from simulate_chain_stats()   simulate_chain_stats_eg ) #> [1] TRUE"},{"path":"https://epiverse-trace.github.io/epichains/articles/epichains.html","id":"aggregating","dir":"Articles","previous_headings":"S3 Methods","what":"Aggregating","title":"Getting started with epichains","text":"can aggregate <epichains_tree> objects returned simulate_chains() <data.frame> columns “cases” either “generation” “time”, depending value . aggregate “time”, must specified generation time distribution (generation_time) simulation step.","code":"# Example with simulate_chains() set.seed(32)  # Define generation time generation_time_fn <- function(n) {   gt <- rep(3, n)   return(gt) }  sim_chains <- simulate_chains(   n_chains = 10,   statistic = \"size\",   offspring_dist = rpois,   stat_threshold = 10,   generation_time = generation_time_fn,   lambda = 0.9 )  aggregate(sim_chains, by = \"time\") #>   time cases #> 1    0    10 #> 2    3    12 #> 3    6    14 #> 4    9    17 #> 5   12     3 #> 6   15     4 #> 7   18     3"},{"path":"https://epiverse-trace.github.io/epichains/articles/epichains.html","id":"plotting","dir":"Articles","previous_headings":"S3 Methods","what":"Plotting","title":"Getting started with epichains","text":"can plot individual chains <epichains> object using {epicontacts} package. , first need create <epicontacts> object using epicontacts::make_epicontacts() function, requires linelist contacts data.frame (See ?epicontacts::make_epicontacts()).","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/epichains.html","id":"some-notes-about-interoperability-between-epicontacts-and-epichains-objects","dir":"Articles","previous_headings":"S3 Methods","what":"Some notes about interoperability between <epicontacts> and <epichains> objects","title":"Getting started with epichains","text":"epicontacts::make_epicontacts() function work: linelist contacts data.frames must column named “id” uniquely identifies case. linelist contacts objects can . <epichains> object contains multiple independent chains unique infectee ids, work box make_epicontacts() unless use subset chain. now, select visualise individual chains <epichains> object. future versions package, make interaction seamless providing user-friendly functionality convert <epichains> object <epicontacts> way allows us plot chains .","code":""},{"path":[]},{"path":"https://epiverse-trace.github.io/epichains/articles/interventions.html","id":"reducing-the-strength-of-transmission","dir":"Articles","previous_headings":"","what":"Reducing the strength of transmission","title":"Modelling disease control interventions","text":"Following (Lloyd-Smith et al. 2005) consider two ways disease control interventions can reduce reproduction number: population-wide individual-specific control.","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/interventions.html","id":"population-wide-control","dir":"Articles","previous_headings":"Reducing the strength of transmission","what":"Population-wide control","title":"Modelling disease control interventions","text":"population-level control mean intervention reduces mean number offspring (.e. reproduction number) fixed proportion. example, reduce R 25% population level scale mu parameter 1.2 0.9:","code":"sims <- simulate_chain_stats(   n_chains = 200, offspring_dist = rnbinom, stat_threshold = 99, mu = 0.9,   size = 0.5, statistic = \"size\" ) sims[is.infinite(sims)] <- 100 # Replace infections > 99 with 100 for plotting. ggplot(data.frame(x = sims), aes(x = x)) +   geom_histogram(breaks = seq(0, 100, by = 5), closed = \"left\") +   scale_x_continuous(breaks = c(0, 25, 50, 75, 100),                      labels = c(0, 25, 50, 75, \">99\")) +   theme_bw()"},{"path":"https://epiverse-trace.github.io/epichains/articles/interventions.html","id":"individual-level-control-","dir":"Articles","previous_headings":"Reducing the strength of transmission","what":"Individual-level control.","title":"Modelling disease control interventions","text":"simulating population-level control now apply reduction (25%) instead assuming mean reduced apply 25% individuals transmit , whereas remaining 75% generate offspring uncontrolled case. , can longer use standard negative binomial distribution comes R. Instead, define random generator modified negative binomial distribution includes individual-level control control argument indicating level individual-level control (0: control; 1: full control): defined , can generate simulations :","code":"rnbinom_ind <- function(n, ..., control = 0) {   ## initialise number of offspring to 0   offspring <- rep(0L, n)   ## for each individual, decide whether they transmit further   transmits <- rbinom(n = n, prob = 1 - control, size = 1)   ## check if anyone transmits further   if (any(transmits == 1L)) {     ## for those that transmit, sample from negative binomial with given     ## parameters     offspring[which(transmits == 1L)] <- rnbinom(n = n, ...)   }   return(offspring) } sims <- simulate_chain_stats(   n_chains = 200, offspring_dist = rnbinom_ind, stat_threshold = 99, mu = 1.2,   size = 0.5, control = 0.25, statistic = \"size\" ) sims[is.infinite(sims)] <- 100 # Replace infections > 99 with 100 for plotting. ggplot(data.frame(x = sims), aes(x = x)) +   geom_histogram(breaks = seq(0, 100, by = 5), closed = \"left\") +   scale_x_continuous(breaks = c(0, 25, 50, 75, 100),                      labels = c(0, 25, 50, 75, \">99\")) +   theme_bw()"},{"path":"https://epiverse-trace.github.io/epichains/articles/interventions.html","id":"preventing-superspreading-events","dir":"Articles","previous_headings":"","what":"Preventing superspreading events","title":"Modelling disease control interventions","text":"Another way controlling disease prevent individuals spreading large number others, example preventing mass gatherings , generally, settings superspreading events can occur. can model truncating offspring distribution certain size. can done, example, using truncdist R package. use define truncated negative binomial offspring distribution: use simulate chains situation maximum secondary cases infected person can generate 10. can likened disease control strategy gatherings limited 10 people.","code":"rnbinom_truncated <- function(n, ..., max = Inf) {   return(rtrunc(n = n, spec = \"nbinom\", b = max, ...)) } sims <- simulate_chain_stats(   n_chains = 200, offspring_dist = rnbinom_truncated, stat_threshold = 99,   mu = 1.2, size = 0.5, max =  10, statistic = \"size\" ) sims[is.infinite(sims)] <- 100 # Replace infections > 99 with 100 for plotting. ggplot(data.frame(x = sims), aes(x = x)) +   geom_histogram(breaks = seq(0, 100, by = 5), closed = \"left\") +   scale_x_continuous(breaks = c(0, 25, 50, 75, 100),                      labels = c(0, 25, 50, 75, \">99\")) +   theme_bw()"},{"path":"https://epiverse-trace.github.io/epichains/articles/interventions.html","id":"truncating-the-generation-interval","dir":"Articles","previous_headings":"","what":"Truncating the generation interval","title":"Modelling disease control interventions","text":"Lastly, consider situation generation interval shortened. model explicitly instead consider effect offspring distribution. example, generation interval gamma distribution shape = 25 rate = 5 (corresponding mean 5 standard deviation 1), stop transmission normally occur 6 days infection, can calculate proportion transmissions prevented words, prevent 16% infections example. value control can used examples study effect outbreak sizes.","code":"control <- 1 - pgamma(6, shape = 25, rate = 5) signif(control, 2) #> [1] 0.16"},{"path":[]},{"path":"https://epiverse-trace.github.io/epichains/articles/projecting_incidence.html","id":"overview","dir":"Articles","previous_headings":"","what":"Overview","title":"Projecting infectious disease incidence: a COVID-19 example","text":"Branching processes can used project stochastic infectious disease trends time provided can characterize distribution times successive cases (serial interval), distribution secondary cases produced single individual (offspring distribution). simulations can achieved epichains simulate_chains() function Pearson et al. (2020), Abbott et al. (2020) illustrate application COVID-19. purpose vignette use early data COVID-19 South Africa (Marivate Combrink 2020) illustrate epichains can used project outbreak. Let’s load required packages","code":"library(\"epichains\") library(\"dplyr\") library(\"ggplot2\") library(\"lubridate\")"},{"path":"https://epiverse-trace.github.io/epichains/articles/projecting_incidence.html","id":"data","dir":"Articles","previous_headings":"","what":"Data","title":"Projecting infectious disease incidence: a COVID-19 example","text":"Included epichains cleaned time series first 15 days COVID-19 outbreak South Africa. can loaded memory follows: use first \\(5\\) observations demonstration. assume cases subset imported infect . Let us subset view aspect data.","code":"data(\"covid19_sa\", package = \"epichains\") seed_cases <- covid19_sa[1:5, ] head(seed_cases) #> # A tibble: 5 × 2 #>   date       cases #>   <date>     <int> #> 1 2020-03-05     1 #> 2 2020-03-07     1 #> 3 2020-03-08     1 #> 4 2020-03-09     4 #> 5 2020-03-11     6"},{"path":"https://epiverse-trace.github.io/epichains/articles/projecting_incidence.html","id":"setting-up-the-inputs","dir":"Articles","previous_headings":"","what":"Setting up the inputs","title":"Projecting infectious disease incidence: a COVID-19 example","text":"now proceed set simulate_chains() simulations.","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/projecting_incidence.html","id":"onset-times","dir":"Articles","previous_headings":"Setting up the inputs","what":"Onset times","title":"Projecting infectious disease incidence: a COVID-19 example","text":"simulate_chains() requires vector seeding times, t0, chain/individual/simulation. get , use observation date index case reference find difference observed dates reference. Using vector start times time series, create corresponding seeding time individual, ’ll call t0.","code":"days_since_index <- as.integer(seed_cases$date - min(seed_cases$date)) days_since_index #> [1] 0 2 3 4 6 t0 <- rep(days_since_index, seed_cases$cases) t0 #>  [1] 0 2 3 4 4 4 4 6 6 6 6 6 6"},{"path":"https://epiverse-trace.github.io/epichains/articles/projecting_incidence.html","id":"generation-time","dir":"Articles","previous_headings":"Setting up the inputs","what":"Generation time","title":"Projecting infectious disease incidence: a COVID-19 example","text":"epidemiology, generation time (also called generation interval) duration successive infectious events chain transmission. Similarly, serial interval duration observed symptom onset times successive cases transmission chain. generation interval often hard observe exact times infection hard measure hence, serial interval often used instead. , use serial interval interpret simulated case data represent symptom onset. example, assume based COVID-19 literature serial interval, S, log-normal distributed parameters, \\(\\mu = 4.7\\) \\(\\sigma = 2.9\\) (Pearson et al. 2020). log-normal distribution commonly used epidemiology characterise quantities serial interval large variance can positive-valued (Nishiura 2007; Limpert, Stahel, Abbt 2001). Note distribution described way, means \\(\\mu\\) \\(\\sigma\\) expected value standard deviation natural logarithm serial interval. Hence, order sample “back-transformed” measured serial interval expectation/mean, \\(E[S]\\) standard deviation, \\(SD [S]\\), can use following parametrisation: \\[\\begin{align} E[S] &= \\ln \\left( \\dfrac{\\mu^2}{(\\sqrt{\\mu^2 + \\sigma^2}} \\right) \\\\  SD [S] &= \\sqrt {\\ln \\left(1 + \\dfrac{\\sigma^2}{\\mu^2} \\right)} \\end{align}\\] See “log-normal_distribution” Wikipedia detailed explanation parametrisation. now set generation time function appropriate inputs. adopt R’s random lognormal distribution generator (rlnorm()) takes meanlog sdlog arguments, define parametrisation log_mean() log_sd() respectively wrap generation_time_fn() function. Moreover, generation_time_fn() takes one argument n required epichains (See ?epichains::simulate_chains), passed rlnorm() first argument determine number observations sample (See ?rlnorm).","code":"mu <- 4.7 sgma <- 2.9  log_mean <- log((mu^2) / (sqrt(sgma^2 + mu^2)))  # log mean log_sd <- sqrt(log(1 + (sgma / mu)^2)) # log sd  #' serial interval function generation_time <- function(n) {   gt <- rlnorm(n, meanlog = log_mean, sdlog = log_sd)   return(gt) }"},{"path":"https://epiverse-trace.github.io/epichains/articles/projecting_incidence.html","id":"offspring-distribution","dir":"Articles","previous_headings":"Setting up the inputs","what":"Offspring distribution","title":"Projecting infectious disease incidence: a COVID-19 example","text":"Let us now set offspring distribution, distribution drives mechanism behind individual cases infect cases. appropriate way model offspring distribution capture population-level transmissibility (\\(R0\\)) individual-level heterogeneity transmission (“superspreading”). negative binomial distribution commonly used case (Lloyd-Smith et al. 2005). example, assume offspring distribution characterised negative binomial \\(mu = 2.5\\) (Abbott et al. 2020) \\(size = 0.58\\) (Wang et al. 2020). parameterization, \\(mu\\) represents \\(R_0\\), defined average number cases produced single individual entirely susceptible population. parameter \\(size\\) represents superspreading, , degree heterogeneity transmission single individuals.","code":"mu <- 2.5 size <- 0.58"},{"path":"https://epiverse-trace.github.io/epichains/articles/projecting_incidence.html","id":"simulation-controls","dir":"Articles","previous_headings":"Setting up the inputs","what":"Simulation controls","title":"Projecting infectious disease incidence: a COVID-19 example","text":"example, simulate outbreaks end \\(21\\) days last date observations seed_cases dataset. simulate_chains() stochastic, meaning results different every time run set parameters. , therefore, run simulations \\(100\\) times aggregate results. Let us specify . Lastly, since, specified \\(R0 > 1\\), means epidemic potentially grow without end. Hence, must specify end point simulations. simulate_chains() provides stat_threshold argument purpose. stat_threshold, simulation cut . value specified, assumes value infinity. , assume maximum chain size \\(1000\\).","code":"#' Date to end simulation projection_window <- 21 tf <- max(days_since_index) + projection_window tf #> [1] 27 #' Number of simulations sim_rep <- 100 #' Maximum chain size allowed stat_threshold <- 1000"},{"path":"https://epiverse-trace.github.io/epichains/articles/projecting_incidence.html","id":"modelling-assumptions","dir":"Articles","previous_headings":"","what":"Modelling assumptions","title":"Projecting infectious disease incidence: a COVID-19 example","text":"exercise makes following simplifying assumptions: cases observed. Cases observed exactly time infection. reporting delay. Reporting rate constant course epidemic. interventions implemented. Population homogeneous well-mixed. summarise whole set far, going simulate chain 100 times, projecting cases 21 days first 6 days, assuming outbreak size exceeds 1000 cases.","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/projecting_incidence.html","id":"running-the-simulations","dir":"Articles","previous_headings":"","what":"Running the simulations","title":"Projecting infectious disease incidence: a COVID-19 example","text":"use function lapply() run simulations bind rows dplyr::bind_rows(). Let us view first rows simulation results.","code":"set.seed(1234) sim_chain_sizes <- lapply(   seq_len(sim_rep),   function(sim) {     simulate_chains(       n_chains = length(t0),       offspring_dist = rnbinom,       mu = mu,       size = size,       statistic = \"size\",       stat_threshold = stat_threshold,       generation_time = generation_time,       t0 = t0,       tf = tf     ) %>%       mutate(sim = sim)   } )  sim_output <- bind_rows(sim_chain_sizes) head(sim_output) #>    chain infector infectee generation      time sim #> 14     3        1        2          2  8.123133   1 #> 15     3        1        3          2  6.842933   1 #> 16     3        1        4          2  7.260639   1 #> 17     3        1        5          2 11.244838   1 #> 18     7        1        2          2  7.022334   1 #> 19     7        1        3          2 12.182368   1"},{"path":"https://epiverse-trace.github.io/epichains/articles/projecting_incidence.html","id":"post-processing","dir":"Articles","previous_headings":"","what":"Post-processing","title":"Projecting infectious disease incidence: a COVID-19 example","text":"Now, summarise simulation results. want plot individual simulated daily time series show median cases per day aggregated simulations. First, create daily time series per simulation aggregating number cases per day simulation. Next, add date column results simulation set. use date first case observed data reference start date. Now aggregate simulations day evaluate median daily cases across simulations.","code":"# Daily number of cases for each simulation incidence_ts <- sim_output %>%   mutate(day = ceiling(time)) %>%   count(sim, day, name = \"cases\") %>%   as_tibble()  head(incidence_ts) #> # A tibble: 6 × 3 #>     sim   day cases #>   <int> <dbl> <int> #> 1     1     0     1 #> 2     1     2     1 #> 3     1     3     1 #> 4     1     4     4 #> 5     1     6     6 #> 6     1     7     1 # Get start date from the observed data index_date <- min(seed_cases$date) index_date #> [1] \"2020-03-05\" # Add a dates column to each simulation result incidence_ts_by_date <- incidence_ts %>%   group_by(sim) %>%   mutate(date = index_date + days(seq(0, n() - 1))) %>%   ungroup()  head(incidence_ts_by_date) #> # A tibble: 6 × 4 #>     sim   day cases date       #>   <int> <dbl> <int> <date>     #> 1     1     0     1 2020-03-05 #> 2     1     2     1 2020-03-06 #> 3     1     3     1 2020-03-07 #> 4     1     4     4 2020-03-08 #> 5     1     6     6 2020-03-09 #> 6     1     7     1 2020-03-10 # Median daily number of cases aggregated across all simulations median_daily_cases <- incidence_ts_by_date %>%   group_by(date) %>%   summarise(median_cases = median(cases)) %>%   ungroup() %>%   arrange(date)  head(median_daily_cases) #> # A tibble: 6 × 2 #>   date       median_cases #>   <date>            <dbl> #> 1 2020-03-05            1 #> 2 2020-03-06            1 #> 3 2020-03-07            1 #> 4 2020-03-08            4 #> 5 2020-03-09            5 #> 6 2020-03-10            8"},{"path":"https://epiverse-trace.github.io/epichains/articles/projecting_incidence.html","id":"visualization","dir":"Articles","previous_headings":"","what":"Visualization","title":"Projecting infectious disease incidence: a COVID-19 example","text":"now plot individual simulation results alongside median aggregated results. Figure 1: COVID-19 incidence South Africa projected two week window 2020. light gray lines represent individual simulations, red line represents median daily cases across simulations, black connected dots represent observed data, dashed vertical line marks beginning projection.","code":"# since all simulations may end at a different date, we will find the minimum # final date for all simulations for the purposes of visualisation. final_date <- incidence_ts_by_date %>%   group_by(sim) %>%   summarise(final_date = max(date), .groups = \"drop\") %>%   summarise(min_final_date = min(final_date)) %>%   pull(min_final_date)  incidence_ts_by_date <- incidence_ts_by_date %>%   filter(date <= final_date)  median_daily_cases <- median_daily_cases %>%   filter(date <= final_date)  ggplot(data = incidence_ts_by_date) +   geom_line(     aes(       x = date,       y = cases,       group = sim     ),     color = \"grey\",     linewidth = 0.2,     alpha = 0.25   ) +   geom_line(     data = median_daily_cases,     aes(       x = date,       y = median_cases     ),     color = \"tomato3\",     linewidth = 1.8   ) +   geom_point(     data = covid19_sa,     aes(       x = date,       y = cases     ),     color = \"black\",     size = 1.75,     shape = 21   ) +   geom_line(     data = covid19_sa,     aes(       x = date,       y = cases     ),     color = \"black\",     linewidth = 1   ) +   scale_x_continuous(     breaks = seq(       min(incidence_ts_by_date$date),       max(incidence_ts_by_date$date),       5     ),     labels = seq(       min(incidence_ts_by_date$date),       max(incidence_ts_by_date$date),       5     )   ) +   scale_y_continuous(     breaks = seq(       0,       max(incidence_ts_by_date$cases),       30     ),     labels = seq(       0,       max(incidence_ts_by_date$cases),       30     )   ) +   geom_vline(     mapping = aes(xintercept = max(seed_cases$date)),     linetype = \"dashed\"   ) +   labs(x = \"Date\", y = \"Daily cases\")"},{"path":[]},{"path":"https://epiverse-trace.github.io/epichains/articles/theoretical_background.html","id":"branching-processes","dir":"Articles","previous_headings":"","what":"Branching processes","title":"Theoretical background for epichains","text":"Branching processes class models used model growth populations. assume member population produces number offspring, \\(Z\\), random variable probability mass function \\(p(Z = z | \\theta)\\), called offspring distribution. use long history epidemiology, population interpreted pathogen, offspring new hosts infects (Farrington, Kanaan, Gay 2003). call infected individuals cases methods applied contexts branching processes used.","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/theoretical_background.html","id":"simulation","dir":"Articles","previous_headings":"","what":"Simulation","title":"Theoretical background for epichains","text":"simulate branching process, start single case proceed discrete steps generations, drawing offspring distribution \\(p(Z=z | \\theta)\\) generate new cases case. Given infector \\(\\) infectee \\(j\\), can additionally assign distribution times \\(T\\) approximates infection event occurred. define \\(T\\) random variable distribution \\(f(T = t; \\theta)\\) can assign case \\(j\\) time \\(t_{j}\\) , case \\(j\\) affected case \\(\\) given \\(f(t_{j} - t_{} | \\theta)\\). identify timing cases time symptom onset serial interval, depending case definitions another interval.","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/theoretical_background.html","id":"summary-statistics","dir":"Articles","previous_headings":"Simulation","what":"Summary statistics","title":"Theoretical background for epichains","text":"Branching process simulations end gone extinct, , offspring produced, stopping criterion. summarise simulations, either study size length resulting chain cases. size \\(S\\) chain number cases occurred course simulation including initial case \\(S \\geq 1\\). length \\(L\\) chain number generations simulated including initial case \\(L \\geq 1\\).","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/theoretical_background.html","id":"inference","dir":"Articles","previous_headings":"","what":"Inference","title":"Theoretical background for epichains","text":"characterising chains cases size length can conduct inference learn underlying parameters \\(\\theta\\) observation chain sizes chain lengths (Blumberg Lloyd-Smith 2013). general possible subcritical branching processes, .e. ones mean number offspring less 1, otherwise branching process grow forever. However, can expand theory supercritical branching processes, .e. ones mean number offspring greater 1, defining cut chain size length beyond treat chain infinite size length, respectively.","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/theoretical_background.html","id":"size-and-length-distributions-for-some-offspring-distributions","dir":"Articles","previous_headings":"Inference","what":"Size and length distributions for some offspring distributions","title":"Theoretical background for epichains","text":"show equations size length distributions offspring distributions can derived analytically: Poisson, negative binomial, geometric, gamma-Borel mixture.","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/theoretical_background.html","id":"negative-binomial-and-special-cases","dir":"Articles","previous_headings":"Inference > Size and length distributions for some offspring distributions","what":"Negative binomial and special cases","title":"Theoretical background for epichains","text":"offspring distribution Poisson distribution, can interpret rate parameter \\(\\lambda\\) basic reproduction number \\(R_{0}\\) pathogen. general case offspring definition can overdispersed leading superspreading can use negative binomial offspring distribution mean \\(\\mu\\) overdispersion \\(k\\) Blumberg Lloyd-Smith (2013). case, mean parameter \\(\\mu\\) interpreted basic reproduction number \\(R_0\\) pathogen. negative binomial distribution arises Poisson-gamma mixture thus branching process negative binomial distributed offspring can interpreted one Poisson distributed offspring basic reproduction number \\(R_0\\) varies according gamma distribution. amount variation \\(R_0\\) interpreted individual-level variation transmission representing overdispersion superspreading, degree happens given overdispersion parameter \\(k\\).","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/theoretical_background.html","id":"size-distributions","dir":"Articles","previous_headings":"Inference > Size and length distributions for some offspring distributions > Negative binomial and special cases","what":"Size distributions","title":"Theoretical background for epichains","text":"probability \\(p\\) chain size \\(S\\) given \\(R_0\\) \\(k\\) branching process negative binomial offspring distribution given Eq. 9 Blumberg Lloyd-Smith (2013) \\[ p(S|R_0, k) = \\frac{\\Gamma(kS + S - 1)}{\\Gamma(kS)\\Gamma(S + 1)} \\frac{\\left(\\frac{R_0}{k}\\right)^{S - 1}}{\\left( 1 + \\frac{R_0}{k} \\right)^{kS + S - 1}} \\] \\(\\Gamma\\) gamma function. order estimate \\(S\\) given \\(R_0\\) \\(k\\) can define likelihood function \\(L(S) = p(S|R_0, k)\\). corresponding log-likelihood \\[\\begin{align} \\mathrm{LL}(S) = &\\log\\Gamma(kS + S  - 1) - \\left(\\log\\Gamma(kS) + \\log\\Gamma(S - 1) \\right) \\\\ & + (S-1) \\log \\frac{R_0}{k} - (SR_0 + (S - 1)) \\log \\left(1 + \\frac{R_0}{k}\\right) \\end{align}\\] log-likelihood Poisson distributed offspring follows \\(k\\) tends infinity (corresponding Eq. 2.2 Farrington, Kanaan, Gay (2003)) \\[ \\mathrm{LL}(S) = (S - 1) \\log R_0 - S R_0 + (S - 2) \\log S - \\log\\Gamma(S) \\] cases point estimate basic reproduction number \\(\\hat{R_0}\\) related mean chain size \\(\\bar{S}\\) \\[ \\hat{R_0} = 1 - \\frac{1}{\\bar{S}} \\]","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/theoretical_background.html","id":"length-distributions","dir":"Articles","previous_headings":"Inference > Size and length distributions for some offspring distributions > Negative binomial and special cases","what":"Length distributions","title":"Theoretical background for epichains","text":"cumulative mass function \\(F(L)\\) observing chain length \\(L\\) offspring Poisson distributed given Eq. (2.5) Farrington, Kanaan, Gay (2003) (called “outbreak duration”): \\[ F(L) = e^{-R_0} E_L \\left( e^{R_0 e^{-R_0} } \\right) \\] \\(E_L(x)\\) iterated exponential function, \\(E_0(x) = 1\\), \\(E_{L + 1}(x) = x^{E_L(x)}\\). geometric distributed offspring (corresponding negative Binomial \\(k=1\\)) function given \\[ F(L) = \\frac{ 1- R_0^{L + 1} } {1 - R_0^{L - 2}} \\] cases \\(f(L)\\) denotes cumulative mass functions therefore probability observing chain length \\(L\\) therefore \\(f(L) - f(L - 1)\\).","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/theoretical_background.html","id":"gamma-borel-mixture","dir":"Articles","previous_headings":"Inference > Size and length distributions for some offspring distributions","what":"Gamma-Borel mixture","title":"Theoretical background for epichains","text":"probability distribution outbreak sizes branching process Poisson offspring distribution (Eq. 2.2 Farrington, Kanaan, Gay (2003)) special case Borel-Tanner distribution starting 1 individual. alternative negative binomial offspring distribution represents Poisson-gamma mixture Borel-gamma mixture. represent situations variation individual level chain level, .e. transmission chains homogeneous heterogeneity chains. case, can shown resulting log-likelihood chain sizes \\[\\begin{align} \\mathrm{LL}(S) = &\\log\\Gamma(k + S - 1) - \\left(\\log\\Gamma(k) + \\log\\Gamma(S + 1) \\right) \\\\ & + (S-1) \\log S - k \\log \\left(S + \\frac{R_0}{k}\\right) \\end{align}\\]","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/theoretical_background.html","id":"numerical-approximations-of-chain-size-and-length-distributions","dir":"Articles","previous_headings":"Inference","what":"Numerical approximations of chain size and length distributions","title":"Theoretical background for epichains","text":"analytic likelihoods available numerical approximation used derive distributions. order , simulation functionality used generate \\(n\\) simulated chains value cumulative mass function \\(P(S|\\theta)\\) observed \\(S\\) approximated empirical cumulative distribution function: \\[ P(S|\\theta) \\approx \\sum_i \\mathbf{1}(x_i <= S) \\] \\(\\mathbf{1}\\) indicator function \\(x_i\\) -th observed chain size (length, interest \\(L\\)). order improve approximation linear approximation applied values empirical distribution function (expense normalisation 1). (unnormalised) probability observing \\(S\\) given \\[ p(S|\\theta) = P(S|\\theta) - P(S - 1|\\theta) \\] equivalent relationship used \\(L\\).","code":""},{"path":"https://epiverse-trace.github.io/epichains/authors.html","id":null,"dir":"","previous_headings":"","what":"Authors","title":"Authors and Citation","text":"James M. Azam. Author, maintainer, copyright holder. Sebastian Funk. Author. Flavio Finger. Author. Zhian N. Kamvar. Contributor. Hugo Gruson. Contributor, reviewer. Karim Mané. Reviewer. Pratik Gupte. Reviewer. Joshua W. Lambert. Reviewer.","code":""},{"path":"https://epiverse-trace.github.io/epichains/authors.html","id":"citation","dir":"","previous_headings":"","what":"Citation","title":"Authors and Citation","text":"Azam J, Funk S, Finger F (2024). epichains: Simulating Analysing Transmission Chain Statistics Using Branching Process Models. R package version 0.1.0, https://epiverse-trace.github.io/epichains/, https://github.com/epiverse-trace/epichains.","code":"@Manual{,   title = {epichains: Simulating and Analysing Transmission Chain Statistics Using Branching Process Models},   author = {James M. Azam and Sebastian Funk and Flavio Finger},   year = {2024},   note = {R package version 0.1.0, https://epiverse-trace.github.io/epichains/},   url = {https://github.com/epiverse-trace/epichains}, }"},{"path":"https://epiverse-trace.github.io/epichains/index.html","id":"epichains-methods-for-simulating-and-analysing-the-size-and-length-of-transmission-chains-from-branching-process-models-","dir":"","previous_headings":"","what":"Simulating and Analysing Transmission Chain Statistics Using Branching Process Models","title":"Simulating and Analysing Transmission Chain Statistics Using Branching Process Models","text":"epichains R package simulate, analyse, visualize size length branching processes given offspring distribution. models often used infectious disease epidemiology, chains represent chains transmission, offspring distribution represents distribution secondary infections caused infected individual. epichains re-implements bpmodels providing bespoke functions data structures allow easy manipulation interoperability Epiverse-TRACE packages, example, superspreading epiparameter, potentially existing packages handling transmission chains, example, epicontacts. epichains developed Centre Mathematical Modelling Infectious Diseases London School Hygiene Tropical Medicine part Epiverse Initiative.","code":""},{"path":"https://epiverse-trace.github.io/epichains/index.html","id":"installation","dir":"","previous_headings":"","what":"Installation","title":"Simulating and Analysing Transmission Chain Statistics Using Branching Process Models","text":"latest development version epichains package can installed via fails, try using pak R package via options fail, please file issue full log error messages. example issue reporting installation failure. help us improve installation process. load package, use","code":"# check whether {remotes} is installed if (!require(\"remotes\")) install.packages(\"remotes\") remotes::install_github(\"epiverse-trace/epichains\") # check whether {pak} is installed if (!require(\"pak\")) install.packages(\"pak\") pak::pak(\"epiverse-trace/epichains\") library(\"epichains\")"},{"path":"https://epiverse-trace.github.io/epichains/index.html","id":"quick-start","dir":"","previous_headings":"","what":"Quick start","title":"Simulating and Analysing Transmission Chain Statistics Using Branching Process Models","text":"epichains provides three main functions: simulate_chains(): simulates transmission chains using simple branching process model accepts index number cases seed outbreak, distribution offspring per case, chain statistic track (size length/duration). optionally accepts population related inputs population size (defaults Inf) percentage population initially immune (defaults 0). function returns object columns track information infected , generation infection , generation time function specified, time infection. simulate_chain_stats(): provides performant version simulate_chains() tracks return vector realized chain sizes lengths/durations index case without details infection tree. likelihood(): calculates loglikelihood (likelihood, depending value log) observing vector transmission chain sizes lengths. objects returned simulate_*() functions can summarised summary(). Running summary() output simulate_chains() return output simulate_chain_stats() using inputs. Objects returned simulate_chains() can aggregated <data.frame> cases per time generation function aggregate(). simulated <epichains> object can plotted various ways using plot(). See plotting section vignette(\"epichains\") two use cases.","code":""},{"path":"https://epiverse-trace.github.io/epichains/index.html","id":"simulation","dir":"","previous_headings":"Quick start","what":"Simulation","title":"Simulating and Analysing Transmission Chain Statistics Using Branching Process Models","text":"simulation functionality, let’s look simple example simulate transmission chain 2020 index cases, constant generation time 33, poisson offspring distribution mean 11. tracking chain “size” statistic cap chain sizes 2525 cases. look summary simulation, aggregate cases per generation.","code":"set.seed(32) # Simulate chains sim_chains <- simulate_chains(   n_chains = 20,   statistic = \"size\",   offspring_dist = rpois,   stat_threshold = 25,   generation_time = function(n) {rep(3, n)}, # constant generation time of 3   lambda = 1 # mean of the Poisson distribution ) # View the head of the simulation head(sim_chains) #>    chain infector infectee generation time #> 21     1        1        2          2    3 #> 22     2        1        2          2    3 #> 23     3        1        2          2    3 #> 24     3        1        3          2    3 #> 25     4        1        2          2    3 #> 26     6        1        2          2    3 # Summarise the simulation summary(sim_chains) #> `epichains_summary` object  #>  #>  [1]   5  17   4   8   1  16   9 Inf   5  18   5   1 Inf  24   1  14  19   2   4 #> [20]  14 #>  #>  Simulated sizes:  #>  #> Max: >=25 #> Min: 1 # Aggregate the simulation into cases per generation chains_agregegated <- aggregate(sim_chains, by = \"generation\")  # view the time series of cases per generation chains_agregegated #>    generation cases #> 1           1    20 #> 2           2    26 #> 3           3    36 #> 4           4    43 #> 5           5    31 #> 6           6    25 #> 7           7    20 #> 8           8     9 #> 9           9     3 #> 10         10     1 #> 11         11     1 #> 12         12     1 #> 13         13     1"},{"path":"https://epiverse-trace.github.io/epichains/index.html","id":"inference","dir":"","previous_headings":"Quick start","what":"Inference","title":"Simulating and Analysing Transmission Chain Statistics Using Branching Process Models","text":"Let’s look following example estimate log-likelihood observing hypothetical chain_lengths dataset. listed functionalities demonstrated detail “Getting Started” vignette.","code":"set.seed(32) # randomly generate 20 chain lengths between 1 to 40 chain_lengths <- sample(1:40, 20, replace = TRUE) chain_lengths #>  [1]  6 11 20  9 40 33 39 27  6 12 39 35  9 25  6 15 12  6 37 35 # estimate loglikelihood of the observed chain sizes likelihood_eg <- likelihood(   chains = chain_lengths,   statistic = \"length\",   offspring_dist = rpois,   lambda = 0.99 ) # Print the estimate likelihood_eg #> [1] -104.2917"},{"path":"https://epiverse-trace.github.io/epichains/index.html","id":"package-vignettes","dir":"","previous_headings":"","what":"Package vignettes","title":"Simulating and Analysing Transmission Chain Statistics Using Branching Process Models","text":"theory behind models provided can found theory vignette. also collated bibliography branching process applications epidemiology. can found literature vignette. Specific use cases epichains can found online documentation package vignettes, “Articles”.","code":""},{"path":"https://epiverse-trace.github.io/epichains/index.html","id":"related-r-packages","dir":"","previous_headings":"","what":"Related R packages","title":"Simulating and Analysing Transmission Chain Statistics Using Branching Process Models","text":"far know, existing R packages simulating branching processes transmission chains. bpmodels: provides methods analysing size length transmission chains branching process models. epichains intended supersede {bpmodels}. ringbp: branching process model, parameterised 2019-nCoV outbreak, used quantify potential effectiveness contact tracing isolation cases. covidhm: code simulating COVID-19 dynamics range scenarios across real-world social network. model conceptually based {ringbp}. epicontacts: provides methods handling, analysing, visualizing transmission chains contact-tracing data/linelists. simulist: uses branching process model simulate individual-level infectious disease outbreak data, including line lists contact tracing data. package part Epiverse-TRACE Initiative. superspreading: provides set functions estimate understand individual-level variation transmission infectious diseases data secondary cases. useful understanding role superspreading spread infectious diseases informing public health interventions. earlyR: estimates reproduction number (R), early stages outbreak. model requires specified serial interval distribution, characterised mean standard deviation (Gamma) distribution, data daily disease incidence, including confirmed probable cases. projections: uses data daily incidence, serial interval (time onsets infectors infectees) reproduction number simulate plausible epidemic trajectories project future incidence. relies branching process daily incidence follows Poisson Negative Binomial distribution governed force infection. simulacr: simulates outbreaks specified values reproduction number, incubation period, duration infectiousness, optionally reporting delays. Outputs linelist stored data.frame class outbreak, including information transmission chains; output can converted <epicontacts> objects visualisation. outbreakr: implements Bayesian approach reconstructing outbreak data pathogen genome sequences. also implements tool outbreak simulation. outbreakr2: Bayesian framework integrating epidemiological genetic data reconstruct transmission trees densely sampled outbreaks. re-implements, generalises replaces model outbreaker, uses modular approach enables fine customisation priors, likelihoods parameter movements. o2geosocial: integrates geographical social contact data reconstruct transmission chains. combines age group, location, onset date genotype cases infer import status, likely infector. nosoi: simulates agent-based transmission chains taking account influence multiple variables transmission process (e.g. dual-host systems (arboviruses), within-host viral dynamics, transportation, population structure), alone taken together, create complex relatively intuitive epidemiological simulations. TransPhylo: reconstructs infectious disease transmission using genomic data.","code":""},{"path":"https://epiverse-trace.github.io/epichains/index.html","id":"reporting-bugs","dir":"","previous_headings":"","what":"Reporting bugs","title":"Simulating and Analysing Transmission Chain Statistics Using Branching Process Models","text":"report bug please open issue.","code":""},{"path":"https://epiverse-trace.github.io/epichains/index.html","id":"contribute","dir":"","previous_headings":"","what":"Contribute","title":"Simulating and Analysing Transmission Chain Statistics Using Branching Process Models","text":"Contributions {epichains} welcomed. Please follow package contributing guide.","code":""},{"path":"https://epiverse-trace.github.io/epichains/index.html","id":"code-of-conduct","dir":"","previous_headings":"","what":"Code of conduct","title":"Simulating and Analysing Transmission Chain Statistics Using Branching Process Models","text":"Please note epichains project released Contributor Code Conduct. contributing project, agree abide terms.","code":""},{"path":"https://epiverse-trace.github.io/epichains/index.html","id":"citing-this-package","dir":"","previous_headings":"","what":"Citing this package","title":"Simulating and Analysing Transmission Chain Statistics Using Branching Process Models","text":"","code":"citation(\"epichains\") #> To cite package 'epichains' in publications use: #>  #>   Azam J, Funk S, Finger F (2024). _epichains: Simulating and Analysing #>   Transmission Chain Statistics Using Branching Process Models_. R #>   package version 0.1.0, https://epiverse-trace.github.io/epichains/, #>   <https://github.com/epiverse-trace/epichains>. #>  #> A BibTeX entry for LaTeX users is #>  #>   @Manual{, #>     title = {epichains: Simulating and Analysing Transmission Chain Statistics Using #> Branching Process Models}, #>     author = {James M. Azam and Sebastian Funk and Flavio Finger}, #>     year = {2024}, #>     note = {R package version 0.1.0,  #> https://epiverse-trace.github.io/epichains/}, #>     url = {https://github.com/epiverse-trace/epichains}, #>   }"},{"path":"https://epiverse-trace.github.io/epichains/reference/aggregate.epichains.html","id":null,"dir":"Reference","previous_headings":"","what":"Aggregate cases in <epichains> objects by ","title":"Aggregate cases in <epichains> objects by ","text":"function provides quick way create time series cases generation time (generation_time specified) simulated <epichains> objects.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/aggregate.epichains.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Aggregate cases in <epichains> objects by ","text":"","code":"# S3 method for class 'epichains' aggregate(x, by = c(\"time\", \"generation\"), ...)"},{"path":"https://epiverse-trace.github.io/epichains/reference/aggregate.epichains.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Aggregate cases in <epichains> objects by ","text":"x <epichains> object. variable aggregate ; character string options \"time\" \"generation\". ... used.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/aggregate.epichains.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Aggregate cases in <epichains> objects by ","text":"<data.frame> object cases .","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/aggregate.epichains.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Aggregate cases in <epichains> objects by ","text":"James M. Azam","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/aggregate.epichains.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Aggregate cases in <epichains> objects by ","text":"","code":"set.seed(32) chains <- simulate_chains(   n_chains = 10,   statistic = \"size\",   offspring_dist = rpois,   stat_threshold = 10,   generation_time = function(n) rep(3, n),   lambda = 2 ) chains #> `<epichains>` object #>  #> < epichains head (from first known infector) > #>  #>    chain infector infectee generation time #> 11     1        1        2          2    3 #> 12     1        1        3          2    3 #> 13     2        1        2          2    3 #> 14     2        1        3          2    3 #> 15     3        1        2          2    3 #> 16     3        1        3          2    3 #>  #>  #> Number of chains: 10 #> Number of infectors (known): 9 #> Number of generations: 4 #> Use `as.data.frame(<object_name>)` to view the full output in the console.  # Aggregate cases per time cases_per_time <- aggregate(chains, by = \"time\") head(cases_per_time) #>   time cases #> 1    0    10 #> 2    3    25 #> 3    6    61 #> 4    9    33  # Aggregate cases per generation cases_per_gen <- aggregate(chains, by = \"generation\") head(cases_per_gen) #>   generation cases #> 1          1    10 #> 2          2    25 #> 3          3    61 #> 4          4    33"},{"path":"https://epiverse-trace.github.io/epichains/reference/covid19_sa.html","id":null,"dir":"Reference","previous_headings":"","what":"COVID-19 Data Repository for South Africa — covid19_sa","title":"COVID-19 Data Repository for South Africa — covid19_sa","text":"aggregated subset COVID-19 Data Repository South Africa created, maintained hosted Data Science Social Impact research group, led Dr. Vukosi Marivate.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/covid19_sa.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"COVID-19 Data Repository for South Africa — covid19_sa","text":"","code":"covid19_sa"},{"path":[]},{"path":"https://epiverse-trace.github.io/epichains/reference/covid19_sa.html","id":"covid-sa","dir":"Reference","previous_headings":"","what":"covid19_sa","title":"COVID-19 Data Repository for South Africa — covid19_sa","text":"data frame 19 rows 2 columns: date Date case reported cases Number cases","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/covid19_sa.html","id":"source","dir":"Reference","previous_headings":"","what":"Source","title":"COVID-19 Data Repository for South Africa — covid19_sa","text":"https://github.com/dsfsi/covid19za details data-raw/covid19_sa.R.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/covid19_sa.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"COVID-19 Data Repository for South Africa — covid19_sa","text":"data originally provided linelist subsetted cleaned data-raw/covid19_sa.R.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dborel.html","id":null,"dir":"Reference","previous_headings":"","what":"Density of the Borel distribution — dborel","title":"Density of the Borel distribution — dborel","text":"Density Borel distribution","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dborel.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Density of the Borel distribution — dborel","text":"","code":"dborel(x, mu, log = FALSE)"},{"path":"https://epiverse-trace.github.io/epichains/reference/dborel.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Density of the Borel distribution — dborel","text":"x numeric vector quantiles. mu non-negative number poisson mean. log Logical; TRUE, probabilities p given log(p).","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dborel.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Density of the Borel distribution — dborel","text":"numeric vector borel probability density.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dborel.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Density of the Borel distribution — dborel","text":"Sebastian Funk","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dborel.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Density of the Borel distribution — dborel","text":"","code":"set.seed(32) dborel(1:5, 1) #> [1] 0.36787944 0.13533528 0.07468060 0.04884170 0.03509347"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-adjust_next_gen.html","id":null,"dir":"Reference","previous_headings":"","what":"Adjust new offspring if it exceeds the susceptible population size — .adjust_next_gen","title":"Adjust new offspring if it exceeds the susceptible population size — .adjust_next_gen","text":"function used internally, input checking performed , context used. Using directly recommended.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-adjust_next_gen.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Adjust new offspring if it exceeds the susceptible population size — .adjust_next_gen","text":"","code":".adjust_next_gen(next_gen, susc_pop)"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-adjust_next_gen.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Adjust new offspring if it exceeds the susceptible population size — .adjust_next_gen","text":"next_gen numeric vector next generation offspring. susc_pop susceptible population size; number coercible integer.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-adjust_next_gen.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Adjust new offspring if it exceeds the susceptible population size — .adjust_next_gen","text":"numeric vector adjusted next generation offspring.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-check_generation_time_valid.html","id":null,"dir":"Reference","previous_headings":"","what":"Check if the generation_time argument is specified as a function — .check_generation_time_valid","title":"Check if the generation_time argument is specified as a function — .check_generation_time_valid","text":"Check generation_time argument specified function","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-check_generation_time_valid.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Check if the generation_time argument is specified as a function — .check_generation_time_valid","text":"","code":".check_generation_time_valid(generation_time)"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-check_generation_time_valid.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Check if the generation_time argument is specified as a function — .check_generation_time_valid","text":"generation_time generation time function; name user-defined named anonymous function one argument n, representing number generation times sample.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-check_offspring_func_valid.html","id":null,"dir":"Reference","previous_headings":"","what":"Check if constructed random number generator for offspring exists and has an n argument. — .check_offspring_func_valid","title":"Check if constructed random number generator for offspring exists and has an n argument. — .check_offspring_func_valid","text":"Check constructed random number generator offspring exists n argument.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-check_offspring_func_valid.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Check if constructed random number generator for offspring exists and has an n argument. — .check_offspring_func_valid","text":"","code":".check_offspring_func_valid(offspring_dist)"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-check_offspring_func_valid.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Check if constructed random number generator for offspring exists and has an n argument. — .check_offspring_func_valid","text":"offspring_dist Offspring distribution: <function> like ones provided R generate random numbers given distributions (e.g., rpois Poisson). specifically, function needs accept least one argument, n, number random numbers generate. can accept arguments, passed random number generating functions. Examples can provided rpois Poisson distributed offspring, rnbinom negative binomial offspring, custom functions.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-check_sim_args.html","id":null,"dir":"Reference","previous_headings":"","what":"Check inputs to simulate_chains() and simulate_summary() — .check_sim_args","title":"Check inputs to simulate_chains() and simulate_summary() — .check_sim_args","text":"Check inputs simulate_chains() simulate_summary()","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-check_sim_args.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Check inputs to simulate_chains() and simulate_summary() — .check_sim_args","text":"","code":".check_sim_args(   n_chains,   statistic,   offspring_dist,   stat_threshold,   pop,   percent_immune )"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-check_sim_args.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Check inputs to simulate_chains() and simulate_summary() — .check_sim_args","text":"n_chains Number chains simulate. statistic chain statistic track stopping criteria chain simulated stat_threshold Inf; <string>. can one : \"size\": total number cases produced chain goes extinct. \"length\": total number generations reached chain goes extinct. offspring_dist Offspring distribution: <function> like ones provided R generate random numbers given distributions (e.g., rpois Poisson). specifically, function needs accept least one argument, n, number random numbers generate. can accept arguments, passed random number generating functions. Examples can provided rpois Poisson distributed offspring, rnbinom negative binomial offspring, custom functions. stat_threshold stopping criterion individual chain simulations; positive number coercible integer. chain's cumulative statistic reaches surpasses stat_threshold, chain ends. Defaults Inf. example, statistic = \"size\" stat_threshold = 10, chain produces 10 cases stop. Note setting stat_threshold guarantee chains stop value. pop Population size; <Integer>. Used alongside percent_immune define susceptible population. Defaults Inf. percent_immune Percent population immune infection start simulation; <numeric> 0 1. Used alongside pop initialise susceptible population. Defaults 0.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-check_sim_args.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Check inputs to simulate_chains() and simulate_summary() — .check_sim_args","text":"NULL; called side effects","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-check_statistic_args.html","id":null,"dir":"Reference","previous_headings":"","what":"Check that the statistic and stat_threshold arguments are valid — .check_statistic_args","title":"Check that the statistic and stat_threshold arguments are valid — .check_statistic_args","text":"function treats two arguments related checks one place remove repeated checks several places package.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-check_statistic_args.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Check that the statistic and stat_threshold arguments are valid — .check_statistic_args","text":"","code":".check_statistic_args(statistic, stat_threshold)"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-check_statistic_args.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Check that the statistic and stat_threshold arguments are valid — .check_statistic_args","text":"statistic chain statistic track stopping criteria chain simulated stat_threshold Inf; <string>. can one : \"size\": total number cases produced chain goes extinct. \"length\": total number generations reached chain goes extinct. stat_threshold stopping criterion individual chain simulations; positive number coercible integer. chain's cumulative statistic reaches surpasses stat_threshold, chain ends. Defaults Inf. example, statistic = \"size\" stat_threshold = 10, chain produces 10 cases stop. Note setting stat_threshold guarantee chains stop value.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-check_statistic_args.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Check that the statistic and stat_threshold arguments are valid — .check_statistic_args","text":"NULL; called side effects","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-check_time_args.html","id":null,"dir":"Reference","previous_headings":"","what":"Check inputs that control time events — .check_time_args","title":"Check inputs that control time events — .check_time_args","text":"function checks time-related inputs, .e., start time chain, t0, end time simulation, tf, generation time, generation_time. also checks generation_time argument specified tf specified go hand--hand.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-check_time_args.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Check inputs that control time events — .check_time_args","text":"","code":".check_time_args(tf_specified, tf, generation_time, t0)"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-check_time_args.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Check inputs that control time events — .check_time_args","text":"tf_specified <logical>; Whether tf argument specified. makes sense context function called, .e., simulate_chains(). tf specified, generation_time must specified. tf number cut-infection times (generation time given); Defaults Inf. generation_time generation time function; name user-defined named anonymous function one argument n, representing number generation times sample. t0 Start time (generation time given); either single value vector length n_chains (number initial cases) corresponding initial times. Defaults 0, meaning cases started time 0.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-check_time_args.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Check inputs that control time events — .check_time_args","text":"NULL; called side effects","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-complementary_logprob.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculates the complementary log-probability — .complementary_logprob","title":"Calculates the complementary log-probability — .complementary_logprob","text":"Given x norm, calculates log(1-sum(exp(x)))","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-complementary_logprob.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculates the complementary log-probability — .complementary_logprob","text":"","code":".complementary_logprob(x)"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-complementary_logprob.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculates the complementary log-probability — .complementary_logprob","text":"x numeric vector log-probabilities. Must negative.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-complementary_logprob.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculates the complementary log-probability — .complementary_logprob","text":"numeric value complementary log-probability.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-complementary_logprob.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Calculates the complementary log-probability — .complementary_logprob","text":"Sebastian Funk","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-epichains.html","id":null,"dir":"Reference","previous_headings":"","what":"Create an <epichains> object — .epichains","title":"Create an <epichains> object — .epichains","text":"epichains() constructs <epichains> object, inherently <data.frame> object stores inputs passed simulate_chains() simulated output. stored attributes useful downstream analyses reproducibility. function checks validity object created ensure right columns column types. <epichains> object contains <data.frame> simulated outbreak ids infector infectee, generation, optionally, time, number chains simulated, chain statistic tracked, whether susceptible population tracked.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-epichains.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Create an <epichains> object — .epichains","text":"","code":".epichains(   sim_df,   n_chains,   offspring_dist,   track_pop,   statistic = c(\"size\", \"length\"), stat_threshold = Inf )"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-epichains.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Create an <epichains> object — .epichains","text":"sim_df <data.frame> containing least columns \"infectee_id\", \"infector_id\", \"generation\". Also optional columns \"time\", \"chain_id\". n_chains Number chains simulate. offspring_dist Offspring distribution: <function> like ones provided R generate random numbers given distributions (e.g., rpois Poisson). specifically, function needs accept least one argument, n, number random numbers generate. can accept arguments, passed random number generating functions. Examples can provided rpois Poisson distributed offspring, rnbinom negative binomial offspring, custom functions. track_pop susceptible population tracked? Logical. statistic chain statistic track stopping criteria chain simulated stat_threshold Inf; <string>. can one : \"size\": total number cases produced chain goes extinct. \"length\": total number generations reached chain goes extinct. stat_threshold stopping criterion individual chain simulations; positive number coercible integer. chain's cumulative statistic reaches surpasses stat_threshold, chain ends. Defaults Inf. example, statistic = \"size\" stat_threshold = 10, chain produces 10 cases stop. Note setting stat_threshold guarantee chains stop value.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-epichains.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Create an <epichains> object — .epichains","text":"<epichains> object.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-epichains.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Create an <epichains> object — .epichains","text":"James M. Azam","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-epichains_summary.html","id":null,"dir":"Reference","previous_headings":"","what":"Create an <epichains_summary> object — .epichains_summary","title":"Create an <epichains_summary> object — .epichains_summary","text":"epichains_summary() constructs <epichains_summary> object. <epichains_summary> object <vector> simulated chain sizes lengths. also stores information number chains simulated, statistic tracked.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-epichains_summary.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Create an <epichains_summary> object — .epichains_summary","text":"","code":".epichains_summary(   chains_summary,   n_chains,   offspring_dist,   statistic = c(\"size\", \"length\"), stat_threshold = Inf )"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-epichains_summary.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Create an <epichains_summary> object — .epichains_summary","text":"chains_summary numeric <vector> chain sizes lengths. n_chains Number chains simulate. offspring_dist Offspring distribution: <function> like ones provided R generate random numbers given distributions (e.g., rpois Poisson). specifically, function needs accept least one argument, n, number random numbers generate. can accept arguments, passed random number generating functions. Examples can provided rpois Poisson distributed offspring, rnbinom negative binomial offspring, custom functions. statistic chain statistic track stopping criteria chain simulated stat_threshold Inf; <string>. can one : \"size\": total number cases produced chain goes extinct. \"length\": total number generations reached chain goes extinct. stat_threshold stopping criterion individual chain simulations; positive number coercible integer. chain's cumulative statistic reaches surpasses stat_threshold, chain ends. also serves censoring limit results specified value, set Inf. Defaults Inf.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-epichains_summary.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Create an <epichains_summary> object — .epichains_summary","text":"<epichains_summary> object.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-epichains_summary.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Create an <epichains_summary> object — .epichains_summary","text":"James M. Azam","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-gborel_size_ll.html","id":null,"dir":"Reference","previous_headings":"","what":"Log-likelihood of the size of chains with gamma-Borel offspring distribution — .gborel_size_ll","title":"Log-likelihood of the size of chains with gamma-Borel offspring distribution — .gborel_size_ll","text":"Log-likelihood size chains gamma-Borel offspring distribution","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-gborel_size_ll.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Log-likelihood of the size of chains with gamma-Borel offspring distribution — .gborel_size_ll","text":"","code":".gborel_size_ll(x, size, prob, mu)"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-gborel_size_ll.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Log-likelihood of the size of chains with gamma-Borel offspring distribution — .gborel_size_ll","text":"x numeric vector chain sizes. size dispersion parameter (often called k ecological applications); positive number. prob Probability success (parameterisation prob, see also NegBinomial); number 0 1. mu Mean; positive number.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-gborel_size_ll.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Log-likelihood of the size of chains with gamma-Borel offspring distribution — .gborel_size_ll","text":"numeric vector log-likelihood values.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-gborel_size_ll.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Log-likelihood of the size of chains with gamma-Borel offspring distribution — .gborel_size_ll","text":"Sebastian Funk","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-geom_length_ll.html","id":null,"dir":"Reference","previous_headings":"","what":"Log-likelihood of the length of chains with geometric offspring distribution — .geom_length_ll","title":"Log-likelihood of the length of chains with geometric offspring distribution — .geom_length_ll","text":"Log-likelihood length chains geometric offspring distribution","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-geom_length_ll.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Log-likelihood of the length of chains with geometric offspring distribution — .geom_length_ll","text":"","code":".geom_length_ll(x, prob)"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-geom_length_ll.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Log-likelihood of the length of chains with geometric offspring distribution — .geom_length_ll","text":"x numeric vector chain lengths. prob probability geometric distribution mean 1/prob. single numeric value 0 1.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-geom_length_ll.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Log-likelihood of the length of chains with geometric offspring distribution — .geom_length_ll","text":"numeric vector log-likelihood values.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-geom_length_ll.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Log-likelihood of the length of chains with geometric offspring distribution — .geom_length_ll","text":"Sebastian Funk","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-get_statistic_func.html","id":null,"dir":"Reference","previous_headings":"","what":"Return a function for calculating chain statistics — .get_statistic_func","title":"Return a function for calculating chain statistics — .get_statistic_func","text":"Return function calculating chain statistics","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-get_statistic_func.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Return a function for calculating chain statistics — .get_statistic_func","text":"","code":".get_statistic_func(chain_statistic)"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-get_statistic_func.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Return a function for calculating chain statistics — .get_statistic_func","text":"function calculating chain statistics.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-get_susceptible_offspring.html","id":null,"dir":"Reference","previous_headings":"","what":"Sample the number of susceptible offspring from all possible offspring — .get_susceptible_offspring","title":"Sample the number of susceptible offspring from all possible offspring — .get_susceptible_offspring","text":"Sample susceptible offspring infected possible offspring. function used internally, input checking performed , context used. Using directly recommended.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-get_susceptible_offspring.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Sample the number of susceptible offspring from all possible offspring — .get_susceptible_offspring","text":"","code":".get_susceptible_offspring(new_offspring, susc_pop, pop)"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-get_susceptible_offspring.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Sample the number of susceptible offspring from all possible offspring — .get_susceptible_offspring","text":"new_offspring numeric vector possible new offspring per chain produced .sample_possible_offspring(). pop Population size; <Integer>. Used alongside percent_immune define susceptible population. Defaults Inf.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-get_susceptible_offspring.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Sample the number of susceptible offspring from all possible offspring — .get_susceptible_offspring","text":"numeric vector number offspring can infected given current susceptible population size.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-init_susc_pop.html","id":null,"dir":"Reference","previous_headings":"","what":"Adjust next generation vector to match susceptible population size — .init_susc_pop","title":"Adjust next generation vector to match susceptible population size — .init_susc_pop","text":"Calculates initial susceptible population size given total population size, percent immune, number index cases. function used internally, input checking performed , context used. Using directly recommended.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-init_susc_pop.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Adjust next generation vector to match susceptible population size — .init_susc_pop","text":"","code":".init_susc_pop(pop, percent_immune, index_cases)"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-init_susc_pop.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Adjust next generation vector to match susceptible population size — .init_susc_pop","text":"pop Population size; <Integer>. Used alongside percent_immune define susceptible population. Defaults Inf. percent_immune Percent population immune infection start simulation; <numeric> 0 1. Used alongside pop initialise susceptible population. Defaults 0.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-init_susc_pop.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Adjust next generation vector to match susceptible population size — .init_susc_pop","text":"Initial susceptible population size; numeric coercible integer.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-is_epichains.html","id":null,"dir":"Reference","previous_headings":"","what":"Test if x is an epichains object — .is_epichains","title":"Test if x is an epichains object — .is_epichains","text":"Test x epichains object","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-is_epichains.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Test if x is an epichains object — .is_epichains","text":"","code":".is_epichains(x)"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-is_epichains.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Test if x is an epichains object — .is_epichains","text":"x R object.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-is_epichains.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Test if x is an epichains object — .is_epichains","text":"Logical; TRUE object <epichains> FALSE otherwise.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-is_epichains.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Test if x is an epichains object — .is_epichains","text":"James M. Azam","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-is_epichains_summary.html","id":null,"dir":"Reference","previous_headings":"","what":"Test if x is an epichains_summary object — .is_epichains_summary","title":"Test if x is an epichains_summary object — .is_epichains_summary","text":"Test x epichains_summary object","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-is_epichains_summary.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Test if x is an epichains_summary object — .is_epichains_summary","text":"","code":".is_epichains_summary(x)"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-is_epichains_summary.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Test if x is an epichains_summary object — .is_epichains_summary","text":"x R object.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-is_epichains_summary.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Test if x is an epichains_summary object — .is_epichains_summary","text":"Logical; TRUE object <epichains_summary> FALSE otherwise.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-is_epichains_summary.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Test if x is an epichains_summary object — .is_epichains_summary","text":"James M. Azam","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-nbinom_size_ll.html","id":null,"dir":"Reference","previous_headings":"","what":"Log-likelihood of the size of chains with Negative-Binomial offspring distribution — .nbinom_size_ll","title":"Log-likelihood of the size of chains with Negative-Binomial offspring distribution — .nbinom_size_ll","text":"Log-likelihood size chains Negative-Binomial offspring distribution","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-nbinom_size_ll.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Log-likelihood of the size of chains with Negative-Binomial offspring distribution — .nbinom_size_ll","text":"","code":".nbinom_size_ll(x, size, prob, mu)"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-nbinom_size_ll.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Log-likelihood of the size of chains with Negative-Binomial offspring distribution — .nbinom_size_ll","text":"x numeric vector chain sizes. size dispersion parameter (often called k ecological applications); positive number. prob Probability success (parameterisation prob, see also NegBinomial); number 0 1. mu Mean; positive number.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-nbinom_size_ll.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Log-likelihood of the size of chains with Negative-Binomial offspring distribution — .nbinom_size_ll","text":"numeric vector log-likelihood values.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-nbinom_size_ll.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Log-likelihood of the size of chains with Negative-Binomial offspring distribution — .nbinom_size_ll","text":"Sebastian Funk","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-new_epichains.html","id":null,"dir":"Reference","previous_headings":"","what":"Construct an <epichains> object — .new_epichains","title":"Construct an <epichains> object — .new_epichains","text":"new_epichains() constructs <epichains> object supplied <data.frame> extra attributes passed individual arguments. meant lazy performant, creating object without checking arguments correctness. safe call new_epichains() called within epichains() arguments checked. create <epichains> object, use epichains().","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-new_epichains.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Construct an <epichains> object — .new_epichains","text":"","code":".new_epichains(   sim_df,   n_chains,   statistic,   offspring_dist,   stat_threshold,   track_pop )"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-new_epichains.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Construct an <epichains> object — .new_epichains","text":"sim_df <data.frame> containing least columns \"infectee_id\", \"infector_id\", \"generation\". Also optional columns \"time\", \"chain_id\". n_chains Number chains simulate. statistic chain statistic track stopping criteria chain simulated stat_threshold Inf; <string>. can one : \"size\": total number cases produced chain goes extinct. \"length\": total number generations reached chain goes extinct. offspring_dist Offspring distribution: <function> like ones provided R generate random numbers given distributions (e.g., rpois Poisson). specifically, function needs accept least one argument, n, number random numbers generate. can accept arguments, passed random number generating functions. Examples can provided rpois Poisson distributed offspring, rnbinom negative binomial offspring, custom functions. stat_threshold stopping criterion individual chain simulations; positive number coercible integer. chain's cumulative statistic reaches surpasses stat_threshold, chain ends. Defaults Inf. example, statistic = \"size\" stat_threshold = 10, chain produces 10 cases stop. Note setting stat_threshold guarantee chains stop value. track_pop susceptible population tracked? Logical.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-new_epichains.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Construct an <epichains> object — .new_epichains","text":"James M. Azam","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-new_epichains_summary.html","id":null,"dir":"Reference","previous_headings":"","what":"Construct a <epichains_summary> object — .new_epichains_summary","title":"Construct a <epichains_summary> object — .new_epichains_summary","text":"new_epichains_summary() constructs <epichains_summary> object supplied <vector> chain sizes lengths. also stores extra attributes passed individual arguments. new_epichains_summary() meant lazy performant, creating object without checking arguments correctness. safe call new_epichains_summary() called within epichains_summary() arguments checked. create new <epichains_summary> object safely, use epichains_summary().","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-new_epichains_summary.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Construct a <epichains_summary> object — .new_epichains_summary","text":"","code":".new_epichains_summary(   chains_summary,   n_chains,   statistic,   offspring_dist,   stat_threshold )"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-new_epichains_summary.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Construct a <epichains_summary> object — .new_epichains_summary","text":"chains_summary numeric <vector> chain sizes lengths. n_chains Number chains simulate. statistic chain statistic track stopping criteria chain simulated stat_threshold Inf; <string>. can one : \"size\": total number cases produced chain goes extinct. \"length\": total number generations reached chain goes extinct. offspring_dist Offspring distribution: <function> like ones provided R generate random numbers given distributions (e.g., rpois Poisson). specifically, function needs accept least one argument, n, number random numbers generate. can accept arguments, passed random number generating functions. Examples can provided rpois Poisson distributed offspring, rnbinom negative binomial offspring, custom functions. stat_threshold stopping criterion individual chain simulations; positive number coercible integer. chain's cumulative statistic reaches surpasses stat_threshold, chain ends. also serves censoring limit results specified value, set Inf. Defaults Inf.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-new_epichains_summary.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Construct a <epichains_summary> object — .new_epichains_summary","text":"James M. Azam","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-offspring_ll.html","id":null,"dir":"Reference","previous_headings":"","what":"Log-likelihood of the summary (size/length) of chains with generic offspring distribution — .offspring_ll","title":"Log-likelihood of the summary (size/length) of chains with generic offspring distribution — .offspring_ll","text":"log-likelihoods calculated crude approximation using simulated chain summaries linearly approximating missing values empirical cumulative distribution function (ecdf).","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-offspring_ll.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Log-likelihood of the summary (size/length) of chains with generic offspring distribution — .offspring_ll","text":"","code":".offspring_ll(x, offspring_dist, statistic, nsim_offspring = 100, ...)"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-offspring_ll.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Log-likelihood of the summary (size/length) of chains with generic offspring distribution — .offspring_ll","text":"x numeric vector chain summaries (sizes/lengths). offspring_dist Offspring distribution: <function> like ones provided R generate random numbers given distributions (e.g., rpois Poisson). specifically, function needs accept least one argument, n, number random numbers generate. can accept arguments, passed random number generating functions. Examples can provided rpois Poisson distributed offspring, rnbinom negative binomial offspring, custom functions. statistic chain statistic track stopping criteria chain simulated stat_threshold Inf; <string>. can one : \"size\": total number cases produced chain goes extinct. \"length\": total number generations reached chain goes extinct. nsim_offspring Number simulations offspring distribution approximating distribution chain statistic summary (size/length) ... parameters pass simulate_chain_stats","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-offspring_ll.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Log-likelihood of the summary (size/length) of chains with generic offspring distribution — .offspring_ll","text":"numeric vector log-likelihood values.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-offspring_ll.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Log-likelihood of the summary (size/length) of chains with generic offspring distribution — .offspring_ll","text":"Sebastian Funk","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-pois_length_ll.html","id":null,"dir":"Reference","previous_headings":"","what":"Log-likelihood of the length of chains with Poisson offspring distribution — .pois_length_ll","title":"Log-likelihood of the length of chains with Poisson offspring distribution — .pois_length_ll","text":"Log-likelihood length chains Poisson offspring distribution","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-pois_length_ll.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Log-likelihood of the length of chains with Poisson offspring distribution — .pois_length_ll","text":"","code":".pois_length_ll(x, lambda)"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-pois_length_ll.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Log-likelihood of the length of chains with Poisson offspring distribution — .pois_length_ll","text":"x numeric vector chain lengths. lambda rate Poisson distribution. single numeric value. Must positive.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-pois_length_ll.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Log-likelihood of the length of chains with Poisson offspring distribution — .pois_length_ll","text":"numeric vector log-likelihood values.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-pois_length_ll.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Log-likelihood of the length of chains with Poisson offspring distribution — .pois_length_ll","text":"Sebastian Funk","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-pois_size_ll.html","id":null,"dir":"Reference","previous_headings":"","what":"Log-likelihood of the size of chains with Poisson offspring distribution — .pois_size_ll","title":"Log-likelihood of the size of chains with Poisson offspring distribution — .pois_size_ll","text":"Log-likelihood size chains Poisson offspring distribution","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-pois_size_ll.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Log-likelihood of the size of chains with Poisson offspring distribution — .pois_size_ll","text":"","code":".pois_size_ll(x, lambda)"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-pois_size_ll.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Log-likelihood of the size of chains with Poisson offspring distribution — .pois_size_ll","text":"x numeric vector sizes lambda rate Poisson distribution; single numeric value.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-pois_size_ll.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Log-likelihood of the size of chains with Poisson offspring distribution — .pois_size_ll","text":"numeric vector log-likelihood values.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-pois_size_ll.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Log-likelihood of the size of chains with Poisson offspring distribution — .pois_size_ll","text":"Sebastian Funk","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-rbinom_size.html","id":null,"dir":"Reference","previous_headings":"","what":"Samples size (the number of trials) of a binomial distribution — .rbinom_size","title":"Samples size (the number of trials) of a binomial distribution — .rbinom_size","text":"Samples size parameter binomial distribution fixed x (number successes) p (success probability)","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-rbinom_size.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Samples size (the number of trials) of a binomial distribution — .rbinom_size","text":"","code":".rbinom_size(n, x, prob)"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-rbinom_size.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Samples size (the number of trials) of a binomial distribution — .rbinom_size","text":"n number samples generate. Must positive integer. x number successes. Must positive integer. prob probability success. numeric 0 1.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-rbinom_size.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Samples size (the number of trials) of a binomial distribution — .rbinom_size","text":"numeric vector sampled sizes.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-rbinom_size.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Samples size (the number of trials) of a binomial distribution — .rbinom_size","text":"Sebastian Funk","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-rgen_length.html","id":null,"dir":"Reference","previous_headings":"","what":"Samples chain lengths with given observation probabilities — .rgen_length","title":"Samples chain lengths with given observation probabilities — .rgen_length","text":"Samples length transmission chain individual element observed binomial probability parameters n (number successes) p (success probability)","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-rgen_length.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Samples chain lengths with given observation probabilities — .rgen_length","text":"","code":".rgen_length(n, x, prob)"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-rgen_length.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Samples chain lengths with given observation probabilities — .rgen_length","text":"n number samples generate. Must positive integer. x numeric vector observed chain lengths. prob probability observation. numeric 0 1.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-rgen_length.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Samples chain lengths with given observation probabilities — .rgen_length","text":"numeric vector sampled chain lengths.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-rgen_length.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Samples chain lengths with given observation probabilities — .rgen_length","text":"Sebastian Funk","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-sample_possible_offspring.html","id":null,"dir":"Reference","previous_headings":"","what":"Sample all possible offspring for the next generation — .sample_possible_offspring","title":"Sample all possible offspring for the next generation — .sample_possible_offspring","text":"Sample next generation offspring using offspring distribution associated parameters. function used internally, input checking performed , context used. Using directly recommended.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-sample_possible_offspring.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Sample all possible offspring for the next generation — .sample_possible_offspring","text":"","code":".sample_possible_offspring(   offspring_func,   offspring_func_pars,   n_offspring,   chains )"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-sample_possible_offspring.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Sample all possible offspring for the next generation — .sample_possible_offspring","text":"offspring_func function sample offspring. offspring_func_pars list parameters offspring function. n_offspring numeric vector number offspring per chain. chains Numeric indices chains/infectors simulated","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-sample_possible_offspring.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Sample all possible offspring for the next generation — .sample_possible_offspring","text":"numeric vector number offspring per chain.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-update_chain_stat.html","id":null,"dir":"Reference","previous_headings":"","what":"Determine and update the chain statistic being tracked — .update_chain_stat","title":"Determine and update the chain statistic being tracked — .update_chain_stat","text":"Determine update chain statistic tracked","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-update_chain_stat.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Determine and update the chain statistic being tracked — .update_chain_stat","text":"","code":".update_chain_stat(stat_type, stat_latest, n_offspring)"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-update_chain_stat.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Determine and update the chain statistic being tracked — .update_chain_stat","text":"stat_type Chain statistic (size/length) update; character string. Must one 'size' 'length'. stat_latest latest chain statistic numeric vector updated. n_offspring vector offspring per chain. numeric vector (coercible integer).","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-update_chain_stat.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Determine and update the chain statistic being tracked — .update_chain_stat","text":"vector chain statistics (size/length). numeric vector coercible integer.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-validate_epichains.html","id":null,"dir":"Reference","previous_headings":"","what":"Validate an <epichains> object — .validate_epichains","title":"Validate an <epichains> object — .validate_epichains","text":"Validate <epichains> object","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-validate_epichains.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Validate an <epichains> object — .validate_epichains","text":"","code":".validate_epichains(x)"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-validate_epichains.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Validate an <epichains> object — .validate_epichains","text":"x <epichains> object.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-validate_epichains.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Validate an <epichains> object — .validate_epichains","text":"Invisibly returns object valid.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-validate_epichains.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Validate an <epichains> object — .validate_epichains","text":"James M. Azam","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-validate_epichains_summary.html","id":null,"dir":"Reference","previous_headings":"","what":"Validate an <epichains_summary> object — .validate_epichains_summary","title":"Validate an <epichains_summary> object — .validate_epichains_summary","text":"Validate <epichains_summary> object","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-validate_epichains_summary.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Validate an <epichains_summary> object — .validate_epichains_summary","text":"","code":".validate_epichains_summary(x)"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-validate_epichains_summary.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Validate an <epichains_summary> object — .validate_epichains_summary","text":"x <epichains_summary> object.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-validate_epichains_summary.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Validate an <epichains_summary> object — .validate_epichains_summary","text":"Invisibly returns object valid.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-validate_epichains_summary.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Validate an <epichains_summary> object — .validate_epichains_summary","text":"James M. Azam","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/epichains-package.html","id":null,"dir":"Reference","previous_headings":"","what":"epichains: Simulating and Analysing Transmission Chain Statistics Using Branching Process Models — epichains-package","title":"epichains: Simulating and Analysing Transmission Chain Statistics Using Branching Process Models — epichains-package","text":"Provides methods simulate analyse size length branching processes arbitrary offspring distribution. can used, example, analyse distribution chain sizes length infectious disease outbreaks, discussed Farrington et al. (2003) doi:10.1093/biostatistics/4.2.279 .","code":""},{"path":[]},{"path":"https://epiverse-trace.github.io/epichains/reference/epichains-package.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"epichains: Simulating and Analysing Transmission Chain Statistics Using Branching Process Models — epichains-package","text":"Maintainer: James M. Azam james.azam@lshtm.ac.uk (ORCID) [copyright holder] Authors: Sebastian Funk sebastian.funk@lshtm.ac.uk (ORCID) Flavio Finger flavio.finger@epicentre.msf.org (ORCID) contributors: Zhian N. Kamvar zkamvar@gmail.com (ORCID) [contributor] Hugo Gruson hugo@data.org (ORCID) [contributor, reviewer] Karim Mané karim.mane@lshtm.ac.uk (ORCID) [reviewer] Pratik Gupte pratik.gupte@lshtm.ac.uk (ORCID) [reviewer] Joshua W. Lambert joshua.lambert@lshtm.ac.uk (ORCID) [reviewer]","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/head.epichains.html","id":null,"dir":"Reference","previous_headings":"","what":"head and tail method for <epichains> class — head.epichains","title":"head and tail method for <epichains> class — head.epichains","text":"head tail method <epichains> class","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/head.epichains.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"head and tail method for <epichains> class — head.epichains","text":"","code":"# S3 method for class 'epichains' head(x, ...)  # S3 method for class 'epichains' tail(x, ...)"},{"path":"https://epiverse-trace.github.io/epichains/reference/head.epichains.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"head and tail method for <epichains> class — head.epichains","text":"x <epichains> object. ... arguments passed methods.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/head.epichains.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"head and tail method for <epichains> class — head.epichains","text":"object class <data.frame>.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/head.epichains.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"head and tail method for <epichains> class — head.epichains","text":"returns top rows <epichains> object, starting first known infectors. view full output, use .data.frame(<object_name>).","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/head.epichains.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"head and tail method for <epichains> class — head.epichains","text":"James M. Azam","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/head.epichains.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"head and tail method for <epichains> class — head.epichains","text":"","code":"set.seed(32) chains_pois_offspring <- simulate_chains(   n_chains = 10,   statistic = \"size\",   offspring_dist = rpois,   stat_threshold = 10,   generation_time = function(n) rep(3, n),   lambda = 2 ) head(chains_pois_offspring) #>    chain infector infectee generation time #> 11     1        1        2          2    3 #> 12     1        1        3          2    3 #> 13     2        1        2          2    3 #> 14     2        1        3          2    3 #> 15     3        1        2          2    3 #> 16     3        1        3          2    3 set.seed(32) chains_pois_offspring <- simulate_chains(   n_chains = 10,   statistic = \"size\",   offspring_dist = rpois,   stat_threshold = 10,   generation_time = function(n) rep(3, n),   lambda = 2 ) tail(chains_pois_offspring) #>     chain infector infectee generation time #> 124    10        3        6          4    9 #> 125    10        4        7          4    9 #> 126    10        4        8          4    9 #> 127    10        4        9          4    9 #> 128    10        4       10          4    9 #> 129    10        4       11          4    9"},{"path":"https://epiverse-trace.github.io/epichains/reference/likelihood.html","id":null,"dir":"Reference","previous_headings":"","what":"Estimate the log-likelihood/likelihood for observed branching processes — likelihood","title":"Estimate the log-likelihood/likelihood for observed branching processes — likelihood","text":"Estimate log-likelihood/likelihood observed branching processes","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/likelihood.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Estimate the log-likelihood/likelihood for observed branching processes — likelihood","text":"","code":"likelihood(   chains,   statistic = c(\"size\", \"length\"),   offspring_dist,   nsim_obs,   obs_prob = 1,   stat_threshold = Inf,   log = TRUE,   exclude = NULL,   individual = FALSE,   ... )"},{"path":"https://epiverse-trace.github.io/epichains/reference/likelihood.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Estimate the log-likelihood/likelihood for observed branching processes — likelihood","text":"chains Vector chain summaries (sizes/lengths). Can <numeric> vector object class <epichains> <epichains_summary> (obtained simulate_chains() simulate_chain_stats()). See examples . statistic chain statistic track stopping criteria chain simulated stat_threshold Inf; <string>. can one : \"size\": total number cases produced chain goes extinct. \"length\": total number generations reached chain goes extinct. offspring_dist Offspring distribution: <function> like ones provided R generate random numbers given distributions (e.g., rpois Poisson). specifically, function needs accept least one argument, n, number random numbers generate. can accept arguments, passed random number generating functions. Examples can provided rpois Poisson distributed offspring, rnbinom negative binomial offspring, custom functions. nsim_obs Number simulations used approximate log-likelihood/likelihood obs_prob < 1 (imperfect observation). obs_prob == 1, argument ignored. obs_prob Observation probability. number (probability) 0 1. value greater 0 less 1 implies imperfect observation simulations used approximate (log)likelihood. also require specifying nsim_obs. simulation, observation process assumed constant. stat_threshold stopping criterion individual chain simulations; positive number coercible integer. chain's cumulative statistic reaches surpasses stat_threshold, chain ends. also serves censoring limit results specified value, set Inf. Defaults Inf. NOTE: objects class <epichains> <epichains_summary>, stat_threshold used simulation extracted used argument specified, ignored warning thrown. log log-likelihoods transformed likelihoods? Logical. Defaults TRUE. exclude vector indices sizes/lengths exclude log-likelihood calculation. individual Logical; TRUE, vector individual log-likelihood/likelihood contributions returned rather sum/product. ... parameters pass simulate_chain_stats","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/likelihood.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Estimate the log-likelihood/likelihood for observed branching processes — likelihood","text":"log = TRUE joint log-likelihood (sum individual log-likelihoods), individual == FALSE (default) obs_prob == 1 (default), list individual log-likelihoods, individual == TRUE obs_prob == 1 (default), list individual log-likelihoods (length nsim_obs), individual == TRUE 0 <= obs_prob < 1, vector joint log-likelihoods (length nsim_obs), individual == FALSE 0 <= obs_prob < 1 (imperfect observation). log = FALSE, structure outputs returned, except likelihoods, instead log-likelihoods, calculated cases. Moreover, joint likelihoods product, instead sum, individual likelihoods.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/likelihood.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Estimate the log-likelihood/likelihood for observed branching processes — likelihood","text":"Sebastian Funk, James M. Azam","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/likelihood.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Estimate the log-likelihood/likelihood for observed branching processes — likelihood","text":"","code":"# example of observed chain sizes set.seed(121) # randomly generate 20 chains of size 1 to 10 chain_sizes <- sample(1:10, 20, replace = TRUE) likelihood(   chains = chain_sizes,   statistic = \"size\",   offspring_dist = rpois,   nsim_obs = 100,   lambda = 0.5 ) #> [1] -67.82879 # Example using an <epichains> object set.seed(32) epichains_obj_eg <- simulate_chains(  n_chains = 10,  pop = 100,  percent_immune = 0,  statistic = \"size\",  offspring_dist = rnbinom,  stat_threshold = 10,  generation_time = function(n) rep(3, n),  mu = 2,  size = 0.2 )  epichains_obj_eg_lik <- likelihood(   chains = epichains_obj_eg,   statistic = \"size\",   offspring_dist = rnbinom,   mu = 2,   size = 0.2,   stat_threshold = 10 ) #> Warning: `stat_threshold` specified but will be ignored. Using `stat_threshold` = 10 as used in the simulation. epichains_obj_eg_lik #> [1] -18.97756  # Example using a <epichains_summary> object set.seed(32) epichains_summary_eg <- simulate_chain_stats(   n_chains = 10,   pop = 100,   percent_immune = 0,   statistic = \"size\",   offspring_dist = rnbinom,   stat_threshold = 10,   mu = 2,   size = 0.2 ) epichains_summary_eg_lik <- likelihood(   chains = epichains_summary_eg,   statistic = \"size\",   offspring_dist = rnbinom,   mu = 2,   size = 0.2 ) epichains_summary_eg_lik #> [1] -18.97756"},{"path":"https://epiverse-trace.github.io/epichains/reference/print.epichains.html","id":null,"dir":"Reference","previous_headings":"","what":"Print an <epichains> object — print.epichains","title":"Print an <epichains> object — print.epichains","text":"Print <epichains> object","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/print.epichains.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Print an <epichains> object — print.epichains","text":"","code":"# S3 method for class 'epichains' print(x, ...)"},{"path":"https://epiverse-trace.github.io/epichains/reference/print.epichains.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Print an <epichains> object — print.epichains","text":"x <epichains> object. ... parameters passed print().","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/print.epichains.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Print an <epichains> object — print.epichains","text":"Invisibly returns <epichains>. Called side-effects.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/print.epichains.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Print an <epichains> object — print.epichains","text":"James M. Azam","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/print.epichains.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Print an <epichains> object — print.epichains","text":"","code":"# Using a Poisson offspring distribution and simulating from an infinite # population up to chain size 10. set.seed(32) chains_pois_offspring <- simulate_chains(  n_chains = 10,  statistic = \"size\",  offspring_dist = rpois,  stat_threshold = 10,  generation_time = function(n) rep(3, n),  lambda = 2 ) chains_pois_offspring # Print the object #> `<epichains>` object #>  #> < epichains head (from first known infector) > #>  #>    chain infector infectee generation time #> 11     1        1        2          2    3 #> 12     1        1        3          2    3 #> 13     2        1        2          2    3 #> 14     2        1        3          2    3 #> 15     3        1        2          2    3 #> 16     3        1        3          2    3 #>  #>  #> Number of chains: 10 #> Number of infectors (known): 9 #> Number of generations: 4 #> Use `as.data.frame(<object_name>)` to view the full output in the console."},{"path":"https://epiverse-trace.github.io/epichains/reference/print.epichains_summary.html","id":null,"dir":"Reference","previous_headings":"","what":"Print an <epichains_summary> object — print.epichains_summary","title":"Print an <epichains_summary> object — print.epichains_summary","text":"Prints summary <epichains_summary> object. particular, prints number chains simulated, range statistic, represented maximum (max_stat) minimum (min_stat). minimum maximum infinite, represented >= stat_threshold stat_threshold value censoring limit. See ?epichains_summary() definition stat_threshold.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/print.epichains_summary.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Print an <epichains_summary> object — print.epichains_summary","text":"","code":"# S3 method for class 'epichains_summary' print(x, ...)"},{"path":"https://epiverse-trace.github.io/epichains/reference/print.epichains_summary.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Print an <epichains_summary> object — print.epichains_summary","text":"x <epichains_summary> object. ... used.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/print.epichains_summary.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Print an <epichains_summary> object — print.epichains_summary","text":"Invisibly returns <epichains_summary>. Called side-effects.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/print.epichains_summary.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Print an <epichains_summary> object — print.epichains_summary","text":"James M. Azam","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/print.epichains_summary.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Print an <epichains_summary> object — print.epichains_summary","text":"","code":"# Using a Poisson offspring distribution and simulating from an infinite # population up to chain size 10. set.seed(32) chain_summary_print_eg <- simulate_chain_stats(  n_chains = 10,  statistic = \"size\",  offspring_dist = rpois,  stat_threshold = 10,  lambda = 2 ) chain_summary_print_eg # Print the object #> `epichains_summary` object  #>  #>  [1] Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf #>  #>  Simulated sizes:  #>  #> Max: >=10 #> Min: >=10"},{"path":"https://epiverse-trace.github.io/epichains/reference/rborel.html","id":null,"dir":"Reference","previous_headings":"","what":"Generate random numbers from the Borel distribution — rborel","title":"Generate random numbers from the Borel distribution — rborel","text":"Random numbers generated simulating Poisson branching process","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/rborel.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Generate random numbers from the Borel distribution — rborel","text":"","code":"rborel(n, mu, censor_at = Inf)"},{"path":"https://epiverse-trace.github.io/epichains/reference/rborel.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Generate random numbers from the Borel distribution — rborel","text":"n Number random variates generate. mu non-negative number poisson mean. censor_at stopping criterion; <numeric>. Defaults Inf. value simulation ends random number set Inf (form censoring). rborel() simulates chain sizes using simulate_chain_stats() Poisson offspring distribution, mu >= 1, simulation proceed unendingly. parameter used prevent .","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/rborel.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Generate random numbers from the Borel distribution — rborel","text":"numeric vector random numbers.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/rborel.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Generate random numbers from the Borel distribution — rborel","text":"Sebastian Funk","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/rborel.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Generate random numbers from the Borel distribution — rborel","text":"","code":"set.seed(32) rborel(5, 1) #> [1]  25  50 114   5   1"},{"path":"https://epiverse-trace.github.io/epichains/reference/rgborel.html","id":null,"dir":"Reference","previous_headings":"","what":"Generate random numbers from a Gamma-Borel mixture distribution — rgborel","title":"Generate random numbers from a Gamma-Borel mixture distribution — rgborel","text":"Generate random numbers Gamma-Borel mixture distribution","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/rgborel.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Generate random numbers from a Gamma-Borel mixture distribution — rgborel","text":"","code":"rgborel(n, size, prob, mu, censor_at = Inf)"},{"path":"https://epiverse-trace.github.io/epichains/reference/rgborel.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Generate random numbers from a Gamma-Borel mixture distribution — rgborel","text":"n Number random variates generate. size dispersion parameter (often called k ecological applications); positive number. prob Probability success (parameterisation prob, see also NegBinomial); number 0 1. mu Mean; positive number. censor_at stopping criterion; <numeric>. Defaults Inf. value simulation ends random number set Inf (form censoring). rborel() simulates chain sizes using simulate_chain_stats() Poisson offspring distribution, mu >= 1, simulation proceed unendingly. parameter used prevent .","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/rgborel.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Generate random numbers from a Gamma-Borel mixture distribution — rgborel","text":"Numeric vector random numbers","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/rgborel.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Generate random numbers from a Gamma-Borel mixture distribution — rgborel","text":"Sebastian Funk","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/rgborel.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Generate random numbers from a Gamma-Borel mixture distribution — rgborel","text":"","code":"set.seed(32) rgborel(n = 5, size = 0.3, mu = 1, censor_at = 5) #> [1]   1   1 Inf Inf   1"},{"path":"https://epiverse-trace.github.io/epichains/reference/simulate_chain_stats.html","id":null,"dir":"Reference","previous_headings":"","what":"Simulate a vector of transmission chains statistics (sizes/lengths) — simulate_chain_stats","title":"Simulate a vector of transmission chains statistics (sizes/lengths) — simulate_chain_stats","text":"generates vector transmission chain sizes lengths using model simulate_chains() without tracking details individual chains. function useful chain sizes lengths interest. uses simple branching process model simulates independent chains, using offspring distribution chain. chain uses threshold chain size length stopping criterion especially R0 > 1. function also optionally accepts population related inputs population size (defaults Inf) percentage population initially immune (defaults 0).","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/simulate_chain_stats.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Simulate a vector of transmission chains statistics (sizes/lengths) — simulate_chain_stats","text":"","code":"simulate_chain_stats(   n_chains,   statistic = c(\"size\", \"length\"),   offspring_dist,   ...,   stat_threshold = Inf,   pop = Inf, percent_immune = 0 )"},{"path":"https://epiverse-trace.github.io/epichains/reference/simulate_chain_stats.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Simulate a vector of transmission chains statistics (sizes/lengths) — simulate_chain_stats","text":"n_chains Number chains simulate. statistic chain statistic track stopping criteria chain simulated stat_threshold Inf; <string>. can one : \"size\": total number cases produced chain goes extinct. \"length\": total number generations reached chain goes extinct. offspring_dist Offspring distribution: <function> like ones provided R generate random numbers given distributions (e.g., rpois Poisson). specifically, function needs accept least one argument, n, number random numbers generate. can accept arguments, passed random number generating functions. Examples can provided rpois Poisson distributed offspring, rnbinom negative binomial offspring, custom functions. ... Parameters offspring distribution required R. stat_threshold stopping criterion individual chain simulations; positive number coercible integer. chain's cumulative statistic reaches surpasses stat_threshold, chain ends. also serves censoring limit results specified value, set Inf. Defaults Inf. pop Population size; <Integer>. Used alongside percent_immune define susceptible population. Defaults Inf. percent_immune Percent population immune infection start simulation; <numeric> 0 1. Used alongside pop initialise susceptible population. Defaults 0.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/simulate_chain_stats.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Simulate a vector of transmission chains statistics (sizes/lengths) — simulate_chain_stats","text":"object class <epichains_summary>, numeric vector chain sizes lengths extra attributes storing simulation parameters.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/simulate_chain_stats.html","id":"simulate-chain-stats-vs-simulate-chains-","dir":"Reference","previous_headings":"","what":"simulate_chain_stats() vs simulate_chains()","title":"Simulate a vector of transmission chains statistics (sizes/lengths) — simulate_chain_stats","text":"simulate_chain_stats() time-invariant version simulate_chains(). particular, track details individual transmission events deals eventual chain statistics, , statistic realised chain dying . useful generating vector chain sizes lengths given number chains, details infected timing infection interest. function used {epichains} calculating likelihoods likelihood() function sampling borel distribution (See ?epichains::rborel). used extensively vignette modelling disease control, data observed chain sizes lengths available.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/simulate_chain_stats.html","id":"definition-of-a-transmission-chain","dir":"Reference","previous_headings":"","what":"Definition of a transmission chain","title":"Simulate a vector of transmission chains statistics (sizes/lengths) — simulate_chain_stats","text":"transmission chain used independent case secondary cases linked transmission. chain starts single case, case chain generates secondary cases according offspring distribution. chain ends secondary cases generated.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/simulate_chain_stats.html","id":"calculating-chain-sizes-and-lengths","dir":"Reference","previous_headings":"","what":"Calculating chain sizes and lengths","title":"Simulate a vector of transmission chains statistics (sizes/lengths) — simulate_chain_stats","text":"function simulates chain size chain \\(\\) time \\(t\\), \\(I_{t, }\\), : $$I_{t, } = \\sum_{}^{I_{t-1}}X_{t, },$$ chain length/duration chain \\(\\) time \\(t\\), \\(L_{t, }\\), : $$L_{t, } = {\\sf min}(1, X_{t, }), $$ \\(X_{t, }\\) secondary cases generated chain \\(\\) time \\(t\\), \\(I_{0, } = L_{0, } = 1\\). distribution secondary cases, \\(X_{t, }\\) modelled offspring distribution (offspring_dist).","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/simulate_chain_stats.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Simulate a vector of transmission chains statistics (sizes/lengths) — simulate_chain_stats","text":"Jacob C. (2010). Branching processes: role epidemiology. International journal environmental research public health, 7(3), 1186–1204. doi:10.3390/ijerph7031204 Blumberg, S., J. O. Lloyd-Smith. 2013. \"Comparing Methods Estimating R0 Size Distribution Subcritical Transmission Chains.\" Epidemics 5 (3): 131–45. doi:10.1016/j.epidem.2013.05.002 . Farrington, C. P., M. N. Kanaan, N. J. Gay. 2003. \"Branching Process Models Surveillance Infectious Diseases Controlled Mass Vaccination.” Biostatistics (Oxford, England) 4 (2): 279–95. doi:10.1093/biostatistics/4.2.279 .","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/simulate_chain_stats.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Simulate a vector of transmission chains statistics (sizes/lengths) — simulate_chain_stats","text":"James M. Azam, Sebastian Funk","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/simulate_chain_stats.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Simulate a vector of transmission chains statistics (sizes/lengths) — simulate_chain_stats","text":"","code":"# Simulate chain sizes with a poisson offspring distribution, assuming an # infinite population and no immunity. set.seed(32) simulate_chain_stats(   n_chains = 20,   statistic = \"size\",   offspring_dist = rpois,   stat_threshold = 10,   lambda = 0.9 ) #> `epichains_summary` object  #>  #>  [1]   6   7   5   7   1 Inf   3   4   6   1   9   1 Inf Inf   1   3 Inf Inf   2 #> [20]   5 #>  #>  Simulated sizes:  #>  #> Max: >=10 #> Min: 1 # Simulate chain sizes with a negative binomial distribution and assuming # a finite population and 10% immunity. set.seed(32) simulate_chain_stats(   pop = 1000,   percent_immune = 0.1,   n_chains = 20,   statistic = \"size\",   offspring_dist = rnbinom,   stat_threshold = 10,   mu = 0.9,   size = 0.36 ) #> `epichains_summary` object  #>  #>  [1] 1 1 1 2 2 4 2 1 1 4 1 1 2 1 1 2 1 1 1 1 #>  #>  Simulated sizes:  #>  #> Max: 4 #> Min: 1"},{"path":"https://epiverse-trace.github.io/epichains/reference/simulate_chains.html","id":null,"dir":"Reference","previous_headings":"","what":"Simulate transmission chains — simulate_chains","title":"Simulate transmission chains — simulate_chains","text":"generates independent transmission chains starting single case per chain, using simple branching process model (See details definition \"chains\" assumptions). Offspring chain generated offspring distribution, optional generation time distribution function. individual chain simulations controlled customisable stopping criteria, including threshold chain size length, generation time cut . function also optionally accepts population related inputs population size (defaults Inf) percentage population initially immune (defaults 0).","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/simulate_chains.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Simulate transmission chains — simulate_chains","text":"","code":"simulate_chains(   n_chains,   statistic = c(\"size\", \"length\"),   offspring_dist,   ...,   stat_threshold = Inf,   pop = Inf,   percent_immune = 0,   generation_time = NULL,   t0 = 0, tf = Inf )"},{"path":"https://epiverse-trace.github.io/epichains/reference/simulate_chains.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Simulate transmission chains — simulate_chains","text":"n_chains Number chains simulate. statistic chain statistic track stopping criteria chain simulated stat_threshold Inf; <string>. can one : \"size\": total number cases produced chain goes extinct. \"length\": total number generations reached chain goes extinct. offspring_dist Offspring distribution: <function> like ones provided R generate random numbers given distributions (e.g., rpois Poisson). specifically, function needs accept least one argument, n, number random numbers generate. can accept arguments, passed random number generating functions. Examples can provided rpois Poisson distributed offspring, rnbinom negative binomial offspring, custom functions. ... Parameters offspring distribution required R. stat_threshold stopping criterion individual chain simulations; positive number coercible integer. chain's cumulative statistic reaches surpasses stat_threshold, chain ends. Defaults Inf. example, statistic = \"size\" stat_threshold = 10, chain produces 10 cases stop. Note setting stat_threshold guarantee chains stop value. pop Population size; <Integer>. Used alongside percent_immune define susceptible population. Defaults Inf. percent_immune Percent population immune infection start simulation; <numeric> 0 1. Used alongside pop initialise susceptible population. Defaults 0. generation_time generation time function; name user-defined named anonymous function one argument n, representing number generation times sample. t0 Start time (generation time given); either single value vector length n_chains (number initial cases) corresponding initial times. Defaults 0, meaning cases started time 0. tf number cut-infection times (generation time given); Defaults Inf.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/simulate_chains.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Simulate transmission chains — simulate_chains","text":"<epichains> object, basically <data.frame> columns: chain - ID active/ongoing chains, infectee - unique ID infectee. infector - ID infector infectee. generation - discrete time point infection occurs, optionally, time - time infection.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/simulate_chains.html","id":"definition-of-a-transmission-chain","dir":"Reference","previous_headings":"","what":"Definition of a transmission chain","title":"Simulate transmission chains — simulate_chains","text":"transmission chain used independent case secondary cases linked transmission. chain starts single case, case chain generates secondary cases according offspring distribution. chain ends secondary cases generated.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/simulate_chains.html","id":"calculating-chain-sizes-and-lengths","dir":"Reference","previous_headings":"","what":"Calculating chain sizes and lengths","title":"Simulate transmission chains — simulate_chains","text":"function simulates chain size chain \\(\\) time \\(t\\), \\(I_{t, }\\), : $$I_{t, } = \\sum_{}^{I_{t-1}}X_{t, },$$ chain length/duration chain \\(\\) time \\(t\\), \\(L_{t, }\\), : $$L_{t, } = {\\sf min}(1, X_{t, }), $$ \\(X_{t, }\\) secondary cases generated chain \\(\\) time \\(t\\), \\(I_{0, } = L_{0, } = 1\\). distribution secondary cases, \\(X_{t, }\\) modelled offspring distribution (offspring_dist).","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/simulate_chains.html","id":"specifying-generation-time","dir":"Reference","previous_headings":"","what":"Specifying generation_time","title":"Simulate transmission chains — simulate_chains","text":"argument generation_time must specified function one argument, n. example, assuming want specify generation time random log-normally distributed variable meanlog = 0.58 sdlog = 1.58, define named function, call \"generation_time_fn\", one argument representing number generation times sample: generation_time_fn <- function(n){rlnorm(n, 0.58, 1.38)}, assign name function generation_time simulation function, .e. `simulate_*`(..., generation_time = generation_time_fn), ... arguments simulate_*() * placeholder rest simulation function's name. Alternatively, assign anonymous function generation_time simulate_*() call, .e. simulate_*(..., generation_time = function(n){rlnorm(n, 0.58, 1.38)}) simulate_*(..., generation_time = \\(n){rlnorm(n, 0.58, 1.38)}), ... arguments simulate_*().","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/simulate_chains.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Simulate transmission chains — simulate_chains","text":"Jacob C. (2010). Branching processes: role epidemiology. International journal environmental research public health, 7(3), 1186–1204. doi:10.3390/ijerph7031204 Blumberg, S., J. O. Lloyd-Smith. 2013. \"Comparing Methods Estimating R0 Size Distribution Subcritical Transmission Chains.\" Epidemics 5 (3): 131–45. doi:10.1016/j.epidem.2013.05.002 . Farrington, C. P., M. N. Kanaan, N. J. Gay. 2003. \"Branching Process Models Surveillance Infectious Diseases Controlled Mass Vaccination.” Biostatistics (Oxford, England) 4 (2): 279–95. doi:10.1093/biostatistics/4.2.279 .","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/simulate_chains.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Simulate transmission chains — simulate_chains","text":"James M. Azam, Sebastian Funk","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/simulate_chains.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Simulate transmission chains — simulate_chains","text":"","code":"# Using a Poisson offspring distribution and simulating from an infinite # population up to chain size 10. set.seed(32) chains_pois_offspring <- simulate_chains(   n_chains = 10,   statistic = \"size\",   offspring_dist = rpois,   stat_threshold = 10,   generation_time = function(n) rep(3, n),   lambda = 2 ) chains_pois_offspring #> `<epichains>` object #>  #> < epichains head (from first known infector) > #>  #>    chain infector infectee generation time #> 11     1        1        2          2    3 #> 12     1        1        3          2    3 #> 13     2        1        2          2    3 #> 14     2        1        3          2    3 #> 15     3        1        2          2    3 #> 16     3        1        3          2    3 #>  #>  #> Number of chains: 10 #> Number of infectors (known): 9 #> Number of generations: 4 #> Use `as.data.frame(<object_name>)` to view the full output in the console.  # Using a Negative binomial offspring distribution and simulating from a # finite population up to chain size 10. set.seed(32) chains_nbinom_offspring <- simulate_chains(   n_chains = 10,   pop = 100,   percent_immune = 0,   statistic = \"size\",   offspring_dist = rnbinom,   stat_threshold = 10,   generation_time = function(n) rep(3, n),   mu = 2,   size = 0.2 ) chains_nbinom_offspring #> `<epichains>` object #>  #> < epichains head (from first known infector) > #>  #>    chain infector infectee generation time #> 11     1        1        2          2    3 #> 12     2        1        2          2    3 #> 13     2        1        3          2    3 #> 14     2        1        4          2    3 #> 15     2        1        5          2    3 #> 16     2        1        6          2    3 #>  #>  #> Number of chains: 10 #> Number of infectors (known): 5 #> Number of generations: 4 #> Use `as.data.frame(<object_name>)` to view the full output in the console."},{"path":"https://epiverse-trace.github.io/epichains/reference/summary.epichains.html","id":null,"dir":"Reference","previous_headings":"","what":"Summary method for <epichains> class — summary.epichains","title":"Summary method for <epichains> class — summary.epichains","text":"calculates chain statistic (size/length) simulated chains returns object information returned equivalent simulate_chain_stats() call.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/summary.epichains.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Summary method for <epichains> class — summary.epichains","text":"","code":"# S3 method for class 'epichains' summary(object, ...)"},{"path":"https://epiverse-trace.github.io/epichains/reference/summary.epichains.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Summary method for <epichains> class — summary.epichains","text":"object <epichains> object. ... used.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/summary.epichains.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Summary method for <epichains> class — summary.epichains","text":"<epichains_summary> object containing chain summary statistics follows: \"size\": total number offspring produced chain goes extinct. \"length\": number generations achieved chain goes extinct.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/summary.epichains.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Summary method for <epichains> class — summary.epichains","text":"James M. Azam","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/summary.epichains.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Summary method for <epichains> class — summary.epichains","text":"","code":"# Using a negative binomial offspring distribution and simulating from a # finite population up to chain size 10. set.seed(32) sim_chains_nbinom <- simulate_chains(   n_chains = 10,   pop = 100,   percent_immune = 0,   statistic = \"size\",   offspring_dist = rnbinom,   stat_threshold = 10,   mu = 2,   size = 0.2 ) # Summarise the simulated chains sim_chains_nbinom_summary <- summary(sim_chains_nbinom) sim_chains_nbinom_summary #> `epichains_summary` object  #>  #>  [1]   3 Inf Inf   5   6 Inf   1   1   1   1 #>  #>  Simulated sizes:  #>  #> Max: >=10 #> Min: 1  # Same results can be obtained using `simulate_chain_stats()` set.seed(32) sim_summary_nbinom <- simulate_chain_stats(   n_chains = 10,   pop = 100,   percent_immune = 0,   statistic = \"size\",   offspring_dist = rnbinom,   stat_threshold = 10,   mu = 2,   size = 0.2 ) sim_summary_nbinom #> `epichains_summary` object  #>  #>  [1]   3 Inf Inf   5   6 Inf   1   1   1   1 #>  #>  Simulated sizes:  #>  #> Max: >=10 #> Min: 1  # Check that the results are the same setequal(sim_chains_nbinom_summary, sim_summary_nbinom) #> [1] TRUE"},{"path":"https://epiverse-trace.github.io/epichains/reference/summary.epichains_summary.html","id":null,"dir":"Reference","previous_headings":"","what":"Summary method for <epichains_summary> class — summary.epichains_summary","title":"Summary method for <epichains_summary> class — summary.epichains_summary","text":"Summary method <epichains_summary> class","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/summary.epichains_summary.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Summary method for <epichains_summary> class — summary.epichains_summary","text":"","code":"# S3 method for class 'epichains_summary' summary(object, ...)"},{"path":"https://epiverse-trace.github.io/epichains/reference/summary.epichains_summary.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Summary method for <epichains_summary> class — summary.epichains_summary","text":"object <epichains_summary> object. ... used.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/summary.epichains_summary.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Summary method for <epichains_summary> class — summary.epichains_summary","text":"list chain summaries. list contains following elements: n_chains: number chains simulated. max_stat: maximum chain statistic (size/length) achieved chains. min_stat: minimum chain statistic (size/length) achieved chains.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/summary.epichains_summary.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Summary method for <epichains_summary> class — summary.epichains_summary","text":"James M. Azam","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/summary.epichains_summary.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Summary method for <epichains_summary> class — summary.epichains_summary","text":"","code":"# Using a Poisson offspring distribution and simulating from an infinite # population up to chain size 10. set.seed(32) chain_stats <- simulate_chain_stats(  n_chains = 10,  statistic = \"size\",  offspring_dist = rpois,  stat_threshold = 10,  lambda = 2 ) summary(chain_stats) #> $n_chains #> [1] 10 #>  #> $max_stat #> [1] Inf #>  #> $min_stat #> [1] Inf #>"},{"path":"https://epiverse-trace.github.io/epichains/news/index.html","id":"epichains-010","dir":"Changelog","previous_headings":"","what":"epichains 0.1.0","title":"epichains 0.1.0","text":"excited announce first minor release epichains. epichains re-implements {bpmodels}, focusing unified simulation framework using branching processes simulate transmission chains data. framework incorporates susceptible depletion pre-existing immunity provides dedicated data structures handling analysing transmission chains tabular vector formats. goal provide seamless interoperability packages within Epiverse-TRACE Initiative broader epidemiological tool ecosystem.","code":""},{"path":[]},{"path":"https://epiverse-trace.github.io/epichains/news/index.html","id":"documentation-0-1-0","dir":"Changelog","previous_headings":"New Features","what":"Documentation","title":"epichains 0.1.0","text":"Dedicated Website: Explore features documentation epichains website. Help: function comes extensive documentation. welcome feedback suggestions improvements. Getting Started: quick guide key functions. Modelling Disease Control Interventions: Learn model various intervention strategies. Projecting Infectious Disease Incidence: case study projecting COVID-19 incidence. Literature: curation literature branching process applications epidemiology. Theoretical Background: deep dive theoretical background functions package (Contributor documentation). Design principles: design principles epichains (Contributor documentation).","code":""},{"path":"https://epiverse-trace.github.io/epichains/news/index.html","id":"simulation-0-1-0","dir":"Changelog","previous_headings":"New Features","what":"Simulation","title":"epichains 0.1.0","text":"simulate_chains(): Simulate independent transmission chains specified number initial cases, incorporating susceptible depletion pre-existing immunity. simulate_chain_stats(): Generate vector chain sizes lengths specified number initial cases, incorporating susceptible depletion pre-existing immunity.","code":""},{"path":"https://epiverse-trace.github.io/epichains/news/index.html","id":"inference-0-1-0","dir":"Changelog","previous_headings":"New Features","what":"Inference","title":"epichains 0.1.0","text":"likelihood(): Estimate (log)likelihood transmission chain sizes lengths, support numeric vectors <epichains> <epichains_summary> objects.","code":""},{"path":"https://epiverse-trace.github.io/epichains/news/index.html","id":"transmission-chain-data-manipulation-0-1-0","dir":"Changelog","previous_headings":"New Features","what":"Transmission Chain Data Manipulation","title":"epichains 0.1.0","text":"summary(): Extract vectors chain sizes lengths <epichains> objects. aggregate(): Generate case time series aggregating generation time infection. plot(): Visualize individual transmission chains filtered id.","code":""}]
+[{"path":"https://epiverse-trace.github.io/epichains/LICENSE.html","id":null,"dir":"","previous_headings":"","what":"MIT License","title":"MIT License","text":"Copyright (c) 2024 epichains authors Permission hereby granted, free charge, person obtaining copy software associated documentation files (“Software”), deal Software without restriction, including without limitation rights use, copy, modify, merge, publish, distribute, sublicense, /sell copies Software, permit persons Software furnished , subject following conditions: copyright notice permission notice shall included copies substantial portions Software. SOFTWARE PROVIDED “”, WITHOUT WARRANTY KIND, EXPRESS IMPLIED, INCLUDING LIMITED WARRANTIES MERCHANTABILITY, FITNESS PARTICULAR PURPOSE NONINFRINGEMENT. EVENT SHALL AUTHORS COPYRIGHT HOLDERS LIABLE CLAIM, DAMAGES LIABILITY, WHETHER ACTION CONTRACT, TORT OTHERWISE, ARISING , CONNECTION SOFTWARE USE DEALINGS SOFTWARE.","code":""},{"path":[]},{"path":"https://epiverse-trace.github.io/epichains/articles/design-principles.html","id":"scope","dir":"Articles","previous_headings":"","what":"Scope","title":"Design Principles for {epichains}","text":"{epichains} aims facilitate: Simulation transmission chains using branching processes methods, Handling transmission chains using objected-orientated design, Analytical/closed-form likelihoods take form <distribution>_<chain_statistic_type>_ll>, example, gborel_size_ll() pois_length_ll(). Numerical likelihood simulation using offspring_ll(). Additionally, package provides mixture probability distributions generating offspring distributions, example, rborel().","code":""},{"path":[]},{"path":"https://epiverse-trace.github.io/epichains/articles/design-principles.html","id":"simulation-functions","dir":"Articles","previous_headings":"Design decisions","what":"Simulation functions","title":"Design Principles for {epichains}","text":"Simulation branching processes achieved simulate_chains() simulate_chain_stats(). details underlying methods, see theory vignette. simulations stochastic, meaning one set inputs can produce varied results. models can also use explore scenario analyses varying inputs. Often, cases need one run model /one set parameter values, inputs outputs stored separate data structures. However, approach can limiting performing scenario analyses, user manually manipulate two objects reshaping joining operations. potential lead errors loss information. Hence, simulate_chains() simulate_chain_stats() return objects dedicated classes <epichains> <epichains_summary> respectively store input parameters output simulation single object. <epichains> class extends <data.frame>, using columns store information simulated transmission chains parameter values attributes. <data.frame> chosen tabular structure allows us store information rows columns, widely used data structure R. Similarly, <epichains_summary> class superclass (extension) R’s <numeric> class stores parameter values attributes. <epichains> object contains information whole outbreak, key summaries easily deduced quick glance object. Hence, class dedicated format()/print() method print simulated transmission chains manner similar <dataframe>, accompanied extra summary information including number chains simulated, number generations reached, number infectors created. summaries useful quickly assessing output simulation. Importantly, <epichains> class summary() method returns <epichains_summary> object. design decision taken allow easy coercion <epichains> object obtained simulate_chains() summaries <epichains> object otherwise attainable separate run simulate_chain_stats() parameter values passed simulate_chains(). Lastly, <epichains> objects aggregate() method aggregates simulated outbreak cases “generation” “time”. syntactic sugar dplyr::group_by() dplyr::summarise() style aggregation added benefit taking dplyr dependency achieve goal. summary, <epichains> object following structure: chain (<integer>) infector (<integer>) infectee (<integer>) generation (<integer>), optionally, time (<numeric>), generation_time specified n_chains, statistic, stat_threshold, offspring_dist, track_pop (pop finite, .e., specified).","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/design-principles.html","id":"likelihood-estimation","dir":"Articles","previous_headings":"Design decisions","what":"likelihood estimation","title":"Design Principles for {epichains}","text":"Likelihoods estimated using likelihood() function. function designed flexible two inputs: data can supplied vector chain summaries, <epichains> object, <epichains_summary> object, offspring distribution can supplied function, allowing user use custom offspring distributions. likelihood() uses either analytical numerical methods estimate likelihood observing input chain summaries. analytical methods closed-form likelihoods take form .<offspring_dist>_<statistic>_ll(), example, .gborel_size_ll() .pois_length_ll() shipped package. user supplies offspring distribution statistic solution exists, internally, used. , simulations used estimate likelihood. numerical likelihood simulation achieved using .offspring_ll(), internal wrapper around simulate_chain_stats(). output type likelihood() depends combination arguments individual, obs_prob, nsim_obs summarised table :","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/design-principles.html","id":"naming-and-documentation-style","dir":"Articles","previous_headings":"","what":"Naming and documentation style","title":"Design Principles for {epichains}","text":"package uses following naming conventions: Functions arguments named using snake_case, example, simulate_chains(). Internal functions prefixed period, example, .offspring_ll(). visual cue technical implications. documentation: Classes objects enclosed angle brackets, example, <epichains>. Packages enclosed curly braces, example, epichains. function arguments defined sentence case punctuated (especially full stops). Function titles imperative form. Functions referred function_name()","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/design-principles.html","id":"dependencies","dir":"Articles","previous_headings":"","what":"Dependencies","title":"Design Principles for {epichains}","text":"checkmate: exports many test_*(), check_*() assert_*() functions available CRAN.","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/design-principles.html","id":"development-journey","dir":"Articles","previous_headings":"","what":"Development journey","title":"Design Principles for {epichains}","text":"{epichains} successor bpmodels package, retired {epichains} released. {epichains} born need refactor {bpmodels}, led name change subsequent changes design required significant disruptive changes {bpmodels}. {epichains} major refactoring {bpmodels} provide simulation function accounts susceptible depletion population immunity without restrictions offspring distributions, better function long form documentation, object-oriented approach simulating handling transmission chains R. Future plans include simulation contacts infectees, incorporation network effects, object-oriented approach estimating chain size length likelihoods, interoperability {epiparameter} package ease setting various epidemiological delays.","code":""},{"path":[]},{"path":"https://epiverse-trace.github.io/epichains/articles/epichains.html","id":"use-case","dir":"Articles","previous_headings":"Transmission chains likelihoods","what":"Use case","title":"Getting started with epichains","text":"Suppose observed number transmission chains, arising separate index case. likely transmission properties (reproduction number /superspreading coefficient) generated chains (assuming parameters across chains)? first step answering question calculate likelihood observing observed chain summaries given transmission properties. likelihood() function comes . returned estimate can used infer transmission properties using estimation frameworks maximum likelihood Bayesian inference. epichains provide estimation frameworks.","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/epichains.html","id":"what-we-have","dir":"Articles","previous_headings":"Transmission chains likelihoods","what":"What we have","title":"Getting started with epichains","text":"Data observed transmission chains summaries (sizes lengths).","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/epichains.html","id":"what-we-assume","dir":"Articles","previous_headings":"Transmission chains likelihoods","what":"What we assume","title":"Getting started with epichains","text":"offspring distribution governs number secondary cases produced case. Parameters offspring distribution (example, mean overdispersion using negative binomial; can interpreted reproduction number superspreading coefficient, respectively) (optional) observation process/probability generates observed chain summaries. (optional) threshold chain summaries considered large consistent reproduction number R<1R<1 (e.g., NN cases TT generations total).","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/epichains.html","id":"likelihood","dir":"Articles","previous_headings":"Transmission chains likelihoods","what":"likelihood()","title":"Getting started with epichains","text":"function calculates likelihood/loglikelihood observing vector outbreak summaries obtained transmission chains. “Outbreak summaries” refer transmission chain sizes lengths/durations. likelihood() requires vector chain summaries (sizes lengths), chains, corresponding statistic use, statistic, offspring distribution, offspring_dist associated parameters. offspring_dist specified R function used generate random numbers, .e. rpois Poisson, rnbinom negative binomial, custom function. default, result log-likelihood log = FALSE, likelihoods returned (See ?likelihood details). understand likelihood() works see section likelihood() works. Let’s look following example estimate log-likelihood observing chain_sizes.","code":"set.seed(121) # example of observed chain sizes # randomly generate 20 chains of size between 1 to 10 chain_sizes <- sample(1:10, 20, replace = TRUE) chain_sizes #>  [1]  4  7  4  9  1  3  7  5  1  8 10  2  1  2  4  5 10  6  8  7 # estimate loglikelihood of the observed chain sizes for given lambda likelihood_eg <- likelihood(   chains = chain_sizes,   statistic = \"size\",   offspring_dist = rpois,   nsim_obs = 100,   lambda = 0.5 ) # Print the estimate likelihood_eg #> [1] -67.82879"},{"path":"https://epiverse-trace.github.io/epichains/articles/epichains.html","id":"joint-and-individual-log-likelihoods","dir":"Articles","previous_headings":"Transmission chains likelihoods","what":"Joint and individual log-likelihoods","title":"Getting started with epichains","text":"likelihood(), default, returns joint log-likelihood, given sum log-likelihoods observed chain. instead individual log-likelihoods desired (example calculating Watanabe–Akaike information criterion values, individual argument must set TRUE. return likelihoods instead, set log = FALSE.","code":"set.seed(121) # example of observed chain sizes # randomly generate 20 chains of size between 1 to 10 chain_sizes <- sample(1:10, 20, replace = TRUE) chain_sizes #>  [1]  4  7  4  9  1  3  7  5  1  8 10  2  1  2  4  5 10  6  8  7  # estimate loglikelihood of the observed chain sizes likelihood_ind_eg <- likelihood(   chains = chain_sizes,   statistic = \"size\",   offspring_dist = rpois,   nsim_obs = 100,   lambda = 0.5,   individual = TRUE ) # Print the estimate likelihood_ind_eg #> [[1]] #>  [1] -3.098612 -4.508584 -3.098612 -5.269208 -0.500000 -2.480829 -4.508584 #>  [8] -3.622329 -0.500000 -4.900542 -5.619471 -1.693147 -0.500000 -1.693147 #> [15] -3.098612 -3.622329 -5.619471 -4.086190 -4.900542 -4.508584"},{"path":"https://epiverse-trace.github.io/epichains/articles/epichains.html","id":"observation-probability","dir":"Articles","previous_headings":"Transmission chains likelihoods","what":"Observation probability","title":"Getting started with epichains","text":"likelihood() uses argument obs_prob model observation probability. default, assumes perfect observation, obs_prob = 1 (See ?likelihood), meaning transmission events observed recorded data. observations imperfect, obs_prob must less 1. case imperfect observation, “true” chain sizes lengths simulated nsim_obs times, likelihood calculated simulations. example, probability observing case obs_prob = 0.30, use returns 10 likelihood values (nsim_obs = 10), can averaged come overall likelihood estimate.","code":"set.seed(121) # example of observed chain sizes; randomly generate 20 chains of size 1 to 10 chain_sizes <- sample(1:10, 20, replace = TRUE) # get their likelihood liks <- likelihood(   chains = chain_sizes,   statistic = \"size\",   offspring_dist = rpois,   obs_prob = 0.3,   lambda = 0.5,   nsim_obs = 10 ) liks #>  [1] -183.8670 -162.1382 -166.6720 -170.1077 -152.9557 -157.9814 -166.0587 #>  [8] -174.8488 -156.4197 -160.0229"},{"path":"https://epiverse-trace.github.io/epichains/articles/epichains.html","id":"how-likelihood-works","dir":"Articles","previous_headings":"Transmission chains likelihoods","what":"How likelihood() works","title":"Getting started with epichains","text":"likelihood() first checks analytical solution likelihood exists given offspring distribution chain statistic specified. ’s none, simulations used estimate likelihoods. epichains package includes closed-form (analytical) solutions calculating likelihoods associated certain summaries transmission chains (“size” “length”) specific offspring distributions. size distributions, package provides Poisson, negative binomial, gamma-borel mixture. provide gamma-Borel size likelihood, Borel distribution needed. However, base R provide distribution natively like poisson gamma, epichains provides density random generator. length distribution, ’s Poisson geometric distributions. can used likelihood() based specified offspring_dist statistic. analytical solution exist, internal simulation function, .offspring_ll() employed. uses simulations approximate probability distributions (using linear approximation cumulative distribution unobserved sizes/lengths). simulation used, extra argument nsim_offspring must passed likelihood() specify number simulations used approximation. Approximate values likelihood vary every call simulation (simulations used estimation vary), may worth calling likelihood() multiple times case see error may introduce. example, let’s look example chain_sizes observed want calculate likelihood drawn binomial distribution probability prob = 0.9.","code":"set.seed(121) # example of observed chain sizes; randomly generate 20 chains of size 1 to 10 chain_sizes <- sample(1:10, 20, replace = TRUE) # get their likelihood liks <- likelihood(   chains = chain_sizes,   offspring_dist = rbinom,   statistic = \"size\",   size = 1,   prob = 0.9,   nsim_offspring = 250 ) liks #> [1] -56.76805"},{"path":"https://epiverse-trace.github.io/epichains/articles/epichains.html","id":"transmission-chain-simulation","dir":"Articles","previous_headings":"","what":"Transmission chain simulation","title":"Getting started with epichains","text":"two simulation functions, herein referred collectively simulate_*() functions can help us achieve .","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/epichains.html","id":"use-case-1","dir":"Articles","previous_headings":"Transmission chain simulation","what":"Use case","title":"Getting started with epichains","text":"want simulate scenario number chains produced separate index case. want simulate chains transmission result cases, given specific offspring distribution reproduction number.","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/epichains.html","id":"what-we-have-1","dir":"Articles","previous_headings":"Transmission chain simulation","what":"What we have","title":"Getting started with epichains","text":"initial number cases seed outbreak.","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/epichains.html","id":"what-we-assume-1","dir":"Articles","previous_headings":"Transmission chain simulation","what":"What we assume","title":"Getting started with epichains","text":"offspring distribution governs number secondary cases produced case. Parameters offspring distribution (example, mean overdispersion using negative binomial; can interpreted reproduction number superspreading coefficient, respectively) (optional) threshold chain summaries considered large consistent reproduction number R<1R<1 (e.g., NN cases TT generations total). (optional) generation time distribution governs time successive cases.","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/epichains.html","id":"simulate_chains","dir":"Articles","previous_headings":"Transmission chain simulation","what":"simulate_chains()","title":"Getting started with epichains","text":"simulate_chains() simulates outbreak given number infections offspring distribution. default, assumes population infinite pre-existing immunity. function tracks returns information infectors (ancestors), infectees, generation infection, time, generation time function specified. Let’s look example simulate transmission tree 1010 index cases. assume poisson offspring distribution mean, lambda=0.9\\text{lambda} = 0.9, generation time 33 days: default, simulate_chains() assumes infinite population can account susceptible depletion finite pop specified. Pre-existing immunity levels can also specified, applied pop simulation initialised. quick example simulate outbreak population size 10001000 1010 index cases 10/10/% pre-existing immunity. assume individuals poisson offspring distribution mean, lambda=1\\text{lambda} = 1, fixed generation time 33:","code":"set.seed(32) # Define generation time generation_time_fn <- function(n) {   gt <- rep(3, n)   return(gt) }  sim_chains <- simulate_chains(   n_chains = 10,   statistic = \"size\",   offspring_dist = rpois,   stat_threshold = 10,   generation_time = generation_time_fn,   lambda = 0.9 )  head(sim_chains) #>    chain infector infectee generation time #> 11     1        1        2          2    3 #> 12     2        1        2          2    3 #> 13     3        1        2          2    3 #> 14     3        1        3          2    3 #> 15     4        1        2          2    3 #> 16     6        1        2          2    3 set.seed(32) # Define generation time generation_time_fn <- function(n) {   gt <- rep(3, n)   return(gt) }  sim_chains_with_pop <- simulate_chains(   pop = 1000,   n_chains = 10,   percent_immune = 0.1,   offspring_dist = rpois,   statistic = \"size\",   lambda = 1,   generation_time = generation_time_fn )  head(sim_chains_with_pop) #>    chain infector infectee generation time #> 11     1        1        2          2    3 #> 12     2        1        2          2    3 #> 13     3        1        2          2    3 #> 14     3        1        3          2    3 #> 15     4        1        2          2    3 #> 16     6        1        2          2    3"},{"path":"https://epiverse-trace.github.io/epichains/articles/epichains.html","id":"simulate_chain_stats","dir":"Articles","previous_headings":"Transmission chain simulation","what":"simulate_chain_stats()","title":"Getting started with epichains","text":"simulate_chain_stats() performant version simulate_chains() track information infector infectee. returns eventual size length/duration transmission chain. function especially useful calculating numerical likelihoods likelihood(). example simulate previous examples without intervention, returning size 1010 chains. assumes Poisson offspring distribution distribution mean 0.90.9.","code":"set.seed(123)  simulate_chain_stats_eg <- simulate_chain_stats(   n_chains = 10,   statistic = \"size\",   offspring_dist = rpois,   stat_threshold = 10,   lambda = 0.9 )  # Print the results simulate_chain_stats_eg #> `epichains_summary` object  #>  #>  [1]   1 Inf   4   4 Inf   1   2 Inf   5   3 #>  #>  Simulated sizes:  #>  #> Max: >=10 #> Min: 1"},{"path":"https://epiverse-trace.github.io/epichains/articles/epichains.html","id":"s3-methods","dir":"Articles","previous_headings":"","what":"S3 Methods","title":"Getting started with epichains","text":"Let’s subset one chains biggest size sim_chains object created . Now, can plot chain using epicontacts package. Aggregated <epichains_tree> objects can also plotted using base R ggplot2 little data manipulation. end--end example simulation aggregation plotting.","code":"# Get the biggest chain longest_chain <- sim_chains[sim_chains$chain == which.max(   unname(table(sim_chains$chain)) ), ]  # Convert to data.frame to view the whole data as.data.frame(longest_chain) #>    chain infector infectee generation time #> 6      6       NA        1          1    0 #> 16     6        1        2          2    3 #> 17     6        1        3          2    3 #> 18     6        1        4          2    3 #> 27     6        2        5          3    6 #> 28     6        3        6          3    6 #> 29     6        3        7          3    6 #> 30     6        4        8          3    6 #> 42     6        5        9          4    9 #> 43     6        6       10          4    9 #> 44     6        7       11          4    9 #> 45     6        8       12          4    9 # Create an `<epicontacts>` object epc <- make_epicontacts(   linelist = longest_chain,   contacts = longest_chain,   id = \"infectee\",   from = \"infector\",   to = \"infectee\",   directed = TRUE )  # Plot the chain plot(epc) # Run simulation with simulate_chains() set.seed(32) # Define generation time generation_time_fn <- function(n) {   gt <- rep(3, n)   return(gt) }  sim_chains <- simulate_chains(   n_chains = 10,   statistic = \"size\",   offspring_dist = rpois,   stat_threshold = 1000,   generation_time = generation_time_fn,   lambda = 2 )  # Aggregate cases over time sim_chains_aggreg <- aggregate(sim_chains, by = \"time\")  # Plot cases over time plot(   sim_chains_aggreg,   type = \"b\",   col = \"red\",   lwd = 2,   xlab = \"Time\",   ylab = \"Cases\" )"},{"path":"https://epiverse-trace.github.io/epichains/articles/epichains.html","id":"summarising","dir":"Articles","previous_headings":"S3 Methods","what":"Summarising","title":"Getting started with epichains","text":"can run summary() object returned simulate_chains() obtain chain summaries per index case. summary output simulate_chain_stats() inputs used. simulate_chain_stats() performant version simulate_chains(), hence, can use instead, interested summary simulated chains without details infection tree. ::: can confirm two outputs using base::setequal(), checks two objects equal returns TRUE/FALSE.","code":"set.seed(32) # Define generation time generation_time_fn <- function(n) {   gt <- rep(3, n)   return(gt) }  sim_chains <- simulate_chains(   n_chains = 10,   statistic = \"size\",   offspring_dist = rpois,   stat_threshold = 10,   generation_time = generation_time_fn,   lambda = 0.9 )  summary(sim_chains) #> `epichains_summary` object  #>  #>  [1] Inf   2 Inf   2   1 Inf   3 Inf   9   1 #>  #>  Simulated sizes:  #>  #> Max: >=10 #> Min: 1  # Example with simulate_chain_stats() set.seed(32)  simulate_chain_stats_eg <- simulate_chain_stats(   n_chains = 10,   statistic = \"size\",   offspring_dist = rpois,   stat_threshold = 10,   lambda = 0.9 )  # Get summaries summary(simulate_chain_stats_eg) #> $n_chains #> [1] 10 #>  #> $max_stat #> [1] Inf #>  #> $min_stat #> [1] 1 setequal(   # summary of output from simulate_chains()   summary(sim_chains),   # results from simulate_chain_stats()   simulate_chain_stats_eg ) #> [1] TRUE"},{"path":"https://epiverse-trace.github.io/epichains/articles/epichains.html","id":"aggregating","dir":"Articles","previous_headings":"S3 Methods","what":"Aggregating","title":"Getting started with epichains","text":"can aggregate <epichains_tree> objects returned simulate_chains() <data.frame> columns “cases” either “generation” “time”, depending value . aggregate “time”, must specified generation time distribution (generation_time) simulation step.","code":"# Example with simulate_chains() set.seed(32)  # Define generation time generation_time_fn <- function(n) {   gt <- rep(3, n)   return(gt) }  sim_chains <- simulate_chains(   n_chains = 10,   statistic = \"size\",   offspring_dist = rpois,   stat_threshold = 10,   generation_time = generation_time_fn,   lambda = 0.9 )  aggregate(sim_chains, by = \"time\") #>   time cases #> 1    0    10 #> 2    3    12 #> 3    6    14 #> 4    9    17 #> 5   12     3 #> 6   15     4 #> 7   18     3"},{"path":"https://epiverse-trace.github.io/epichains/articles/epichains.html","id":"plotting","dir":"Articles","previous_headings":"S3 Methods","what":"Plotting","title":"Getting started with epichains","text":"can plot individual chains <epichains> object using {epicontacts} package. , first need create <epicontacts> object using epicontacts::make_epicontacts() function, requires linelist contacts data.frame (See ?epicontacts::make_epicontacts()).","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/epichains.html","id":"some-notes-about-interoperability-between-epicontacts-and-epichains-objects","dir":"Articles","previous_headings":"S3 Methods","what":"Some notes about interoperability between <epicontacts> and <epichains> objects","title":"Getting started with epichains","text":"epicontacts::make_epicontacts() function work: linelist contacts data.frames must column named “id” uniquely identifies case. linelist contacts objects can . <epichains> object contains multiple independent chains unique infectee ids, work box make_epicontacts() unless use subset chain. now, select visualise individual chains <epichains> object. future versions package, make interaction seamless providing user-friendly functionality convert <epichains> object <epicontacts> way allows us plot chains .","code":""},{"path":[]},{"path":"https://epiverse-trace.github.io/epichains/articles/interventions.html","id":"reducing-the-strength-of-transmission","dir":"Articles","previous_headings":"","what":"Reducing the strength of transmission","title":"Modelling disease control interventions","text":"Following (Lloyd-Smith et al. 2005) consider two ways disease control interventions can reduce reproduction number: population-wide individual-specific control.","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/interventions.html","id":"population-wide-control","dir":"Articles","previous_headings":"Reducing the strength of transmission","what":"Population-wide control","title":"Modelling disease control interventions","text":"population-level control mean intervention reduces mean number offspring (.e. reproduction number) fixed proportion. example, reduce R 25% population level scale mu parameter 1.2 0.9:","code":"sims <- simulate_chain_stats(   n_chains = 200, offspring_dist = rnbinom, stat_threshold = 99, mu = 0.9,   size = 0.5, statistic = \"size\" ) sims[is.infinite(sims)] <- 100 # Replace infections > 99 with 100 for plotting. ggplot(data.frame(x = sims), aes(x = x)) +   geom_histogram(breaks = seq(0, 100, by = 5), closed = \"left\") +   scale_x_continuous(breaks = c(0, 25, 50, 75, 100),                      labels = c(0, 25, 50, 75, \">99\")) +   theme_bw()"},{"path":"https://epiverse-trace.github.io/epichains/articles/interventions.html","id":"individual-level-control-","dir":"Articles","previous_headings":"Reducing the strength of transmission","what":"Individual-level control.","title":"Modelling disease control interventions","text":"simulating population-level control now apply reduction (25%) instead assuming mean reduced apply 25% individuals transmit , whereas remaining 75% generate offspring uncontrolled case. , can longer use standard negative binomial distribution comes R. Instead, define random generator modified negative binomial distribution includes individual-level control control argument indicating level individual-level control (0: control; 1: full control): defined , can generate simulations :","code":"rnbinom_ind <- function(n, ..., control = 0) {   ## initialise number of offspring to 0   offspring <- rep(0L, n)   ## for each individual, decide whether they transmit further   transmits <- rbinom(n = n, prob = 1 - control, size = 1)   ## check if anyone transmits further   if (any(transmits == 1L)) {     ## for those that transmit, sample from negative binomial with given     ## parameters     offspring[which(transmits == 1L)] <- rnbinom(n = n, ...)   }   return(offspring) } sims <- simulate_chain_stats(   n_chains = 200, offspring_dist = rnbinom_ind, stat_threshold = 99, mu = 1.2,   size = 0.5, control = 0.25, statistic = \"size\" ) sims[is.infinite(sims)] <- 100 # Replace infections > 99 with 100 for plotting. ggplot(data.frame(x = sims), aes(x = x)) +   geom_histogram(breaks = seq(0, 100, by = 5), closed = \"left\") +   scale_x_continuous(breaks = c(0, 25, 50, 75, 100),                      labels = c(0, 25, 50, 75, \">99\")) +   theme_bw()"},{"path":"https://epiverse-trace.github.io/epichains/articles/interventions.html","id":"preventing-superspreading-events","dir":"Articles","previous_headings":"","what":"Preventing superspreading events","title":"Modelling disease control interventions","text":"Another way controlling disease prevent individuals spreading large number others, example preventing mass gatherings , generally, settings superspreading events can occur. can model truncating offspring distribution certain size. can done, example, using truncdist R package. use define truncated negative binomial offspring distribution: use simulate chains situation maximum secondary cases infected person can generate 10. can likened disease control strategy gatherings limited 10 people.","code":"rnbinom_truncated <- function(n, ..., max = Inf) {   return(rtrunc(n = n, spec = \"nbinom\", b = max, ...)) } sims <- simulate_chain_stats(   n_chains = 200, offspring_dist = rnbinom_truncated, stat_threshold = 99,   mu = 1.2, size = 0.5, max =  10, statistic = \"size\" ) sims[is.infinite(sims)] <- 100 # Replace infections > 99 with 100 for plotting. ggplot(data.frame(x = sims), aes(x = x)) +   geom_histogram(breaks = seq(0, 100, by = 5), closed = \"left\") +   scale_x_continuous(breaks = c(0, 25, 50, 75, 100),                      labels = c(0, 25, 50, 75, \">99\")) +   theme_bw()"},{"path":"https://epiverse-trace.github.io/epichains/articles/interventions.html","id":"truncating-the-generation-interval","dir":"Articles","previous_headings":"","what":"Truncating the generation interval","title":"Modelling disease control interventions","text":"Lastly, consider situation generation interval shortened. model explicitly instead consider effect offspring distribution. example, generation interval gamma distribution shape = 25 rate = 5 (corresponding mean 5 standard deviation 1), stop transmission normally occur 6 days infection, can calculate proportion transmissions prevented words, prevent 16% infections example. value control can used examples study effect outbreak sizes.","code":"control <- 1 - pgamma(6, shape = 25, rate = 5) signif(control, 2) #> [1] 0.16"},{"path":[]},{"path":"https://epiverse-trace.github.io/epichains/articles/projecting_incidence.html","id":"overview","dir":"Articles","previous_headings":"","what":"Overview","title":"Projecting infectious disease incidence: a COVID-19 example","text":"Branching processes can used project stochastic infectious disease trends time provided can characterize distribution times successive cases (serial interval), distribution secondary cases produced single individual (offspring distribution). simulations can achieved epichains simulate_chains() function Pearson et al. (2020), Abbott et al. (2020) illustrate application COVID-19. purpose vignette use early data COVID-19 South Africa (Marivate Combrink 2020) illustrate epichains can used project outbreak. Let’s load required packages","code":"library(\"epichains\") library(\"dplyr\") library(\"ggplot2\") library(\"lubridate\")"},{"path":"https://epiverse-trace.github.io/epichains/articles/projecting_incidence.html","id":"data","dir":"Articles","previous_headings":"","what":"Data","title":"Projecting infectious disease incidence: a COVID-19 example","text":"Included epichains cleaned time series first 15 days COVID-19 outbreak South Africa. can loaded memory follows: use first 55 observations demonstration. assume cases subset imported infect . Let us subset view aspect data.","code":"data(\"covid19_sa\", package = \"epichains\") seed_cases <- covid19_sa[1:5, ] head(seed_cases) #> # A tibble: 5 × 2 #>   date       cases #>   <date>     <int> #> 1 2020-03-05     1 #> 2 2020-03-07     1 #> 3 2020-03-08     1 #> 4 2020-03-09     4 #> 5 2020-03-11     6"},{"path":"https://epiverse-trace.github.io/epichains/articles/projecting_incidence.html","id":"setting-up-the-inputs","dir":"Articles","previous_headings":"","what":"Setting up the inputs","title":"Projecting infectious disease incidence: a COVID-19 example","text":"now proceed set simulate_chains() simulations.","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/projecting_incidence.html","id":"onset-times","dir":"Articles","previous_headings":"Setting up the inputs","what":"Onset times","title":"Projecting infectious disease incidence: a COVID-19 example","text":"simulate_chains() requires vector seeding times, t0, chain/individual/simulation. get , use observation date index case reference find difference observed dates reference. Using vector start times time series, create corresponding seeding time individual, ’ll call t0.","code":"days_since_index <- as.integer(seed_cases$date - min(seed_cases$date)) days_since_index #> [1] 0 2 3 4 6 t0 <- rep(days_since_index, seed_cases$cases) t0 #>  [1] 0 2 3 4 4 4 4 6 6 6 6 6 6"},{"path":"https://epiverse-trace.github.io/epichains/articles/projecting_incidence.html","id":"generation-time","dir":"Articles","previous_headings":"Setting up the inputs","what":"Generation time","title":"Projecting infectious disease incidence: a COVID-19 example","text":"epidemiology, generation time (also called generation interval) duration successive infectious events chain transmission. Similarly, serial interval duration observed symptom onset times successive cases transmission chain. generation interval often hard observe exact times infection hard measure hence, serial interval often used instead. , use serial interval interpret simulated case data represent symptom onset. example, assume based COVID-19 literature serial interval, S, log-normal distributed parameters, μ=4.7\\mu = 4.7 σ=2.9\\sigma = 2.9(Pearson et al. 2020). log-normal distribution commonly used epidemiology characterise quantities serial interval large variance can positive-valued (Nishiura 2007; Limpert, Stahel, Abbt 2001). Note distribution described way, means μ\\mu σ\\sigma expected value standard deviation natural logarithm serial interval. Hence, order sample “back-transformed” measured serial interval expectation/mean, E[S]E[S] standard deviation, SD[S]SD [S], can use following parametrisation: E[S]=ln(μ2(μ2+σ2)SD[S]=ln(1+σ2μ2)\\begin{align} E[S] &= \\ln \\left( \\dfrac{\\mu^2}{(\\sqrt{\\mu^2 + \\sigma^2}} \\right) \\\\  SD [S] &= \\sqrt {\\ln \\left(1 + \\dfrac{\\sigma^2}{\\mu^2} \\right)}   \\end{align} See “log-normal_distribution” Wikipedia detailed explanation parametrisation. now set generation time function appropriate inputs. adopt R’s random lognormal distribution generator (rlnorm()) takes meanlog sdlog arguments, define parametrisation log_mean() log_sd() respectively wrap generation_time_fn() function. Moreover, generation_time_fn() takes one argument n required epichains (See ?epichains::simulate_chains), passed rlnorm() first argument determine number observations sample (See ?rlnorm).","code":"mu <- 4.7 sgma <- 2.9  log_mean <- log((mu^2) / (sqrt(sgma^2 + mu^2)))  # log mean log_sd <- sqrt(log(1 + (sgma / mu)^2)) # log sd  #' serial interval function generation_time <- function(n) {   gt <- rlnorm(n, meanlog = log_mean, sdlog = log_sd)   return(gt) }"},{"path":"https://epiverse-trace.github.io/epichains/articles/projecting_incidence.html","id":"offspring-distribution","dir":"Articles","previous_headings":"Setting up the inputs","what":"Offspring distribution","title":"Projecting infectious disease incidence: a COVID-19 example","text":"Let us now set offspring distribution, distribution drives mechanism behind individual cases infect cases. appropriate way model offspring distribution capture population-level transmissibility (R0R0) individual-level heterogeneity transmission (“superspreading”). negative binomial distribution commonly used case (Lloyd-Smith et al. 2005). example, assume offspring distribution characterised negative binomial mu=2.5mu = 2.5(Abbott et al. 2020) size=0.58size = 0.58(Wang et al. 2020). parameterization, mumu represents R0R_0, defined average number cases produced single individual entirely susceptible population. parameter sizesize represents superspreading, , degree heterogeneity transmission single individuals.","code":"mu <- 2.5 size <- 0.58"},{"path":"https://epiverse-trace.github.io/epichains/articles/projecting_incidence.html","id":"simulation-controls","dir":"Articles","previous_headings":"Setting up the inputs","what":"Simulation controls","title":"Projecting infectious disease incidence: a COVID-19 example","text":"example, simulate outbreaks end 2121 days last date observations seed_cases dataset. simulate_chains() stochastic, meaning results different every time run set parameters. , therefore, run simulations 100100 times aggregate results. Let us specify . Lastly, since, specified R0>1R0 > 1, means epidemic potentially grow without end. Hence, must specify end point simulations. simulate_chains() provides stat_threshold argument purpose. stat_threshold, simulation cut . value specified, assumes value infinity. , assume maximum chain size 10001000.","code":"#' Date to end simulation projection_window <- 21 tf <- max(days_since_index) + projection_window tf #> [1] 27 #' Number of simulations sim_rep <- 100 #' Maximum chain size allowed stat_threshold <- 1000"},{"path":"https://epiverse-trace.github.io/epichains/articles/projecting_incidence.html","id":"modelling-assumptions","dir":"Articles","previous_headings":"","what":"Modelling assumptions","title":"Projecting infectious disease incidence: a COVID-19 example","text":"exercise makes following simplifying assumptions: cases observed. Cases observed exactly time infection. reporting delay. Reporting rate constant course epidemic. interventions implemented. Population homogeneous well-mixed. summarise whole set far, going simulate chain 100 times, projecting cases 21 days first 6 days, assuming outbreak size exceeds 1000 cases.","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/projecting_incidence.html","id":"running-the-simulations","dir":"Articles","previous_headings":"","what":"Running the simulations","title":"Projecting infectious disease incidence: a COVID-19 example","text":"use function lapply() run simulations bind rows dplyr::bind_rows(). Let us view first rows simulation results.","code":"set.seed(1234) sim_chain_sizes <- lapply(   seq_len(sim_rep),   function(sim) {     simulate_chains(       n_chains = length(t0),       offspring_dist = rnbinom,       mu = mu,       size = size,       statistic = \"size\",       stat_threshold = stat_threshold,       generation_time = generation_time,       t0 = t0,       tf = tf     ) %>%       mutate(sim = sim)   } )  sim_output <- bind_rows(sim_chain_sizes) head(sim_output) #>    chain infector infectee generation      time sim #> 14     3        1        2          2  8.123133   1 #> 15     3        1        3          2  6.842933   1 #> 16     3        1        4          2  7.260639   1 #> 17     3        1        5          2 11.244838   1 #> 18     7        1        2          2  7.022334   1 #> 19     7        1        3          2 12.182368   1"},{"path":"https://epiverse-trace.github.io/epichains/articles/projecting_incidence.html","id":"post-processing","dir":"Articles","previous_headings":"","what":"Post-processing","title":"Projecting infectious disease incidence: a COVID-19 example","text":"Now, summarise simulation results. want plot individual simulated daily time series show median cases per day aggregated simulations. First, create daily time series per simulation aggregating number cases per day simulation. Next, add date column results simulation set. use date first case observed data reference start date. Now aggregate simulations day evaluate median daily cases across simulations.","code":"# Daily number of cases for each simulation incidence_ts <- sim_output %>%   mutate(day = ceiling(time)) %>%   count(sim, day, name = \"cases\") %>%   as_tibble()  head(incidence_ts) #> # A tibble: 6 × 3 #>     sim   day cases #>   <int> <dbl> <int> #> 1     1     0     1 #> 2     1     2     1 #> 3     1     3     1 #> 4     1     4     4 #> 5     1     6     6 #> 6     1     7     1 # Get start date from the observed data index_date <- min(seed_cases$date) index_date #> [1] \"2020-03-05\"  # Add a dates column to each simulation result incidence_ts_by_date <- incidence_ts %>%   group_by(sim) %>%   mutate(date = index_date + days(seq(0, n() - 1))) %>%   ungroup()  head(incidence_ts_by_date) #> # A tibble: 6 × 4 #>     sim   day cases date       #>   <int> <dbl> <int> <date>     #> 1     1     0     1 2020-03-05 #> 2     1     2     1 2020-03-06 #> 3     1     3     1 2020-03-07 #> 4     1     4     4 2020-03-08 #> 5     1     6     6 2020-03-09 #> 6     1     7     1 2020-03-10 # Median daily number of cases aggregated across all simulations median_daily_cases <- incidence_ts_by_date %>%   group_by(date) %>%   summarise(median_cases = median(cases)) %>%   ungroup() %>%   arrange(date)  head(median_daily_cases) #> # A tibble: 6 × 2 #>   date       median_cases #>   <date>            <dbl> #> 1 2020-03-05            1 #> 2 2020-03-06            1 #> 3 2020-03-07            1 #> 4 2020-03-08            4 #> 5 2020-03-09            5 #> 6 2020-03-10            8"},{"path":"https://epiverse-trace.github.io/epichains/articles/projecting_incidence.html","id":"visualization","dir":"Articles","previous_headings":"","what":"Visualization","title":"Projecting infectious disease incidence: a COVID-19 example","text":"now plot individual simulation results alongside median aggregated results. COVID-19 incidence South Africa projected two week window 2020. light gray lines represent individual simulations, red line represents median daily cases across simulations, black connected dots represent observed data, dashed vertical line marks beginning projection.","code":"# since all simulations may end at a different date, we will find the minimum # final date for all simulations for the purposes of visualisation. final_date <- incidence_ts_by_date %>%   group_by(sim) %>%   summarise(final_date = max(date), .groups = \"drop\") %>%   summarise(min_final_date = min(final_date)) %>%   pull(min_final_date)  incidence_ts_by_date <- incidence_ts_by_date %>%   filter(date <= final_date)  median_daily_cases <- median_daily_cases %>%   filter(date <= final_date)  ggplot(data = incidence_ts_by_date) +   geom_line(     aes(       x = date,       y = cases,       group = sim     ),     color = \"grey\",     linewidth = 0.2,     alpha = 0.25   ) +   geom_line(     data = median_daily_cases,     aes(       x = date,       y = median_cases     ),     color = \"tomato3\",     linewidth = 1.8   ) +   geom_point(     data = covid19_sa,     aes(       x = date,       y = cases     ),     color = \"black\",     size = 1.75,     shape = 21   ) +   geom_line(     data = covid19_sa,     aes(       x = date,       y = cases     ),     color = \"black\",     linewidth = 1   ) +   scale_x_continuous(     breaks = seq(       min(incidence_ts_by_date$date),       max(incidence_ts_by_date$date),       5     ),     labels = seq(       min(incidence_ts_by_date$date),       max(incidence_ts_by_date$date),       5     )   ) +   scale_y_continuous(     breaks = seq(       0,       max(incidence_ts_by_date$cases),       30     ),     labels = seq(       0,       max(incidence_ts_by_date$cases),       30     )   ) +   geom_vline(     mapping = aes(xintercept = max(seed_cases$date)),     linetype = \"dashed\"   ) +   labs(x = \"Date\", y = \"Daily cases\")"},{"path":[]},{"path":"https://epiverse-trace.github.io/epichains/articles/theoretical_background.html","id":"branching-processes","dir":"Articles","previous_headings":"","what":"Branching processes","title":"Theoretical background for epichains","text":"Branching processes class models used model growth populations. assume member population produces number offspring, ZZ, random variable probability mass function p(Z=z|θ)p(Z = z | \\theta), called offspring distribution. use long history epidemiology, population interpreted pathogen, offspring new hosts infects (Farrington, Kanaan, Gay 2003). call infected individuals cases methods applied contexts branching processes used.","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/theoretical_background.html","id":"simulation","dir":"Articles","previous_headings":"","what":"Simulation","title":"Theoretical background for epichains","text":"simulate branching process, start single case proceed discrete steps generations, drawing offspring distribution p(Z=z|θ)p(Z=z | \\theta) generate new cases case. Given infector ii infectee jj, can additionally assign distribution times TT approximates infection event occurred. define TT random variable distribution f(T=t;θ)f(T = t; \\theta) can assign case jj time tjt_{j} , case jj affected case ii given f(tj−ti|θ)f(t_{j} - t_{} | \\theta). identify timing cases time symptom onset serial interval, depending case definitions another interval.","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/theoretical_background.html","id":"summary-statistics","dir":"Articles","previous_headings":"Simulation","what":"Summary statistics","title":"Theoretical background for epichains","text":"Branching process simulations end gone extinct, , offspring produced, stopping criterion. summarise simulations, either study size length resulting chain cases. size SS chain number cases occurred course simulation including initial case S≥1S \\geq 1. length LL chain number generations simulated including initial case L≥1L \\geq 1.","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/theoretical_background.html","id":"inference","dir":"Articles","previous_headings":"","what":"Inference","title":"Theoretical background for epichains","text":"characterising chains cases size length can conduct inference learn underlying parameters θ\\theta observation chain sizes chain lengths (Blumberg Lloyd-Smith 2013). general possible subcritical branching processes, .e. ones mean number offspring less 1, otherwise branching process grow forever. However, can expand theory supercritical branching processes, .e. ones mean number offspring greater 1, defining cut chain size length beyond treat chain infinite size length, respectively.","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/theoretical_background.html","id":"size-and-length-distributions-for-some-offspring-distributions","dir":"Articles","previous_headings":"Inference","what":"Size and length distributions for some offspring distributions","title":"Theoretical background for epichains","text":"show equations size length distributions offspring distributions can derived analytically: Poisson, negative binomial, geometric, gamma-Borel mixture.","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/theoretical_background.html","id":"negative-binomial-and-special-cases","dir":"Articles","previous_headings":"Inference > Size and length distributions for some offspring distributions","what":"Negative binomial and special cases","title":"Theoretical background for epichains","text":"offspring distribution Poisson distribution, can interpret rate parameter λ\\lambda basic reproduction number R0R_{0} pathogen. general case offspring definition can overdispersed leading superspreading can use negative binomial offspring distribution mean μ\\mu overdispersion kkBlumberg Lloyd-Smith (2013). case, mean parameter μ\\mu interpreted basic reproduction number R0R_0 pathogen. negative binomial distribution arises Poisson-gamma mixture thus branching process negative binomial distributed offspring can interpreted one Poisson distributed offspring basic reproduction number R0R_0 varies according gamma distribution. amount variation R0R_0 interpreted individual-level variation transmission representing overdispersion superspreading, degree happens given overdispersion parameter kk.","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/theoretical_background.html","id":"size-distributions","dir":"Articles","previous_headings":"Inference > Size and length distributions for some offspring distributions > Negative binomial and special cases","what":"Size distributions","title":"Theoretical background for epichains","text":"probability pp chain size SS given R0R_0 kk branching process negative binomial offspring distribution given Eq. 9 Blumberg Lloyd-Smith (2013) p(S|R0,k)=Γ(kS+S−1)Γ(kS)Γ(S+1)(R0k)S−1(1+R0k)kS+S−1 p(S|R_0, k) = \\frac{\\Gamma(kS + S - 1)}{\\Gamma(kS)\\Gamma(S + 1)} \\frac{\\left(\\frac{R_0}{k}\\right)^{S - 1}}{\\left( 1 + \\frac{R_0}{k} \\right)^{kS + S - 1}} Γ\\Gamma gamma function. order estimate SS given R0R_0 kk can define likelihood function L(S)=p(S|R0,k)L(S) = p(S|R_0, k). corresponding log-likelihood LL(S)=logΓ(kS+S−1)−(logΓ(kS)+logΓ(S−1))+(S−1)logR0k−(SR0+(S−1))log(1+R0k)\\begin{align} \\mathrm{LL}(S) = &\\log\\Gamma(kS + S  - 1) - \\left(\\log\\Gamma(kS) + \\log\\Gamma(S - 1) \\right) \\\\ & + (S-1) \\log \\frac{R_0}{k} - (SR_0 + (S - 1)) \\log \\left(1 + \\frac{R_0}{k}\\right) \\end{align} log-likelihood Poisson distributed offspring follows kk tends infinity (corresponding Eq. 2.2 Farrington, Kanaan, Gay (2003)) LL(S)=(S−1)logR0−SR0+(S−2)logS−logΓ(S) \\mathrm{LL}(S) = (S - 1) \\log R_0 - S R_0 + (S - 2) \\log S - \\log\\Gamma(S) cases point estimate basic reproduction number R0̂\\hat{R_0} related mean chain size S‾\\bar{S} R0̂=1−1S‾ \\hat{R_0} = 1 - \\frac{1}{\\bar{S}}","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/theoretical_background.html","id":"length-distributions","dir":"Articles","previous_headings":"Inference > Size and length distributions for some offspring distributions > Negative binomial and special cases","what":"Length distributions","title":"Theoretical background for epichains","text":"cumulative mass function F(L)F(L) observing chain length LL offspring Poisson distributed given Eq. (2.5) Farrington, Kanaan, Gay (2003) (called “outbreak duration”): F(L)=e−R0EL(eR0e−R0) F(L) = e^{-R_0} E_L \\left( e^{R_0 e^{-R_0} } \\right) EL(x)E_L(x) iterated exponential function, E0(x)=1E_0(x) = 1, EL+1(x)=xEL(x)E_{L + 1}(x) = x^{E_L(x)}. geometric distributed offspring (corresponding negative Binomial k=1k=1) function given F(L)=1−R0L+11−R0L−2 F(L) = \\frac{ 1- R_0^{L + 1} } {1 - R_0^{L - 2}} cases f(L)f(L) denotes cumulative mass functions therefore probability observing chain length LL therefore f(L)−f(L−1)f(L) - f(L - 1).","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/theoretical_background.html","id":"gamma-borel-mixture","dir":"Articles","previous_headings":"Inference > Size and length distributions for some offspring distributions","what":"Gamma-Borel mixture","title":"Theoretical background for epichains","text":"probability distribution outbreak sizes branching process Poisson offspring distribution (Eq. 2.2 Farrington, Kanaan, Gay (2003)) special case Borel-Tanner distribution starting 1 individual. alternative negative binomial offspring distribution represents Poisson-gamma mixture Borel-gamma mixture. represent situations variation individual level chain level, .e. transmission chains homogeneous heterogeneity chains. case, can shown resulting log-likelihood chain sizes LL(S)=logΓ(k+S−1)−(logΓ(k)+logΓ(S+1))+(S−1)logS−klog(S+R0k)\\begin{align} \\mathrm{LL}(S) = &\\log\\Gamma(k + S - 1) - \\left(\\log\\Gamma(k) + \\log\\Gamma(S + 1) \\right) \\\\ & + (S-1) \\log S - k \\log \\left(S + \\frac{R_0}{k}\\right) \\end{align}","code":""},{"path":"https://epiverse-trace.github.io/epichains/articles/theoretical_background.html","id":"numerical-approximations-of-chain-size-and-length-distributions","dir":"Articles","previous_headings":"Inference","what":"Numerical approximations of chain size and length distributions","title":"Theoretical background for epichains","text":"analytic likelihoods available numerical approximation used derive distributions. order , simulation functionality used generate nn simulated chains value cumulative mass function P(S|θ)P(S|\\theta) observed SS approximated empirical cumulative distribution function: P(S|θ)≈∑i𝟏(xi<=S) P(S|\\theta) \\approx \\sum_i \\mathbf{1}(x_i <= S)  𝟏\\mathbf{1} indicator function xix_i -th observed chain size (length, interest LL). order improve approximation linear approximation applied values empirical distribution function (expense normalisation 1). (unnormalised) probability observing SS given p(S|θ)=P(S|θ)−P(S−1|θ) p(S|\\theta) = P(S|\\theta) - P(S - 1|\\theta)  equivalent relationship used LL.","code":""},{"path":"https://epiverse-trace.github.io/epichains/authors.html","id":null,"dir":"","previous_headings":"","what":"Authors","title":"Authors and Citation","text":"James M. Azam. Author, maintainer, copyright holder. Sebastian Funk. Author. Flavio Finger. Author. Zhian N. Kamvar. Contributor. Hugo Gruson. Contributor, reviewer. Karim Mané. Reviewer. Pratik Gupte. Reviewer. Joshua W. Lambert. Reviewer.","code":""},{"path":"https://epiverse-trace.github.io/epichains/authors.html","id":"citation","dir":"","previous_headings":"","what":"Citation","title":"Authors and Citation","text":"Azam J, Funk S, Finger F (2024). epichains: Simulating Analysing Transmission Chain Statistics Using Branching Process Models. R package version 0.1.0.9000, https://epiverse-trace.github.io/epichains/, https://github.com/epiverse-trace/epichains.","code":"@Manual{,   title = {epichains: Simulating and Analysing Transmission Chain Statistics Using Branching Process Models},   author = {James M. Azam and Sebastian Funk and Flavio Finger},   year = {2024},   note = {R package version 0.1.0.9000,     https://epiverse-trace.github.io/epichains/},   url = {https://github.com/epiverse-trace/epichains}, }"},{"path":"https://epiverse-trace.github.io/epichains/index.html","id":"epichains-methods-for-simulating-and-analysing-the-size-and-length-of-transmission-chains-from-branching-process-models-","dir":"","previous_headings":"","what":"Simulating and Analysing Transmission Chain Statistics Using Branching Process Models","title":"Simulating and Analysing Transmission Chain Statistics Using Branching Process Models","text":"epichains R package simulate, analyse, visualize size length branching processes given offspring distribution. models often used infectious disease epidemiology, chains represent chains transmission, offspring distribution represents distribution secondary infections caused infected individual. epichains re-implements bpmodels providing bespoke functions data structures allow easy manipulation interoperability Epiverse-TRACE packages, example, superspreading epiparameter, potentially existing packages handling transmission chains, example, epicontacts. epichains developed Centre Mathematical Modelling Infectious Diseases London School Hygiene Tropical Medicine part Epiverse Initiative.","code":""},{"path":"https://epiverse-trace.github.io/epichains/index.html","id":"installation","dir":"","previous_headings":"","what":"Installation","title":"Simulating and Analysing Transmission Chain Statistics Using Branching Process Models","text":"latest development version epichains package can installed via fails, try using pak R package via options fail, please file issue full log error messages. example issue reporting installation failure. help us improve installation process. load package, use","code":"# check whether {remotes} is installed if (!require(\"remotes\")) install.packages(\"remotes\") remotes::install_github(\"epiverse-trace/epichains\") # check whether {pak} is installed if (!require(\"pak\")) install.packages(\"pak\") pak::pak(\"epiverse-trace/epichains\") library(\"epichains\")"},{"path":"https://epiverse-trace.github.io/epichains/index.html","id":"quick-start","dir":"","previous_headings":"","what":"Quick start","title":"Simulating and Analysing Transmission Chain Statistics Using Branching Process Models","text":"epichains provides three main functions: simulate_chains(): simulates transmission chains using simple branching process model accepts index number cases seed outbreak, distribution offspring per case, chain statistic track (size length/duration). optionally accepts population related inputs population size (defaults Inf) percentage population initially immune (defaults 0). function returns object columns track information infected , generation infection , generation time function specified, time infection. simulate_chain_stats(): provides performant version simulate_chains() tracks return vector realized chain sizes lengths/durations index case without details infection tree. likelihood(): calculates loglikelihood (likelihood, depending value log) observing vector transmission chain sizes lengths. objects returned simulate_*() functions can summarised summary(). Running summary() output simulate_chains() return output simulate_chain_stats() using inputs. Objects returned simulate_chains() can aggregated <data.frame> cases per time generation function aggregate(). simulated <epichains> object can plotted various ways using plot(). See plotting section vignette(\"epichains\") two use cases.","code":""},{"path":"https://epiverse-trace.github.io/epichains/index.html","id":"simulation","dir":"","previous_headings":"Quick start","what":"Simulation","title":"Simulating and Analysing Transmission Chain Statistics Using Branching Process Models","text":"simulation functionality, let’s look simple example simulate transmission chain 2020 index cases, constant generation time 33, poisson offspring distribution mean 11. tracking chain “size” statistic cap chain sizes 2525 cases. look summary simulation, aggregate cases per generation.","code":"set.seed(32) # Simulate chains sim_chains <- simulate_chains(   n_chains = 20,   statistic = \"size\",   offspring_dist = rpois,   stat_threshold = 25,   generation_time = function(n) {rep(3, n)}, # constant generation time of 3   lambda = 1 # mean of the Poisson distribution ) # View the head of the simulation head(sim_chains) #>    chain infector infectee generation time #> 21     1        1        2          2    3 #> 22     2        1        2          2    3 #> 23     3        1        2          2    3 #> 24     3        1        3          2    3 #> 25     4        1        2          2    3 #> 26     6        1        2          2    3 # Summarise the simulation summary(sim_chains) #> `epichains_summary` object  #>  #>  [1]   5  17   4   8   1  16   9 Inf   5  18   5   1 Inf  24   1  14  19   2   4 #> [20]  14 #>  #>  Simulated sizes:  #>  #> Max: >=25 #> Min: 1 # Aggregate the simulation into cases per generation chains_agregegated <- aggregate(sim_chains, by = \"generation\")  # view the time series of cases per generation chains_agregegated #>    generation cases #> 1           1    20 #> 2           2    26 #> 3           3    36 #> 4           4    43 #> 5           5    31 #> 6           6    25 #> 7           7    20 #> 8           8     9 #> 9           9     3 #> 10         10     1 #> 11         11     1 #> 12         12     1 #> 13         13     1"},{"path":"https://epiverse-trace.github.io/epichains/index.html","id":"inference","dir":"","previous_headings":"Quick start","what":"Inference","title":"Simulating and Analysing Transmission Chain Statistics Using Branching Process Models","text":"Let’s look following example estimate log-likelihood observing hypothetical chain_lengths dataset. listed functionalities demonstrated detail “Getting Started” vignette.","code":"set.seed(32) # randomly generate 20 chain lengths between 1 to 40 chain_lengths <- sample(1:40, 20, replace = TRUE) chain_lengths #>  [1]  6 11 20  9 40 33 39 27  6 12 39 35  9 25  6 15 12  6 37 35 # estimate loglikelihood of the observed chain sizes likelihood_eg <- likelihood(   chains = chain_lengths,   statistic = \"length\",   offspring_dist = rpois,   lambda = 0.99 ) # Print the estimate likelihood_eg #> [1] -104.2917"},{"path":"https://epiverse-trace.github.io/epichains/index.html","id":"package-vignettes","dir":"","previous_headings":"","what":"Package vignettes","title":"Simulating and Analysing Transmission Chain Statistics Using Branching Process Models","text":"theory behind models provided can found theory vignette. also collated bibliography branching process applications epidemiology. can found literature vignette. Specific use cases epichains can found online documentation package vignettes, “Articles”.","code":""},{"path":"https://epiverse-trace.github.io/epichains/index.html","id":"related-r-packages","dir":"","previous_headings":"","what":"Related R packages","title":"Simulating and Analysing Transmission Chain Statistics Using Branching Process Models","text":"far know, existing R packages simulating branching processes transmission chains. bpmodels: provides methods analysing size length transmission chains branching process models. epichains intended supersede {bpmodels}. ringbp: branching process model, parameterised 2019-nCoV outbreak, used quantify potential effectiveness contact tracing isolation cases. covidhm: code simulating COVID-19 dynamics range scenarios across real-world social network. model conceptually based {ringbp}. epicontacts: provides methods handling, analysing, visualizing transmission chains contact-tracing data/linelists. simulist: uses branching process model simulate individual-level infectious disease outbreak data, including line lists contact tracing data. package part Epiverse-TRACE Initiative. superspreading: provides set functions estimate understand individual-level variation transmission infectious diseases data secondary cases. useful understanding role superspreading spread infectious diseases informing public health interventions. earlyR: estimates reproduction number (R), early stages outbreak. model requires specified serial interval distribution, characterised mean standard deviation (Gamma) distribution, data daily disease incidence, including confirmed probable cases. projections: uses data daily incidence, serial interval (time onsets infectors infectees) reproduction number simulate plausible epidemic trajectories project future incidence. relies branching process daily incidence follows Poisson Negative Binomial distribution governed force infection. simulacr: simulates outbreaks specified values reproduction number, incubation period, duration infectiousness, optionally reporting delays. Outputs linelist stored data.frame class outbreak, including information transmission chains; output can converted <epicontacts> objects visualisation. outbreakr: implements Bayesian approach reconstructing outbreak data pathogen genome sequences. also implements tool outbreak simulation. outbreakr2: Bayesian framework integrating epidemiological genetic data reconstruct transmission trees densely sampled outbreaks. re-implements, generalises replaces model outbreaker, uses modular approach enables fine customisation priors, likelihoods parameter movements. o2geosocial: integrates geographical social contact data reconstruct transmission chains. combines age group, location, onset date genotype cases infer import status, likely infector. nosoi: simulates agent-based transmission chains taking account influence multiple variables transmission process (e.g. dual-host systems (arboviruses), within-host viral dynamics, transportation, population structure), alone taken together, create complex relatively intuitive epidemiological simulations. TransPhylo: reconstructs infectious disease transmission using genomic data.","code":""},{"path":"https://epiverse-trace.github.io/epichains/index.html","id":"reporting-bugs","dir":"","previous_headings":"","what":"Reporting bugs","title":"Simulating and Analysing Transmission Chain Statistics Using Branching Process Models","text":"report bug please open issue.","code":""},{"path":"https://epiverse-trace.github.io/epichains/index.html","id":"contribute","dir":"","previous_headings":"","what":"Contribute","title":"Simulating and Analysing Transmission Chain Statistics Using Branching Process Models","text":"Contributions {epichains} welcomed. Please follow package contributing guide.","code":""},{"path":"https://epiverse-trace.github.io/epichains/index.html","id":"code-of-conduct","dir":"","previous_headings":"","what":"Code of conduct","title":"Simulating and Analysing Transmission Chain Statistics Using Branching Process Models","text":"Please note epichains project released Contributor Code Conduct. contributing project, agree abide terms.","code":""},{"path":"https://epiverse-trace.github.io/epichains/index.html","id":"citing-this-package","dir":"","previous_headings":"","what":"Citing this package","title":"Simulating and Analysing Transmission Chain Statistics Using Branching Process Models","text":"","code":"citation(\"epichains\") #> To cite package 'epichains' in publications use: #>  #>   Azam J, Funk S, Finger F (2024). _epichains: Simulating and Analysing #>   Transmission Chain Statistics Using Branching Process Models_. R #>   package version 0.1.0, https://epiverse-trace.github.io/epichains/, #>   <https://github.com/epiverse-trace/epichains>. #>  #> A BibTeX entry for LaTeX users is #>  #>   @Manual{, #>     title = {epichains: Simulating and Analysing Transmission Chain Statistics Using #> Branching Process Models}, #>     author = {James M. Azam and Sebastian Funk and Flavio Finger}, #>     year = {2024}, #>     note = {R package version 0.1.0,  #> https://epiverse-trace.github.io/epichains/}, #>     url = {https://github.com/epiverse-trace/epichains}, #>   }"},{"path":"https://epiverse-trace.github.io/epichains/reference/aggregate.epichains.html","id":null,"dir":"Reference","previous_headings":"","what":"Aggregate cases in <epichains> objects by ","title":"Aggregate cases in <epichains> objects by ","text":"function provides quick way create time series cases generation time (generation_time specified) simulated <epichains> objects.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/aggregate.epichains.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Aggregate cases in <epichains> objects by ","text":"","code":"# S3 method for class 'epichains' aggregate(x, by = c(\"time\", \"generation\"), ...)"},{"path":"https://epiverse-trace.github.io/epichains/reference/aggregate.epichains.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Aggregate cases in <epichains> objects by ","text":"x <epichains> object. variable aggregate ; character string options \"time\" \"generation\". ... used.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/aggregate.epichains.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Aggregate cases in <epichains> objects by ","text":"<data.frame> object cases .","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/aggregate.epichains.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Aggregate cases in <epichains> objects by ","text":"James M. Azam","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/aggregate.epichains.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Aggregate cases in <epichains> objects by ","text":"","code":"set.seed(32) chains <- simulate_chains(   n_chains = 10,   statistic = \"size\",   offspring_dist = rpois,   stat_threshold = 10,   generation_time = function(n) rep(3, n),   lambda = 2 ) chains #> `<epichains>` object #>  #> < epichains head (from first known infector) > #>  #>    chain infector infectee generation time #> 11     1        1        2          2    3 #> 12     1        1        3          2    3 #> 13     2        1        2          2    3 #> 14     2        1        3          2    3 #> 15     3        1        2          2    3 #> 16     3        1        3          2    3 #>  #>  #> Number of chains: 10 #> Number of infectors (known): 9 #> Number of generations: 4 #> Use `as.data.frame(<object_name>)` to view the full output in the console.  # Aggregate cases per time cases_per_time <- aggregate(chains, by = \"time\") head(cases_per_time) #>   time cases #> 1    0    10 #> 2    3    25 #> 3    6    61 #> 4    9    33  # Aggregate cases per generation cases_per_gen <- aggregate(chains, by = \"generation\") head(cases_per_gen) #>   generation cases #> 1          1    10 #> 2          2    25 #> 3          3    61 #> 4          4    33"},{"path":"https://epiverse-trace.github.io/epichains/reference/covid19_sa.html","id":null,"dir":"Reference","previous_headings":"","what":"COVID-19 Data Repository for South Africa — covid19_sa","title":"COVID-19 Data Repository for South Africa — covid19_sa","text":"aggregated subset COVID-19 Data Repository South Africa created, maintained hosted Data Science Social Impact research group, led Dr. Vukosi Marivate.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/covid19_sa.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"COVID-19 Data Repository for South Africa — covid19_sa","text":"","code":"covid19_sa"},{"path":[]},{"path":"https://epiverse-trace.github.io/epichains/reference/covid19_sa.html","id":"covid-sa","dir":"Reference","previous_headings":"","what":"covid19_sa","title":"COVID-19 Data Repository for South Africa — covid19_sa","text":"data frame 19 rows 2 columns: date Date case reported cases Number cases","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/covid19_sa.html","id":"source","dir":"Reference","previous_headings":"","what":"Source","title":"COVID-19 Data Repository for South Africa — covid19_sa","text":"https://github.com/dsfsi/covid19za details data-raw/covid19_sa.R.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/covid19_sa.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"COVID-19 Data Repository for South Africa — covid19_sa","text":"data originally provided linelist subsetted cleaned data-raw/covid19_sa.R.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dborel.html","id":null,"dir":"Reference","previous_headings":"","what":"Density of the Borel distribution — dborel","title":"Density of the Borel distribution — dborel","text":"Density Borel distribution","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dborel.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Density of the Borel distribution — dborel","text":"","code":"dborel(x, mu, log = FALSE)"},{"path":"https://epiverse-trace.github.io/epichains/reference/dborel.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Density of the Borel distribution — dborel","text":"x numeric vector quantiles. mu non-negative number poisson mean. log Logical; TRUE, probabilities p given log(p).","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dborel.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Density of the Borel distribution — dborel","text":"numeric vector borel probability density.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dborel.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Density of the Borel distribution — dborel","text":"Sebastian Funk","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dborel.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Density of the Borel distribution — dborel","text":"","code":"set.seed(32) dborel(1:5, 1) #> [1] 0.36787944 0.13533528 0.07468060 0.04884170 0.03509347"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-adjust_next_gen.html","id":null,"dir":"Reference","previous_headings":"","what":"Adjust new offspring if it exceeds the susceptible population size — .adjust_next_gen","title":"Adjust new offspring if it exceeds the susceptible population size — .adjust_next_gen","text":"function used internally, input checking performed , context used. Using directly recommended.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-adjust_next_gen.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Adjust new offspring if it exceeds the susceptible population size — .adjust_next_gen","text":"","code":".adjust_next_gen(next_gen, susc_pop)"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-adjust_next_gen.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Adjust new offspring if it exceeds the susceptible population size — .adjust_next_gen","text":"next_gen numeric vector next generation offspring. susc_pop susceptible population size; number coercible integer.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-adjust_next_gen.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Adjust new offspring if it exceeds the susceptible population size — .adjust_next_gen","text":"numeric vector adjusted next generation offspring.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-check_generation_time_valid.html","id":null,"dir":"Reference","previous_headings":"","what":"Check if the generation_time argument is specified as a function — .check_generation_time_valid","title":"Check if the generation_time argument is specified as a function — .check_generation_time_valid","text":"Check generation_time argument specified function","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-check_generation_time_valid.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Check if the generation_time argument is specified as a function — .check_generation_time_valid","text":"","code":".check_generation_time_valid(generation_time)"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-check_generation_time_valid.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Check if the generation_time argument is specified as a function — .check_generation_time_valid","text":"generation_time generation time function; name user-defined named anonymous function one argument n, representing number generation times sample.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-check_offspring_func_valid.html","id":null,"dir":"Reference","previous_headings":"","what":"Check if constructed random number generator for offspring exists and has an n argument. — .check_offspring_func_valid","title":"Check if constructed random number generator for offspring exists and has an n argument. — .check_offspring_func_valid","text":"Check constructed random number generator offspring exists n argument.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-check_offspring_func_valid.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Check if constructed random number generator for offspring exists and has an n argument. — .check_offspring_func_valid","text":"","code":".check_offspring_func_valid(offspring_dist)"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-check_offspring_func_valid.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Check if constructed random number generator for offspring exists and has an n argument. — .check_offspring_func_valid","text":"offspring_dist Offspring distribution: <function> like ones provided R generate random numbers given distributions (e.g., rpois Poisson). specifically, function needs accept least one argument, n, number random numbers generate. can accept arguments, passed random number generating functions. Examples can provided rpois Poisson distributed offspring, rnbinom negative binomial offspring, custom functions.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-check_sim_args.html","id":null,"dir":"Reference","previous_headings":"","what":"Check inputs to simulate_chains() and simulate_summary() — .check_sim_args","title":"Check inputs to simulate_chains() and simulate_summary() — .check_sim_args","text":"Check inputs simulate_chains() simulate_summary()","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-check_sim_args.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Check inputs to simulate_chains() and simulate_summary() — .check_sim_args","text":"","code":".check_sim_args(   n_chains,   statistic,   offspring_dist,   stat_threshold,   pop,   percent_immune )"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-check_sim_args.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Check inputs to simulate_chains() and simulate_summary() — .check_sim_args","text":"n_chains Number chains simulate. statistic chain statistic track stopping criteria chain simulated stat_threshold Inf; <string>. can one : \"size\": total number cases produced chain goes extinct. \"length\": total number generations reached chain goes extinct. offspring_dist Offspring distribution: <function> like ones provided R generate random numbers given distributions (e.g., rpois Poisson). specifically, function needs accept least one argument, n, number random numbers generate. can accept arguments, passed random number generating functions. Examples can provided rpois Poisson distributed offspring, rnbinom negative binomial offspring, custom functions. stat_threshold stopping criterion individual chain simulations; positive number coercible integer. chain's cumulative statistic reaches surpasses stat_threshold, chain ends. Defaults Inf. example, statistic = \"size\" stat_threshold = 10, chain produces 10 cases stop. Note setting stat_threshold guarantee chains stop value. pop Population size; <Integer>. Used alongside percent_immune define susceptible population. Defaults Inf. percent_immune Percent population immune infection start simulation; <numeric> 0 1. Used alongside pop initialise susceptible population. Defaults 0.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-check_sim_args.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Check inputs to simulate_chains() and simulate_summary() — .check_sim_args","text":"NULL; called side effects","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-check_statistic_args.html","id":null,"dir":"Reference","previous_headings":"","what":"Check that the statistic and stat_threshold arguments are valid — .check_statistic_args","title":"Check that the statistic and stat_threshold arguments are valid — .check_statistic_args","text":"function treats two arguments related checks one place remove repeated checks several places package.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-check_statistic_args.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Check that the statistic and stat_threshold arguments are valid — .check_statistic_args","text":"","code":".check_statistic_args(statistic, stat_threshold)"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-check_statistic_args.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Check that the statistic and stat_threshold arguments are valid — .check_statistic_args","text":"statistic chain statistic track stopping criteria chain simulated stat_threshold Inf; <string>. can one : \"size\": total number cases produced chain goes extinct. \"length\": total number generations reached chain goes extinct. stat_threshold stopping criterion individual chain simulations; positive number coercible integer. chain's cumulative statistic reaches surpasses stat_threshold, chain ends. Defaults Inf. example, statistic = \"size\" stat_threshold = 10, chain produces 10 cases stop. Note setting stat_threshold guarantee chains stop value.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-check_statistic_args.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Check that the statistic and stat_threshold arguments are valid — .check_statistic_args","text":"NULL; called side effects","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-check_time_args.html","id":null,"dir":"Reference","previous_headings":"","what":"Check inputs that control time events — .check_time_args","title":"Check inputs that control time events — .check_time_args","text":"function checks time-related inputs, .e., start time chain, t0, end time simulation, tf, generation time, generation_time. also checks generation_time argument specified tf specified go hand--hand.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-check_time_args.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Check inputs that control time events — .check_time_args","text":"","code":".check_time_args(tf_specified, tf, generation_time, t0)"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-check_time_args.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Check inputs that control time events — .check_time_args","text":"tf_specified <logical>; Whether tf argument specified. makes sense context function called, .e., simulate_chains(). tf specified, generation_time must specified. tf number cut-infection times (generation time given); Defaults Inf. generation_time generation time function; name user-defined named anonymous function one argument n, representing number generation times sample. t0 Start time (generation time given); either single value vector length n_chains (number initial cases) corresponding initial times. Defaults 0, meaning cases started time 0.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-check_time_args.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Check inputs that control time events — .check_time_args","text":"NULL; called side effects","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-complementary_logprob.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculates the complementary log-probability — .complementary_logprob","title":"Calculates the complementary log-probability — .complementary_logprob","text":"Given x norm, calculates log(1-sum(exp(x)))","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-complementary_logprob.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculates the complementary log-probability — .complementary_logprob","text":"","code":".complementary_logprob(x)"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-complementary_logprob.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculates the complementary log-probability — .complementary_logprob","text":"x numeric vector log-probabilities. Must negative.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-complementary_logprob.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculates the complementary log-probability — .complementary_logprob","text":"numeric value complementary log-probability.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-complementary_logprob.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Calculates the complementary log-probability — .complementary_logprob","text":"Sebastian Funk","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-epichains.html","id":null,"dir":"Reference","previous_headings":"","what":"Create an <epichains> object — .epichains","title":"Create an <epichains> object — .epichains","text":"epichains() constructs <epichains> object, inherently <data.frame> object stores inputs passed simulate_chains() simulated output. stored attributes useful downstream analyses reproducibility. function checks validity object created ensure right columns column types. <epichains> object contains <data.frame> simulated outbreak ids infector infectee, generation, optionally, time, number chains simulated, chain statistic tracked, whether susceptible population tracked.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-epichains.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Create an <epichains> object — .epichains","text":"","code":".epichains(   sim_df,   n_chains,   offspring_dist,   track_pop,   statistic = c(\"size\", \"length\"),   stat_threshold = Inf )"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-epichains.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Create an <epichains> object — .epichains","text":"sim_df <data.frame> containing least columns \"infectee_id\", \"infector_id\", \"generation\". Also optional columns \"time\", \"chain_id\". n_chains Number chains simulate. offspring_dist Offspring distribution: <function> like ones provided R generate random numbers given distributions (e.g., rpois Poisson). specifically, function needs accept least one argument, n, number random numbers generate. can accept arguments, passed random number generating functions. Examples can provided rpois Poisson distributed offspring, rnbinom negative binomial offspring, custom functions. track_pop susceptible population tracked? Logical. statistic chain statistic track stopping criteria chain simulated stat_threshold Inf; <string>. can one : \"size\": total number cases produced chain goes extinct. \"length\": total number generations reached chain goes extinct. stat_threshold stopping criterion individual chain simulations; positive number coercible integer. chain's cumulative statistic reaches surpasses stat_threshold, chain ends. Defaults Inf. example, statistic = \"size\" stat_threshold = 10, chain produces 10 cases stop. Note setting stat_threshold guarantee chains stop value.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-epichains.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Create an <epichains> object — .epichains","text":"<epichains> object.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-epichains.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Create an <epichains> object — .epichains","text":"James M. Azam","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-epichains_summary.html","id":null,"dir":"Reference","previous_headings":"","what":"Create an <epichains_summary> object — .epichains_summary","title":"Create an <epichains_summary> object — .epichains_summary","text":"epichains_summary() constructs <epichains_summary> object. <epichains_summary> object <vector> simulated chain sizes lengths. also stores information number chains simulated, statistic tracked.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-epichains_summary.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Create an <epichains_summary> object — .epichains_summary","text":"","code":".epichains_summary(   chains_summary,   n_chains,   offspring_dist,   statistic = c(\"size\", \"length\"),   stat_threshold = Inf )"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-epichains_summary.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Create an <epichains_summary> object — .epichains_summary","text":"chains_summary numeric <vector> chain sizes lengths. n_chains Number chains simulate. offspring_dist Offspring distribution: <function> like ones provided R generate random numbers given distributions (e.g., rpois Poisson). specifically, function needs accept least one argument, n, number random numbers generate. can accept arguments, passed random number generating functions. Examples can provided rpois Poisson distributed offspring, rnbinom negative binomial offspring, custom functions. statistic chain statistic track stopping criteria chain simulated stat_threshold Inf; <string>. can one : \"size\": total number cases produced chain goes extinct. \"length\": total number generations reached chain goes extinct. stat_threshold stopping criterion individual chain simulations; positive number coercible integer. chain's cumulative statistic reaches surpasses stat_threshold, chain ends. also serves censoring limit results specified value, set Inf. Defaults Inf.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-epichains_summary.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Create an <epichains_summary> object — .epichains_summary","text":"<epichains_summary> object.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-epichains_summary.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Create an <epichains_summary> object — .epichains_summary","text":"James M. Azam","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-gborel_size_ll.html","id":null,"dir":"Reference","previous_headings":"","what":"Log-likelihood of the size of chains with gamma-Borel offspring distribution — .gborel_size_ll","title":"Log-likelihood of the size of chains with gamma-Borel offspring distribution — .gborel_size_ll","text":"Log-likelihood size chains gamma-Borel offspring distribution","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-gborel_size_ll.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Log-likelihood of the size of chains with gamma-Borel offspring distribution — .gborel_size_ll","text":"","code":".gborel_size_ll(x, size, prob, mu)"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-gborel_size_ll.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Log-likelihood of the size of chains with gamma-Borel offspring distribution — .gborel_size_ll","text":"x numeric vector chain sizes. size dispersion parameter (often called k ecological applications); positive number. prob Probability success (parameterisation prob, see also NegBinomial); number 0 1. mu Mean; positive number.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-gborel_size_ll.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Log-likelihood of the size of chains with gamma-Borel offspring distribution — .gborel_size_ll","text":"numeric vector log-likelihood values.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-gborel_size_ll.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Log-likelihood of the size of chains with gamma-Borel offspring distribution — .gborel_size_ll","text":"Sebastian Funk","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-geom_length_ll.html","id":null,"dir":"Reference","previous_headings":"","what":"Log-likelihood of the length of chains with geometric offspring distribution — .geom_length_ll","title":"Log-likelihood of the length of chains with geometric offspring distribution — .geom_length_ll","text":"Log-likelihood length chains geometric offspring distribution","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-geom_length_ll.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Log-likelihood of the length of chains with geometric offspring distribution — .geom_length_ll","text":"","code":".geom_length_ll(x, prob)"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-geom_length_ll.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Log-likelihood of the length of chains with geometric offspring distribution — .geom_length_ll","text":"x numeric vector chain lengths. prob probability geometric distribution mean 1/prob. single numeric value 0 1.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-geom_length_ll.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Log-likelihood of the length of chains with geometric offspring distribution — .geom_length_ll","text":"numeric vector log-likelihood values.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-geom_length_ll.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Log-likelihood of the length of chains with geometric offspring distribution — .geom_length_ll","text":"Sebastian Funk","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-get_statistic_func.html","id":null,"dir":"Reference","previous_headings":"","what":"Return a function for calculating chain statistics — .get_statistic_func","title":"Return a function for calculating chain statistics — .get_statistic_func","text":"Return function calculating chain statistics","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-get_statistic_func.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Return a function for calculating chain statistics — .get_statistic_func","text":"","code":".get_statistic_func(chain_statistic)"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-get_statistic_func.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Return a function for calculating chain statistics — .get_statistic_func","text":"function calculating chain statistics.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-get_susceptible_offspring.html","id":null,"dir":"Reference","previous_headings":"","what":"Sample the number of susceptible offspring from all possible offspring — .get_susceptible_offspring","title":"Sample the number of susceptible offspring from all possible offspring — .get_susceptible_offspring","text":"Sample susceptible offspring infected possible offspring. function used internally, input checking performed , context used. Using directly recommended.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-get_susceptible_offspring.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Sample the number of susceptible offspring from all possible offspring — .get_susceptible_offspring","text":"","code":".get_susceptible_offspring(new_offspring, susc_pop, pop)"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-get_susceptible_offspring.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Sample the number of susceptible offspring from all possible offspring — .get_susceptible_offspring","text":"new_offspring numeric vector possible new offspring per chain produced .sample_possible_offspring(). pop Population size; <Integer>. Used alongside percent_immune define susceptible population. Defaults Inf.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-get_susceptible_offspring.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Sample the number of susceptible offspring from all possible offspring — .get_susceptible_offspring","text":"numeric vector number offspring can infected given current susceptible population size.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-init_susc_pop.html","id":null,"dir":"Reference","previous_headings":"","what":"Adjust next generation vector to match susceptible population size — .init_susc_pop","title":"Adjust next generation vector to match susceptible population size — .init_susc_pop","text":"Calculates initial susceptible population size given total population size, percent immune, number index cases. function used internally, input checking performed , context used. Using directly recommended.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-init_susc_pop.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Adjust next generation vector to match susceptible population size — .init_susc_pop","text":"","code":".init_susc_pop(pop, percent_immune, index_cases)"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-init_susc_pop.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Adjust next generation vector to match susceptible population size — .init_susc_pop","text":"pop Population size; <Integer>. Used alongside percent_immune define susceptible population. Defaults Inf. percent_immune Percent population immune infection start simulation; <numeric> 0 1. Used alongside pop initialise susceptible population. Defaults 0.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-init_susc_pop.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Adjust next generation vector to match susceptible population size — .init_susc_pop","text":"Initial susceptible population size; numeric coercible integer.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-is_epichains.html","id":null,"dir":"Reference","previous_headings":"","what":"Test if x is an epichains object — .is_epichains","title":"Test if x is an epichains object — .is_epichains","text":"Test x epichains object","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-is_epichains.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Test if x is an epichains object — .is_epichains","text":"","code":".is_epichains(x)"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-is_epichains.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Test if x is an epichains object — .is_epichains","text":"x R object.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-is_epichains.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Test if x is an epichains object — .is_epichains","text":"Logical; TRUE object <epichains> FALSE otherwise.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-is_epichains.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Test if x is an epichains object — .is_epichains","text":"James M. Azam","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-is_epichains_summary.html","id":null,"dir":"Reference","previous_headings":"","what":"Test if x is an epichains_summary object — .is_epichains_summary","title":"Test if x is an epichains_summary object — .is_epichains_summary","text":"Test x epichains_summary object","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-is_epichains_summary.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Test if x is an epichains_summary object — .is_epichains_summary","text":"","code":".is_epichains_summary(x)"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-is_epichains_summary.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Test if x is an epichains_summary object — .is_epichains_summary","text":"x R object.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-is_epichains_summary.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Test if x is an epichains_summary object — .is_epichains_summary","text":"Logical; TRUE object <epichains_summary> FALSE otherwise.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-is_epichains_summary.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Test if x is an epichains_summary object — .is_epichains_summary","text":"James M. Azam","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-nbinom_size_ll.html","id":null,"dir":"Reference","previous_headings":"","what":"Log-likelihood of the size of chains with Negative-Binomial offspring distribution — .nbinom_size_ll","title":"Log-likelihood of the size of chains with Negative-Binomial offspring distribution — .nbinom_size_ll","text":"Log-likelihood size chains Negative-Binomial offspring distribution","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-nbinom_size_ll.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Log-likelihood of the size of chains with Negative-Binomial offspring distribution — .nbinom_size_ll","text":"","code":".nbinom_size_ll(x, size, prob, mu)"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-nbinom_size_ll.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Log-likelihood of the size of chains with Negative-Binomial offspring distribution — .nbinom_size_ll","text":"x numeric vector chain sizes. size dispersion parameter (often called k ecological applications); positive number. prob Probability success (parameterisation prob, see also NegBinomial); number 0 1. mu Mean; positive number.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-nbinom_size_ll.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Log-likelihood of the size of chains with Negative-Binomial offspring distribution — .nbinom_size_ll","text":"numeric vector log-likelihood values.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-nbinom_size_ll.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Log-likelihood of the size of chains with Negative-Binomial offspring distribution — .nbinom_size_ll","text":"Sebastian Funk","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-new_epichains.html","id":null,"dir":"Reference","previous_headings":"","what":"Construct an <epichains> object — .new_epichains","title":"Construct an <epichains> object — .new_epichains","text":"new_epichains() constructs <epichains> object supplied <data.frame> extra attributes passed individual arguments. meant lazy performant, creating object without checking arguments correctness. safe call new_epichains() called within epichains() arguments checked. create <epichains> object, use epichains().","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-new_epichains.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Construct an <epichains> object — .new_epichains","text":"","code":".new_epichains(   sim_df,   n_chains,   statistic,   offspring_dist,   stat_threshold,   track_pop )"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-new_epichains.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Construct an <epichains> object — .new_epichains","text":"sim_df <data.frame> containing least columns \"infectee_id\", \"infector_id\", \"generation\". Also optional columns \"time\", \"chain_id\". n_chains Number chains simulate. statistic chain statistic track stopping criteria chain simulated stat_threshold Inf; <string>. can one : \"size\": total number cases produced chain goes extinct. \"length\": total number generations reached chain goes extinct. offspring_dist Offspring distribution: <function> like ones provided R generate random numbers given distributions (e.g., rpois Poisson). specifically, function needs accept least one argument, n, number random numbers generate. can accept arguments, passed random number generating functions. Examples can provided rpois Poisson distributed offspring, rnbinom negative binomial offspring, custom functions. stat_threshold stopping criterion individual chain simulations; positive number coercible integer. chain's cumulative statistic reaches surpasses stat_threshold, chain ends. Defaults Inf. example, statistic = \"size\" stat_threshold = 10, chain produces 10 cases stop. Note setting stat_threshold guarantee chains stop value. track_pop susceptible population tracked? Logical.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-new_epichains.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Construct an <epichains> object — .new_epichains","text":"James M. Azam","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-new_epichains_summary.html","id":null,"dir":"Reference","previous_headings":"","what":"Construct a <epichains_summary> object — .new_epichains_summary","title":"Construct a <epichains_summary> object — .new_epichains_summary","text":"new_epichains_summary() constructs <epichains_summary> object supplied <vector> chain sizes lengths. also stores extra attributes passed individual arguments. new_epichains_summary() meant lazy performant, creating object without checking arguments correctness. safe call new_epichains_summary() called within epichains_summary() arguments checked. create new <epichains_summary> object safely, use epichains_summary().","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-new_epichains_summary.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Construct a <epichains_summary> object — .new_epichains_summary","text":"","code":".new_epichains_summary(   chains_summary,   n_chains,   statistic,   offspring_dist,   stat_threshold )"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-new_epichains_summary.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Construct a <epichains_summary> object — .new_epichains_summary","text":"chains_summary numeric <vector> chain sizes lengths. n_chains Number chains simulate. statistic chain statistic track stopping criteria chain simulated stat_threshold Inf; <string>. can one : \"size\": total number cases produced chain goes extinct. \"length\": total number generations reached chain goes extinct. offspring_dist Offspring distribution: <function> like ones provided R generate random numbers given distributions (e.g., rpois Poisson). specifically, function needs accept least one argument, n, number random numbers generate. can accept arguments, passed random number generating functions. Examples can provided rpois Poisson distributed offspring, rnbinom negative binomial offspring, custom functions. stat_threshold stopping criterion individual chain simulations; positive number coercible integer. chain's cumulative statistic reaches surpasses stat_threshold, chain ends. also serves censoring limit results specified value, set Inf. Defaults Inf.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-new_epichains_summary.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Construct a <epichains_summary> object — .new_epichains_summary","text":"James M. Azam","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-offspring_ll.html","id":null,"dir":"Reference","previous_headings":"","what":"Log-likelihood of the summary (size/length) of chains with generic offspring distribution — .offspring_ll","title":"Log-likelihood of the summary (size/length) of chains with generic offspring distribution — .offspring_ll","text":"log-likelihoods calculated crude approximation using simulated chain summaries linearly approximating missing values empirical cumulative distribution function (ecdf).","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-offspring_ll.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Log-likelihood of the summary (size/length) of chains with generic offspring distribution — .offspring_ll","text":"","code":".offspring_ll(x, offspring_dist, statistic, nsim_offspring = 100, ...)"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-offspring_ll.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Log-likelihood of the summary (size/length) of chains with generic offspring distribution — .offspring_ll","text":"x numeric vector chain summaries (sizes/lengths). offspring_dist Offspring distribution: <function> like ones provided R generate random numbers given distributions (e.g., rpois Poisson). specifically, function needs accept least one argument, n, number random numbers generate. can accept arguments, passed random number generating functions. Examples can provided rpois Poisson distributed offspring, rnbinom negative binomial offspring, custom functions. statistic chain statistic track stopping criteria chain simulated stat_threshold Inf; <string>. can one : \"size\": total number cases produced chain goes extinct. \"length\": total number generations reached chain goes extinct. nsim_offspring Number simulations offspring distribution approximating distribution chain statistic summary (size/length) ... parameters pass simulate_chain_stats","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-offspring_ll.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Log-likelihood of the summary (size/length) of chains with generic offspring distribution — .offspring_ll","text":"numeric vector log-likelihood values.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-offspring_ll.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Log-likelihood of the summary (size/length) of chains with generic offspring distribution — .offspring_ll","text":"Sebastian Funk","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-pois_length_ll.html","id":null,"dir":"Reference","previous_headings":"","what":"Log-likelihood of the length of chains with Poisson offspring distribution — .pois_length_ll","title":"Log-likelihood of the length of chains with Poisson offspring distribution — .pois_length_ll","text":"Log-likelihood length chains Poisson offspring distribution","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-pois_length_ll.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Log-likelihood of the length of chains with Poisson offspring distribution — .pois_length_ll","text":"","code":".pois_length_ll(x, lambda)"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-pois_length_ll.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Log-likelihood of the length of chains with Poisson offspring distribution — .pois_length_ll","text":"x numeric vector chain lengths. lambda rate Poisson distribution. single numeric value. Must positive.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-pois_length_ll.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Log-likelihood of the length of chains with Poisson offspring distribution — .pois_length_ll","text":"numeric vector log-likelihood values.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-pois_length_ll.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Log-likelihood of the length of chains with Poisson offspring distribution — .pois_length_ll","text":"Sebastian Funk","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-pois_size_ll.html","id":null,"dir":"Reference","previous_headings":"","what":"Log-likelihood of the size of chains with Poisson offspring distribution — .pois_size_ll","title":"Log-likelihood of the size of chains with Poisson offspring distribution — .pois_size_ll","text":"Log-likelihood size chains Poisson offspring distribution","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-pois_size_ll.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Log-likelihood of the size of chains with Poisson offspring distribution — .pois_size_ll","text":"","code":".pois_size_ll(x, lambda)"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-pois_size_ll.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Log-likelihood of the size of chains with Poisson offspring distribution — .pois_size_ll","text":"x numeric vector sizes lambda rate Poisson distribution; single numeric value.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-pois_size_ll.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Log-likelihood of the size of chains with Poisson offspring distribution — .pois_size_ll","text":"numeric vector log-likelihood values.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-pois_size_ll.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Log-likelihood of the size of chains with Poisson offspring distribution — .pois_size_ll","text":"Sebastian Funk","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-rbinom_size.html","id":null,"dir":"Reference","previous_headings":"","what":"Samples size (the number of trials) of a binomial distribution — .rbinom_size","title":"Samples size (the number of trials) of a binomial distribution — .rbinom_size","text":"Samples size parameter binomial distribution fixed x (number successes) p (success probability)","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-rbinom_size.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Samples size (the number of trials) of a binomial distribution — .rbinom_size","text":"","code":".rbinom_size(n, x, prob)"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-rbinom_size.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Samples size (the number of trials) of a binomial distribution — .rbinom_size","text":"n number samples generate. Must positive integer. x number successes. Must positive integer. prob probability success. numeric 0 1.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-rbinom_size.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Samples size (the number of trials) of a binomial distribution — .rbinom_size","text":"numeric vector sampled sizes.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-rbinom_size.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Samples size (the number of trials) of a binomial distribution — .rbinom_size","text":"Sebastian Funk","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-rgen_length.html","id":null,"dir":"Reference","previous_headings":"","what":"Samples chain lengths with given observation probabilities — .rgen_length","title":"Samples chain lengths with given observation probabilities — .rgen_length","text":"Samples length transmission chain individual element observed binomial probability parameters n (number successes) p (success probability)","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-rgen_length.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Samples chain lengths with given observation probabilities — .rgen_length","text":"","code":".rgen_length(n, x, prob)"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-rgen_length.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Samples chain lengths with given observation probabilities — .rgen_length","text":"n number samples generate. Must positive integer. x numeric vector observed chain lengths. prob probability observation. numeric 0 1.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-rgen_length.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Samples chain lengths with given observation probabilities — .rgen_length","text":"numeric vector sampled chain lengths.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-rgen_length.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Samples chain lengths with given observation probabilities — .rgen_length","text":"Sebastian Funk","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-sample_possible_offspring.html","id":null,"dir":"Reference","previous_headings":"","what":"Sample all possible offspring for the next generation — .sample_possible_offspring","title":"Sample all possible offspring for the next generation — .sample_possible_offspring","text":"Sample next generation offspring using offspring distribution associated parameters. function used internally, input checking performed , context used. Using directly recommended.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-sample_possible_offspring.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Sample all possible offspring for the next generation — .sample_possible_offspring","text":"","code":".sample_possible_offspring(   offspring_func,   offspring_func_pars,   n_offspring,   chains )"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-sample_possible_offspring.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Sample all possible offspring for the next generation — .sample_possible_offspring","text":"offspring_func function sample offspring. offspring_func_pars list parameters offspring function. n_offspring numeric vector number offspring per chain. chains Numeric indices chains/infectors simulated","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-sample_possible_offspring.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Sample all possible offspring for the next generation — .sample_possible_offspring","text":"numeric vector number offspring per chain.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-update_chain_stat.html","id":null,"dir":"Reference","previous_headings":"","what":"Determine and update the chain statistic being tracked — .update_chain_stat","title":"Determine and update the chain statistic being tracked — .update_chain_stat","text":"Determine update chain statistic tracked","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-update_chain_stat.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Determine and update the chain statistic being tracked — .update_chain_stat","text":"","code":".update_chain_stat(stat_type, stat_latest, n_offspring)"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-update_chain_stat.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Determine and update the chain statistic being tracked — .update_chain_stat","text":"stat_type Chain statistic (size/length) update; character string. Must one 'size' 'length'. stat_latest latest chain statistic numeric vector updated. n_offspring vector offspring per chain. numeric vector (coercible integer).","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-update_chain_stat.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Determine and update the chain statistic being tracked — .update_chain_stat","text":"vector chain statistics (size/length). numeric vector coercible integer.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-validate_epichains.html","id":null,"dir":"Reference","previous_headings":"","what":"Validate an <epichains> object — .validate_epichains","title":"Validate an <epichains> object — .validate_epichains","text":"Validate <epichains> object","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-validate_epichains.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Validate an <epichains> object — .validate_epichains","text":"","code":".validate_epichains(x)"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-validate_epichains.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Validate an <epichains> object — .validate_epichains","text":"x <epichains> object.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-validate_epichains.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Validate an <epichains> object — .validate_epichains","text":"Invisibly returns object valid.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-validate_epichains.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Validate an <epichains> object — .validate_epichains","text":"James M. Azam","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-validate_epichains_summary.html","id":null,"dir":"Reference","previous_headings":"","what":"Validate an <epichains_summary> object — .validate_epichains_summary","title":"Validate an <epichains_summary> object — .validate_epichains_summary","text":"Validate <epichains_summary> object","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-validate_epichains_summary.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Validate an <epichains_summary> object — .validate_epichains_summary","text":"","code":".validate_epichains_summary(x)"},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-validate_epichains_summary.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Validate an <epichains_summary> object — .validate_epichains_summary","text":"x <epichains_summary> object.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-validate_epichains_summary.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Validate an <epichains_summary> object — .validate_epichains_summary","text":"Invisibly returns object valid.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/dot-validate_epichains_summary.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Validate an <epichains_summary> object — .validate_epichains_summary","text":"James M. Azam","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/epichains-package.html","id":null,"dir":"Reference","previous_headings":"","what":"epichains: Simulating and Analysing Transmission Chain Statistics Using Branching Process Models — epichains-package","title":"epichains: Simulating and Analysing Transmission Chain Statistics Using Branching Process Models — epichains-package","text":"Provides methods simulate analyse size length branching processes arbitrary offspring distribution. can used, example, analyse distribution chain sizes length infectious disease outbreaks, discussed Farrington et al. (2003) doi:10.1093/biostatistics/4.2.279 .","code":""},{"path":[]},{"path":"https://epiverse-trace.github.io/epichains/reference/epichains-package.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"epichains: Simulating and Analysing Transmission Chain Statistics Using Branching Process Models — epichains-package","text":"Maintainer: James M. Azam james.azam@lshtm.ac.uk (ORCID) [copyright holder] Authors: Sebastian Funk sebastian.funk@lshtm.ac.uk (ORCID) Flavio Finger flavio.finger@epicentre.msf.org (ORCID) contributors: Zhian N. Kamvar zkamvar@gmail.com (ORCID) [contributor] Hugo Gruson hugo@data.org (ORCID) [contributor, reviewer] Karim Mané karim.mane@lshtm.ac.uk (ORCID) [reviewer] Pratik Gupte pratik.gupte@lshtm.ac.uk (ORCID) [reviewer] Joshua W. Lambert joshua.lambert@lshtm.ac.uk (ORCID) [reviewer]","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/head.epichains.html","id":null,"dir":"Reference","previous_headings":"","what":"head and tail method for <epichains> class — head.epichains","title":"head and tail method for <epichains> class — head.epichains","text":"head tail method <epichains> class","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/head.epichains.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"head and tail method for <epichains> class — head.epichains","text":"","code":"# S3 method for class 'epichains' head(x, ...)  # S3 method for class 'epichains' tail(x, ...)"},{"path":"https://epiverse-trace.github.io/epichains/reference/head.epichains.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"head and tail method for <epichains> class — head.epichains","text":"x <epichains> object. ... arguments passed methods.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/head.epichains.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"head and tail method for <epichains> class — head.epichains","text":"object class <data.frame>.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/head.epichains.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"head and tail method for <epichains> class — head.epichains","text":"returns top rows <epichains> object, starting first known infectors. view full output, use .data.frame(<object_name>).","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/head.epichains.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"head and tail method for <epichains> class — head.epichains","text":"James M. Azam","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/head.epichains.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"head and tail method for <epichains> class — head.epichains","text":"","code":"set.seed(32) chains_pois_offspring <- simulate_chains(   n_chains = 10,   statistic = \"size\",   offspring_dist = rpois,   stat_threshold = 10,   generation_time = function(n) rep(3, n),   lambda = 2 ) head(chains_pois_offspring) #>    chain infector infectee generation time #> 11     1        1        2          2    3 #> 12     1        1        3          2    3 #> 13     2        1        2          2    3 #> 14     2        1        3          2    3 #> 15     3        1        2          2    3 #> 16     3        1        3          2    3 set.seed(32) chains_pois_offspring <- simulate_chains(   n_chains = 10,   statistic = \"size\",   offspring_dist = rpois,   stat_threshold = 10,   generation_time = function(n) rep(3, n),   lambda = 2 ) tail(chains_pois_offspring) #>     chain infector infectee generation time #> 124    10        3        6          4    9 #> 125    10        4        7          4    9 #> 126    10        4        8          4    9 #> 127    10        4        9          4    9 #> 128    10        4       10          4    9 #> 129    10        4       11          4    9"},{"path":"https://epiverse-trace.github.io/epichains/reference/likelihood.html","id":null,"dir":"Reference","previous_headings":"","what":"Estimate the log-likelihood/likelihood for observed branching processes — likelihood","title":"Estimate the log-likelihood/likelihood for observed branching processes — likelihood","text":"Estimate log-likelihood/likelihood observed branching processes","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/likelihood.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Estimate the log-likelihood/likelihood for observed branching processes — likelihood","text":"","code":"likelihood(   chains,   statistic = c(\"size\", \"length\"),   offspring_dist,   nsim_obs,   obs_prob = 1,   stat_threshold = Inf,   log = TRUE,   exclude = NULL,   individual = FALSE,   ... )"},{"path":"https://epiverse-trace.github.io/epichains/reference/likelihood.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Estimate the log-likelihood/likelihood for observed branching processes — likelihood","text":"chains Vector chain summaries (sizes/lengths). Can <numeric> vector object class <epichains> <epichains_summary> (obtained simulate_chains() simulate_chain_stats()). See examples . statistic chain statistic track stopping criteria chain simulated stat_threshold Inf; <string>. can one : \"size\": total number cases produced chain goes extinct. \"length\": total number generations reached chain goes extinct. offspring_dist Offspring distribution: <function> like ones provided R generate random numbers given distributions (e.g., rpois Poisson). specifically, function needs accept least one argument, n, number random numbers generate. can accept arguments, passed random number generating functions. Examples can provided rpois Poisson distributed offspring, rnbinom negative binomial offspring, custom functions. nsim_obs Number simulations used approximate log-likelihood/likelihood obs_prob < 1 (imperfect observation). obs_prob == 1, argument ignored. obs_prob Observation probability. number (probability) 0 1. value greater 0 less 1 implies imperfect observation simulations used approximate (log)likelihood. also require specifying nsim_obs. simulation, observation process assumed constant. stat_threshold stopping criterion individual chain simulations; positive number coercible integer. chain's cumulative statistic reaches surpasses stat_threshold, chain ends. also serves censoring limit results specified value, set Inf. Defaults Inf. NOTE: objects class <epichains> <epichains_summary>, stat_threshold used simulation extracted used argument specified, ignored warning thrown. log log-likelihoods transformed likelihoods? Logical. Defaults TRUE. exclude vector indices sizes/lengths exclude log-likelihood calculation. individual Logical; TRUE, vector individual log-likelihood/likelihood contributions returned rather sum/product. ... parameters pass simulate_chain_stats","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/likelihood.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Estimate the log-likelihood/likelihood for observed branching processes — likelihood","text":"log = TRUE joint log-likelihood (sum individual log-likelihoods), individual == FALSE (default) obs_prob == 1 (default), list individual log-likelihoods, individual == TRUE obs_prob == 1 (default), list individual log-likelihoods (length nsim_obs), individual == TRUE 0 <= obs_prob < 1, vector joint log-likelihoods (length nsim_obs), individual == FALSE 0 <= obs_prob < 1 (imperfect observation). log = FALSE, structure outputs returned, except likelihoods, instead log-likelihoods, calculated cases. Moreover, joint likelihoods product, instead sum, individual likelihoods.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/likelihood.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Estimate the log-likelihood/likelihood for observed branching processes — likelihood","text":"Sebastian Funk, James M. Azam","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/likelihood.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Estimate the log-likelihood/likelihood for observed branching processes — likelihood","text":"","code":"# example of observed chain sizes set.seed(121) # randomly generate 20 chains of size 1 to 10 chain_sizes <- sample(1:10, 20, replace = TRUE) likelihood(   chains = chain_sizes,   statistic = \"size\",   offspring_dist = rpois,   nsim_obs = 100,   lambda = 0.5 ) #> [1] -67.82879 # Example using an <epichains> object set.seed(32) epichains_obj_eg <- simulate_chains(  n_chains = 10,  pop = 100,  percent_immune = 0,  statistic = \"size\",  offspring_dist = rnbinom,  stat_threshold = 10,  generation_time = function(n) rep(3, n),  mu = 2,  size = 0.2 )  epichains_obj_eg_lik <- likelihood(   chains = epichains_obj_eg,   statistic = \"size\",   offspring_dist = rnbinom,   mu = 2,   size = 0.2,   stat_threshold = 10 ) #> Warning: `stat_threshold` specified but will be ignored. Using `stat_threshold` = 10 as used in the simulation. epichains_obj_eg_lik #> [1] -18.97756  # Example using a <epichains_summary> object set.seed(32) epichains_summary_eg <- simulate_chain_stats(   n_chains = 10,   pop = 100,   percent_immune = 0,   statistic = \"size\",   offspring_dist = rnbinom,   stat_threshold = 10,   mu = 2,   size = 0.2 ) epichains_summary_eg_lik <- likelihood(   chains = epichains_summary_eg,   statistic = \"size\",   offspring_dist = rnbinom,   mu = 2,   size = 0.2 ) epichains_summary_eg_lik #> [1] -18.97756"},{"path":"https://epiverse-trace.github.io/epichains/reference/print.epichains.html","id":null,"dir":"Reference","previous_headings":"","what":"Print an <epichains> object — print.epichains","title":"Print an <epichains> object — print.epichains","text":"Print <epichains> object","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/print.epichains.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Print an <epichains> object — print.epichains","text":"","code":"# S3 method for class 'epichains' print(x, ...)"},{"path":"https://epiverse-trace.github.io/epichains/reference/print.epichains.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Print an <epichains> object — print.epichains","text":"x <epichains> object. ... parameters passed print().","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/print.epichains.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Print an <epichains> object — print.epichains","text":"Invisibly returns <epichains>. Called side-effects.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/print.epichains.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Print an <epichains> object — print.epichains","text":"James M. Azam","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/print.epichains.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Print an <epichains> object — print.epichains","text":"","code":"# Using a Poisson offspring distribution and simulating from an infinite # population up to chain size 10. set.seed(32) chains_pois_offspring <- simulate_chains(  n_chains = 10,  statistic = \"size\",  offspring_dist = rpois,  stat_threshold = 10,  generation_time = function(n) rep(3, n),  lambda = 2 ) chains_pois_offspring # Print the object #> `<epichains>` object #>  #> < epichains head (from first known infector) > #>  #>    chain infector infectee generation time #> 11     1        1        2          2    3 #> 12     1        1        3          2    3 #> 13     2        1        2          2    3 #> 14     2        1        3          2    3 #> 15     3        1        2          2    3 #> 16     3        1        3          2    3 #>  #>  #> Number of chains: 10 #> Number of infectors (known): 9 #> Number of generations: 4 #> Use `as.data.frame(<object_name>)` to view the full output in the console."},{"path":"https://epiverse-trace.github.io/epichains/reference/print.epichains_summary.html","id":null,"dir":"Reference","previous_headings":"","what":"Print an <epichains_summary> object — print.epichains_summary","title":"Print an <epichains_summary> object — print.epichains_summary","text":"Prints summary <epichains_summary> object. particular, prints number chains simulated, range statistic, represented maximum (max_stat) minimum (min_stat). minimum maximum infinite, represented >= stat_threshold stat_threshold value censoring limit. See ?epichains_summary() definition stat_threshold.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/print.epichains_summary.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Print an <epichains_summary> object — print.epichains_summary","text":"","code":"# S3 method for class 'epichains_summary' print(x, ...)"},{"path":"https://epiverse-trace.github.io/epichains/reference/print.epichains_summary.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Print an <epichains_summary> object — print.epichains_summary","text":"x <epichains_summary> object. ... used.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/print.epichains_summary.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Print an <epichains_summary> object — print.epichains_summary","text":"Invisibly returns <epichains_summary>. Called side-effects.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/print.epichains_summary.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Print an <epichains_summary> object — print.epichains_summary","text":"James M. Azam","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/print.epichains_summary.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Print an <epichains_summary> object — print.epichains_summary","text":"","code":"# Using a Poisson offspring distribution and simulating from an infinite # population up to chain size 10. set.seed(32) chain_summary_print_eg <- simulate_chain_stats(  n_chains = 10,  statistic = \"size\",  offspring_dist = rpois,  stat_threshold = 10,  lambda = 2 ) chain_summary_print_eg # Print the object #> `epichains_summary` object  #>  #>  [1] Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf #>  #>  Simulated sizes:  #>  #> Max: >=10 #> Min: >=10"},{"path":"https://epiverse-trace.github.io/epichains/reference/rborel.html","id":null,"dir":"Reference","previous_headings":"","what":"Generate random numbers from the Borel distribution — rborel","title":"Generate random numbers from the Borel distribution — rborel","text":"Random numbers generated simulating Poisson branching process","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/rborel.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Generate random numbers from the Borel distribution — rborel","text":"","code":"rborel(n, mu, censor_at = Inf)"},{"path":"https://epiverse-trace.github.io/epichains/reference/rborel.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Generate random numbers from the Borel distribution — rborel","text":"n Number random variates generate. mu non-negative number poisson mean. censor_at stopping criterion; <numeric>. Defaults Inf. value simulation ends random number set Inf (form censoring). rborel() simulates chain sizes using simulate_chain_stats() Poisson offspring distribution, mu >= 1, simulation proceed unendingly. parameter used prevent .","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/rborel.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Generate random numbers from the Borel distribution — rborel","text":"numeric vector random numbers.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/rborel.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Generate random numbers from the Borel distribution — rborel","text":"Sebastian Funk","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/rborel.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Generate random numbers from the Borel distribution — rborel","text":"","code":"set.seed(32) rborel(5, 1) #> [1]  25  50 114   5   1"},{"path":"https://epiverse-trace.github.io/epichains/reference/rgborel.html","id":null,"dir":"Reference","previous_headings":"","what":"Generate random numbers from a Gamma-Borel mixture distribution — rgborel","title":"Generate random numbers from a Gamma-Borel mixture distribution — rgborel","text":"Generate random numbers Gamma-Borel mixture distribution","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/rgborel.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Generate random numbers from a Gamma-Borel mixture distribution — rgborel","text":"","code":"rgborel(n, size, prob, mu, censor_at = Inf)"},{"path":"https://epiverse-trace.github.io/epichains/reference/rgborel.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Generate random numbers from a Gamma-Borel mixture distribution — rgborel","text":"n Number random variates generate. size dispersion parameter (often called k ecological applications); positive number. prob Probability success (parameterisation prob, see also NegBinomial); number 0 1. mu Mean; positive number. censor_at stopping criterion; <numeric>. Defaults Inf. value simulation ends random number set Inf (form censoring). rborel() simulates chain sizes using simulate_chain_stats() Poisson offspring distribution, mu >= 1, simulation proceed unendingly. parameter used prevent .","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/rgborel.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Generate random numbers from a Gamma-Borel mixture distribution — rgborel","text":"Numeric vector random numbers","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/rgborel.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Generate random numbers from a Gamma-Borel mixture distribution — rgborel","text":"Sebastian Funk","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/rgborel.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Generate random numbers from a Gamma-Borel mixture distribution — rgborel","text":"","code":"set.seed(32) rgborel(n = 5, size = 0.3, mu = 1, censor_at = 5) #> [1]   1   1 Inf Inf   1"},{"path":"https://epiverse-trace.github.io/epichains/reference/simulate_chain_stats.html","id":null,"dir":"Reference","previous_headings":"","what":"Simulate a vector of transmission chains statistics (sizes/lengths) — simulate_chain_stats","title":"Simulate a vector of transmission chains statistics (sizes/lengths) — simulate_chain_stats","text":"generates vector transmission chain sizes lengths using model simulate_chains() without tracking details individual chains. function useful chain sizes lengths interest. uses simple branching process model simulates independent chains, using offspring distribution chain. chain uses threshold chain size length stopping criterion especially R0 > 1. function also optionally accepts population related inputs population size (defaults Inf) percentage population initially immune (defaults 0).","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/simulate_chain_stats.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Simulate a vector of transmission chains statistics (sizes/lengths) — simulate_chain_stats","text":"","code":"simulate_chain_stats(   n_chains,   statistic = c(\"size\", \"length\"),   offspring_dist,   ...,   stat_threshold = Inf,   pop = Inf,   percent_immune = 0 )"},{"path":"https://epiverse-trace.github.io/epichains/reference/simulate_chain_stats.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Simulate a vector of transmission chains statistics (sizes/lengths) — simulate_chain_stats","text":"n_chains Number chains simulate. statistic chain statistic track stopping criteria chain simulated stat_threshold Inf; <string>. can one : \"size\": total number cases produced chain goes extinct. \"length\": total number generations reached chain goes extinct. offspring_dist Offspring distribution: <function> like ones provided R generate random numbers given distributions (e.g., rpois Poisson). specifically, function needs accept least one argument, n, number random numbers generate. can accept arguments, passed random number generating functions. Examples can provided rpois Poisson distributed offspring, rnbinom negative binomial offspring, custom functions. ... Parameters offspring distribution required R. stat_threshold stopping criterion individual chain simulations; positive number coercible integer. chain's cumulative statistic reaches surpasses stat_threshold, chain ends. also serves censoring limit results specified value, set Inf. Defaults Inf. pop Population size; <Integer>. Used alongside percent_immune define susceptible population. Defaults Inf. percent_immune Percent population immune infection start simulation; <numeric> 0 1. Used alongside pop initialise susceptible population. Defaults 0.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/simulate_chain_stats.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Simulate a vector of transmission chains statistics (sizes/lengths) — simulate_chain_stats","text":"object class <epichains_summary>, numeric vector chain sizes lengths extra attributes storing simulation parameters.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/simulate_chain_stats.html","id":"simulate-chain-stats-vs-simulate-chains-","dir":"Reference","previous_headings":"","what":"simulate_chain_stats() vs simulate_chains()","title":"Simulate a vector of transmission chains statistics (sizes/lengths) — simulate_chain_stats","text":"simulate_chain_stats() time-invariant version simulate_chains(). particular, track details individual transmission events deals eventual chain statistics, , statistic realised chain dying . useful generating vector chain sizes lengths given number chains, details infected timing infection interest. function used {epichains} calculating likelihoods likelihood() function sampling borel distribution (See ?epichains::rborel). used extensively vignette modelling disease control, data observed chain sizes lengths available.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/simulate_chain_stats.html","id":"definition-of-a-transmission-chain","dir":"Reference","previous_headings":"","what":"Definition of a transmission chain","title":"Simulate a vector of transmission chains statistics (sizes/lengths) — simulate_chain_stats","text":"transmission chain used independent case secondary cases linked transmission. chain starts single case, case chain generates secondary cases according offspring distribution. chain ends secondary cases generated.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/simulate_chain_stats.html","id":"calculating-chain-sizes-and-lengths","dir":"Reference","previous_headings":"","what":"Calculating chain sizes and lengths","title":"Simulate a vector of transmission chains statistics (sizes/lengths) — simulate_chain_stats","text":"function simulates chain size chain \\(\\) time \\(t\\), \\(I_{t, }\\), : $$I_{t, } = \\sum_{}^{I_{t-1}}X_{t, },$$ chain length/duration chain \\(\\) time \\(t\\), \\(L_{t, }\\), : $$L_{t, } = {\\sf min}(1, X_{t, }), $$ \\(X_{t, }\\) secondary cases generated chain \\(\\) time \\(t\\), \\(I_{0, } = L_{0, } = 1\\). distribution secondary cases, \\(X_{t, }\\) modelled offspring distribution (offspring_dist).","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/simulate_chain_stats.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Simulate a vector of transmission chains statistics (sizes/lengths) — simulate_chain_stats","text":"Jacob C. (2010). Branching processes: role epidemiology. International journal environmental research public health, 7(3), 1186–1204. doi:10.3390/ijerph7031204 Blumberg, S., J. O. Lloyd-Smith. 2013. \"Comparing Methods Estimating R0 Size Distribution Subcritical Transmission Chains.\" Epidemics 5 (3): 131–45. doi:10.1016/j.epidem.2013.05.002 . Farrington, C. P., M. N. Kanaan, N. J. Gay. 2003. \"Branching Process Models Surveillance Infectious Diseases Controlled Mass Vaccination.” Biostatistics (Oxford, England) 4 (2): 279–95. doi:10.1093/biostatistics/4.2.279 .","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/simulate_chain_stats.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Simulate a vector of transmission chains statistics (sizes/lengths) — simulate_chain_stats","text":"James M. Azam, Sebastian Funk","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/simulate_chain_stats.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Simulate a vector of transmission chains statistics (sizes/lengths) — simulate_chain_stats","text":"","code":"# Simulate chain sizes with a poisson offspring distribution, assuming an # infinite population and no immunity. set.seed(32) simulate_chain_stats(   n_chains = 20,   statistic = \"size\",   offspring_dist = rpois,   stat_threshold = 10,   lambda = 0.9 ) #> `epichains_summary` object  #>  #>  [1]   6   7   5   7   1 Inf   3   4   6   1   9   1 Inf Inf   1   3 Inf Inf   2 #> [20]   5 #>  #>  Simulated sizes:  #>  #> Max: >=10 #> Min: 1 # Simulate chain sizes with a negative binomial distribution and assuming # a finite population and 10% immunity. set.seed(32) simulate_chain_stats(   pop = 1000,   percent_immune = 0.1,   n_chains = 20,   statistic = \"size\",   offspring_dist = rnbinom,   stat_threshold = 10,   mu = 0.9,   size = 0.36 ) #> `epichains_summary` object  #>  #>  [1] 1 1 1 2 2 4 2 1 1 4 1 1 2 1 1 2 1 1 1 1 #>  #>  Simulated sizes:  #>  #> Max: 4 #> Min: 1"},{"path":"https://epiverse-trace.github.io/epichains/reference/simulate_chains.html","id":null,"dir":"Reference","previous_headings":"","what":"Simulate transmission chains — simulate_chains","title":"Simulate transmission chains — simulate_chains","text":"generates independent transmission chains starting single case per chain, using simple branching process model (See details definition \"chains\" assumptions). Offspring chain generated offspring distribution, optional generation time distribution function. individual chain simulations controlled customisable stopping criteria, including threshold chain size length, generation time cut . function also optionally accepts population related inputs population size (defaults Inf) percentage population initially immune (defaults 0).","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/simulate_chains.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Simulate transmission chains — simulate_chains","text":"","code":"simulate_chains(   n_chains,   statistic = c(\"size\", \"length\"),   offspring_dist,   ...,   stat_threshold = Inf,   pop = Inf,   percent_immune = 0,   generation_time = NULL,   t0 = 0,   tf = Inf )"},{"path":"https://epiverse-trace.github.io/epichains/reference/simulate_chains.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Simulate transmission chains — simulate_chains","text":"n_chains Number chains simulate. statistic chain statistic track stopping criteria chain simulated stat_threshold Inf; <string>. can one : \"size\": total number cases produced chain goes extinct. \"length\": total number generations reached chain goes extinct. offspring_dist Offspring distribution: <function> like ones provided R generate random numbers given distributions (e.g., rpois Poisson). specifically, function needs accept least one argument, n, number random numbers generate. can accept arguments, passed random number generating functions. Examples can provided rpois Poisson distributed offspring, rnbinom negative binomial offspring, custom functions. ... Parameters offspring distribution required R. stat_threshold stopping criterion individual chain simulations; positive number coercible integer. chain's cumulative statistic reaches surpasses stat_threshold, chain ends. Defaults Inf. example, statistic = \"size\" stat_threshold = 10, chain produces 10 cases stop. Note setting stat_threshold guarantee chains stop value. pop Population size; <Integer>. Used alongside percent_immune define susceptible population. Defaults Inf. percent_immune Percent population immune infection start simulation; <numeric> 0 1. Used alongside pop initialise susceptible population. Defaults 0. generation_time generation time function; name user-defined named anonymous function one argument n, representing number generation times sample. t0 Start time (generation time given); either single value vector length n_chains (number initial cases) corresponding initial times. Defaults 0, meaning cases started time 0. tf number cut-infection times (generation time given); Defaults Inf.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/simulate_chains.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Simulate transmission chains — simulate_chains","text":"<epichains> object, basically <data.frame> columns: chain - ID active/ongoing chains, infectee - unique ID infectee. infector - ID infector infectee. generation - discrete time point infection occurs, optionally, time - time infection.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/simulate_chains.html","id":"definition-of-a-transmission-chain","dir":"Reference","previous_headings":"","what":"Definition of a transmission chain","title":"Simulate transmission chains — simulate_chains","text":"transmission chain used independent case secondary cases linked transmission. chain starts single case, case chain generates secondary cases according offspring distribution. chain ends secondary cases generated.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/simulate_chains.html","id":"calculating-chain-sizes-and-lengths","dir":"Reference","previous_headings":"","what":"Calculating chain sizes and lengths","title":"Simulate transmission chains — simulate_chains","text":"function simulates chain size chain \\(\\) time \\(t\\), \\(I_{t, }\\), : $$I_{t, } = \\sum_{}^{I_{t-1}}X_{t, },$$ chain length/duration chain \\(\\) time \\(t\\), \\(L_{t, }\\), : $$L_{t, } = {\\sf min}(1, X_{t, }), $$ \\(X_{t, }\\) secondary cases generated chain \\(\\) time \\(t\\), \\(I_{0, } = L_{0, } = 1\\). distribution secondary cases, \\(X_{t, }\\) modelled offspring distribution (offspring_dist).","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/simulate_chains.html","id":"specifying-generation-time","dir":"Reference","previous_headings":"","what":"Specifying generation_time","title":"Simulate transmission chains — simulate_chains","text":"argument generation_time must specified function one argument, n. example, assuming want specify generation time random log-normally distributed variable meanlog = 0.58 sdlog = 1.58, define named function, call \"generation_time_fn\", one argument representing number generation times sample: generation_time_fn <- function(n){rlnorm(n, 0.58, 1.38)}, assign name function generation_time simulation function, .e. `simulate_*`(..., generation_time = generation_time_fn), ... arguments simulate_*() * placeholder rest simulation function's name. Alternatively, assign anonymous function generation_time simulate_*() call, .e. simulate_*(..., generation_time = function(n){rlnorm(n, 0.58, 1.38)}) simulate_*(..., generation_time = \\(n){rlnorm(n, 0.58, 1.38)}), ... arguments simulate_*().","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/simulate_chains.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Simulate transmission chains — simulate_chains","text":"Jacob C. (2010). Branching processes: role epidemiology. International journal environmental research public health, 7(3), 1186–1204. doi:10.3390/ijerph7031204 Blumberg, S., J. O. Lloyd-Smith. 2013. \"Comparing Methods Estimating R0 Size Distribution Subcritical Transmission Chains.\" Epidemics 5 (3): 131–45. doi:10.1016/j.epidem.2013.05.002 . Farrington, C. P., M. N. Kanaan, N. J. Gay. 2003. \"Branching Process Models Surveillance Infectious Diseases Controlled Mass Vaccination.” Biostatistics (Oxford, England) 4 (2): 279–95. doi:10.1093/biostatistics/4.2.279 .","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/simulate_chains.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Simulate transmission chains — simulate_chains","text":"James M. Azam, Sebastian Funk","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/simulate_chains.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Simulate transmission chains — simulate_chains","text":"","code":"# Using a Poisson offspring distribution and simulating from an infinite # population up to chain size 10. set.seed(32) chains_pois_offspring <- simulate_chains(   n_chains = 10,   statistic = \"size\",   offspring_dist = rpois,   stat_threshold = 10,   generation_time = function(n) rep(3, n),   lambda = 2 ) chains_pois_offspring #> `<epichains>` object #>  #> < epichains head (from first known infector) > #>  #>    chain infector infectee generation time #> 11     1        1        2          2    3 #> 12     1        1        3          2    3 #> 13     2        1        2          2    3 #> 14     2        1        3          2    3 #> 15     3        1        2          2    3 #> 16     3        1        3          2    3 #>  #>  #> Number of chains: 10 #> Number of infectors (known): 9 #> Number of generations: 4 #> Use `as.data.frame(<object_name>)` to view the full output in the console.  # Using a Negative binomial offspring distribution and simulating from a # finite population up to chain size 10. set.seed(32) chains_nbinom_offspring <- simulate_chains(   n_chains = 10,   pop = 100,   percent_immune = 0,   statistic = \"size\",   offspring_dist = rnbinom,   stat_threshold = 10,   generation_time = function(n) rep(3, n),   mu = 2,   size = 0.2 ) chains_nbinom_offspring #> `<epichains>` object #>  #> < epichains head (from first known infector) > #>  #>    chain infector infectee generation time #> 11     1        1        2          2    3 #> 12     2        1        2          2    3 #> 13     2        1        3          2    3 #> 14     2        1        4          2    3 #> 15     2        1        5          2    3 #> 16     2        1        6          2    3 #>  #>  #> Number of chains: 10 #> Number of infectors (known): 5 #> Number of generations: 4 #> Use `as.data.frame(<object_name>)` to view the full output in the console."},{"path":"https://epiverse-trace.github.io/epichains/reference/summary.epichains.html","id":null,"dir":"Reference","previous_headings":"","what":"Summary method for <epichains> class — summary.epichains","title":"Summary method for <epichains> class — summary.epichains","text":"calculates chain statistic (size/length) simulated chains returns object information returned equivalent simulate_chain_stats() call.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/summary.epichains.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Summary method for <epichains> class — summary.epichains","text":"","code":"# S3 method for class 'epichains' summary(object, ...)"},{"path":"https://epiverse-trace.github.io/epichains/reference/summary.epichains.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Summary method for <epichains> class — summary.epichains","text":"object <epichains> object. ... used.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/summary.epichains.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Summary method for <epichains> class — summary.epichains","text":"<epichains_summary> object containing chain summary statistics follows: \"size\": total number offspring produced chain goes extinct. \"length\": number generations achieved chain goes extinct.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/summary.epichains.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Summary method for <epichains> class — summary.epichains","text":"James M. Azam","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/summary.epichains.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Summary method for <epichains> class — summary.epichains","text":"","code":"# Using a negative binomial offspring distribution and simulating from a # finite population up to chain size 10. set.seed(32) sim_chains_nbinom <- simulate_chains(   n_chains = 10,   pop = 100,   percent_immune = 0,   statistic = \"size\",   offspring_dist = rnbinom,   stat_threshold = 10,   mu = 2,   size = 0.2 ) # Summarise the simulated chains sim_chains_nbinom_summary <- summary(sim_chains_nbinom) sim_chains_nbinom_summary #> `epichains_summary` object  #>  #>  [1]   3 Inf Inf   5   6 Inf   1   1   1   1 #>  #>  Simulated sizes:  #>  #> Max: >=10 #> Min: 1  # Same results can be obtained using `simulate_chain_stats()` set.seed(32) sim_summary_nbinom <- simulate_chain_stats(   n_chains = 10,   pop = 100,   percent_immune = 0,   statistic = \"size\",   offspring_dist = rnbinom,   stat_threshold = 10,   mu = 2,   size = 0.2 ) sim_summary_nbinom #> `epichains_summary` object  #>  #>  [1]   3 Inf Inf   5   6 Inf   1   1   1   1 #>  #>  Simulated sizes:  #>  #> Max: >=10 #> Min: 1  # Check that the results are the same setequal(sim_chains_nbinom_summary, sim_summary_nbinom) #> [1] TRUE"},{"path":"https://epiverse-trace.github.io/epichains/reference/summary.epichains_summary.html","id":null,"dir":"Reference","previous_headings":"","what":"Summary method for <epichains_summary> class — summary.epichains_summary","title":"Summary method for <epichains_summary> class — summary.epichains_summary","text":"Summary method <epichains_summary> class","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/summary.epichains_summary.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Summary method for <epichains_summary> class — summary.epichains_summary","text":"","code":"# S3 method for class 'epichains_summary' summary(object, ...)"},{"path":"https://epiverse-trace.github.io/epichains/reference/summary.epichains_summary.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Summary method for <epichains_summary> class — summary.epichains_summary","text":"object <epichains_summary> object. ... used.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/summary.epichains_summary.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Summary method for <epichains_summary> class — summary.epichains_summary","text":"list chain summaries. list contains following elements: n_chains: number chains simulated. max_stat: maximum chain statistic (size/length) achieved chains. min_stat: minimum chain statistic (size/length) achieved chains.","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/summary.epichains_summary.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Summary method for <epichains_summary> class — summary.epichains_summary","text":"James M. Azam","code":""},{"path":"https://epiverse-trace.github.io/epichains/reference/summary.epichains_summary.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Summary method for <epichains_summary> class — summary.epichains_summary","text":"","code":"# Using a Poisson offspring distribution and simulating from an infinite # population up to chain size 10. set.seed(32) chain_stats <- simulate_chain_stats(  n_chains = 10,  statistic = \"size\",  offspring_dist = rpois,  stat_threshold = 10,  lambda = 2 ) summary(chain_stats) #> $n_chains #> [1] 10 #>  #> $max_stat #> [1] Inf #>  #> $min_stat #> [1] Inf #>"},{"path":[]},{"path":"https://epiverse-trace.github.io/epichains/news/index.html","id":"package-development-version","dir":"Changelog","previous_headings":"","what":"Package","title":"epichains (development version)","text":"Removed as_is = TRUE setting vignette YAML headers avoid partial incompatibility incoming pkgdown versions.","code":""},{"path":"https://epiverse-trace.github.io/epichains/news/index.html","id":"epichains-010","dir":"Changelog","previous_headings":"","what":"epichains 0.1.0","title":"epichains 0.1.0","text":"excited announce first minor release epichains. epichains re-implements {bpmodels}, focusing unified simulation framework using branching processes simulate transmission chains data. framework incorporates susceptible depletion pre-existing immunity provides dedicated data structures handling analysing transmission chains tabular vector formats. goal provide seamless interoperability packages within Epiverse-TRACE Initiative broader epidemiological tool ecosystem.","code":""},{"path":[]},{"path":"https://epiverse-trace.github.io/epichains/news/index.html","id":"documentation-0-1-0","dir":"Changelog","previous_headings":"New Features","what":"Documentation","title":"epichains 0.1.0","text":"Dedicated Website: Explore features documentation epichains website. Help: function comes extensive documentation. welcome feedback suggestions improvements. Getting Started: quick guide key functions. Modelling Disease Control Interventions: Learn model various intervention strategies. Projecting Infectious Disease Incidence: case study projecting COVID-19 incidence. Literature: curation literature branching process applications epidemiology. Theoretical Background: deep dive theoretical background functions package (Contributor documentation). Design principles: design principles epichains (Contributor documentation).","code":""},{"path":"https://epiverse-trace.github.io/epichains/news/index.html","id":"simulation-0-1-0","dir":"Changelog","previous_headings":"New Features","what":"Simulation","title":"epichains 0.1.0","text":"simulate_chains(): Simulate independent transmission chains specified number initial cases, incorporating susceptible depletion pre-existing immunity. simulate_chain_stats(): Generate vector chain sizes lengths specified number initial cases, incorporating susceptible depletion pre-existing immunity.","code":""},{"path":"https://epiverse-trace.github.io/epichains/news/index.html","id":"inference-0-1-0","dir":"Changelog","previous_headings":"New Features","what":"Inference","title":"epichains 0.1.0","text":"likelihood(): Estimate (log)likelihood transmission chain sizes lengths, support numeric vectors <epichains> <epichains_summary> objects.","code":""},{"path":"https://epiverse-trace.github.io/epichains/news/index.html","id":"transmission-chain-data-manipulation-0-1-0","dir":"Changelog","previous_headings":"New Features","what":"Transmission Chain Data Manipulation","title":"epichains 0.1.0","text":"summary(): Extract vectors chain sizes lengths <epichains> objects. aggregate(): Generate case time series aggregating generation time infection. plot(): Visualize individual transmission chains filtered id.","code":""}]
