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...c_models/Example SIR Epidemic Project.proj/SIR Epidemic Model.wkgp/SIR Epidemic Model.mdl
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{"is_spatial":false,"defaultID":8,"defaultMode":"discrete","annotation":"The SIR model is a simple mathematical model of epidemics. An epidemic is when the number of people infected with a disease is increasing in a population. S, I, and R stand for:\n\nS - susceptible: These are people that are not infected with the disease yet. However, they are not immune to it either and so they can become infected with the disease in the future.\nI - infected or infectious: These are people that are infected with the disease and can transmit the disease to susceptible people.\nR - recovered: These are people who have recovered from the disease and are immune, so they can no longer be infected with the disease.\n\nThis model is reasonably predictive for infectious diseases that are transmitted from human to human, and where recovery confers lasting resistance, such as measles, mumps and rubella.\nThese variables (S, I, and R) represent the number of people in each compartment at a particular time. To represent that the number of susceptible, infectious and removed individuals may vary over time (even if the total population size remains constant), we make the precise numbers a function of t (time): S(t), I(t) and R(t). For a specific disease in a specific population, these functions may be worked out in order to predict possible outbreaks and bring them under control.\nAs implied by the variable function of t, the model is dynamic in that the numbers in each compartment may fluctuate over time. The importance of this dynamic aspect is most obvious in an endemic disease with a short infectious period, such as measles in the UK prior to the introduction of a vaccine in 1968. Such diseases tend to occur in cycles of outbreaks due to the variation in number of susceptibles (S(t)) over time. During an epidemic, the number of susceptible individuals falls rapidly as more of them are infected and thus enter the infectious and removed compartments. The disease cannot break out again until the number of susceptibles has built back up, e.g. as a result of offspring being born into the susceptible compartment.\nEach member of the population typically progresses from susceptible to infectious to recovered.","modelSettings":{"endSim":20,"timeStep":0.05,"volume":1},"meshSettings":{"count":2},"species":[{"compID":1,"name":"Susceptible","value":999,"mode":"discrete","switchTol":0.03,"switchMin":100,"isSwitchTol":true,"annotation":"Initial population of a species that are\n susceptible to infection\n","diffusionCoeff":0,"subdomains":["subdomain 1:","subdomain 2:"]},{"compID":2,"name":"Infected","value":1,"mode":"discrete","switchTol":0.03,"switchMin":100,"isSwitchTol":true,"annotation":"Initial population of a species that are infected\n","diffusionCoeff":0,"subdomains":["subdomain 1:","subdomain 2:"]},{"compID":3,"name":"Recovered","value":0,"mode":"discrete","switchTol":0.03,"switchMin":100,"isSwitchTol":true,"annotation":"Initial population of a species that have recovered from infection\n","diffusionCoeff":0,"subdomains":["subdomain 1:","subdomain 2:"]}],"initialConditions":[],"parameters":[{"compID":4,"name":"beta","expression":"0.0083","annotation":"Rate at which a Susceptible species becomes infected\n"},{"compID":5,"name":"gamma","expression":"0.3","annotation":"Rate at which an Infected species recovers from the infection.\n\n"}],"reactions":[{"compID":6,"name":"r1","reactionType":"custom-massaction","summary":"Susceptible+Infected \\rightarrow 2Infected","massaction":true,"propensity":"","annotation":"","subdomains":["subdomain 1:","subdomain 2:"],"rate":{"compID":4,"name":"beta","expression":"8.3","annotation":""},"reactants":[{"ratio":1,"specie":{"compID":1,"name":"Susceptible","value":999,"mode":"discrete","switchTol":0.03,"switchMin":100,"isSwitchTol":true,"annotation":"Initial population of a species that are\n susceptible to infection\n","diffusionCoeff":0,"subdomains":["subdomain 1:","subdomain 2:"]}},{"ratio":1,"specie":{"compID":2,"name":"Infected","value":1,"mode":"discrete","switchTol":0.03,"switchMin":100,"isSwitchTol":true,"annotation":"Initial population of a species that are infected\n","diffusionCoeff":0,"subdomains":["subdomain 1:","subdomain 2:"]}}],"products":[{"ratio":2,"specie":{"compID":2,"name":"Infected","value":1,"mode":"discrete","switchTol":0.03,"switchMin":100,"isSwitchTol":true,"annotation":"Initial population of a species that are infected\n","diffusionCoeff":0,"subdomains":["subdomain 1:","subdomain 2:"]}}]},{"compID":7,"name":"r2","reactionType":"change","summary":"Infected \\rightarrow Recovered","massaction":false,"propensity":"","annotation":"","subdomains":["subdomain 1:","subdomain 2:"],"rate":{"compID":5,"name":"gamma","expression":"0.3","annotation":""},"reactants":[{"ratio":1,"specie":{"compID":2,"name":"Infected","value":1,"mode":"discrete","switchTol":0.03,"switchMin":100,"isSwitchTol":true,"annotation":"Initial population of a species that are infected\n","diffusionCoeff":0,"subdomains":["subdomain 1:","subdomain 2:"]}}],"products":[{"ratio":1,"specie":{"compID":3,"name":"Recovered","value":0,"mode":"discrete","switchTol":0.03,"switchMin":100,"isSwitchTol":true,"annotation":"Initial population of a species that have recovered from infection\n","diffusionCoeff":0,"subdomains":["subdomain 1:","subdomain 2:"]}}]}],"rules":[],"eventsCollection":[],"functionDefinitions":[]} | ||
{"is_spatial":false,"defaultID":8,"defaultMode":"discrete","annotation":"The SIR model is a simple mathematical model of epidemics. An epidemic is when the number of people infected with a disease is increasing in a population. S, I, and R stand for:\n\nS - susceptible: These are people that are not infected with the disease yet. However, they are not immune to it either and so they can become infected with the disease in the future.\nI - infected or infectious: These are people that are infected with the disease and can transmit the disease to susceptible people.\nR - recovered: These are people who have recovered from the disease and are immune, so they can no longer be infected with the disease.\n\nThis model is reasonably predictive for infectious diseases that are transmitted from human to human, and where recovery confers lasting resistance, such as measles, mumps and rubella.\nThese variables (S, I, and R) represent the number of people in each compartment at a particular time. To represent that the number of susceptible, infectious and removed individuals may vary over time (even if the total population size remains constant), we make the precise numbers a function of t (time): S(t), I(t) and R(t). For a specific disease in a specific population, these functions may be worked out in order to predict possible outbreaks and bring them under control.\nAs implied by the variable function of t, the model is dynamic in that the numbers in each compartment may fluctuate over time. The importance of this dynamic aspect is most obvious in an endemic disease with a short infectious period, such as measles in the UK prior to the introduction of a vaccine in 1968. Such diseases tend to occur in cycles of outbreaks due to the variation in number of susceptibles (S(t)) over time. During an epidemic, the number of susceptible individuals falls rapidly as more of them are infected and thus enter the infectious and removed compartments. The disease cannot break out again until the number of susceptibles has built back up, e.g. as a result of offspring being born into the susceptible compartment.\nEach member of the population typically progresses from susceptible to infectious to recovered.","modelSettings":{"endSim":20,"timeStep":0.05,"volume":1},"meshSettings":{"count":2},"species":[{"compID":1,"name":"Susceptible","value":999,"mode":"discrete","switchTol":0.03,"switchMin":100,"isSwitchTol":true,"annotation":"Initial population of a species that are\n susceptible to infection\n","diffusionCoeff":0,"subdomains":["subdomain 1:","subdomain 2:"]},{"compID":2,"name":"Infected","value":1,"mode":"discrete","switchTol":0.03,"switchMin":100,"isSwitchTol":true,"annotation":"Initial population of a species that are infected\n","diffusionCoeff":0,"subdomains":["subdomain 1:","subdomain 2:"]},{"compID":3,"name":"Recovered","value":0,"mode":"discrete","switchTol":0.03,"switchMin":100,"isSwitchTol":true,"annotation":"Initial population of a species that have recovered from infection\n","diffusionCoeff":0,"subdomains":["subdomain 1:","subdomain 2:"]}],"initialConditions":[],"parameters":[{"compID":4,"name":"beta","expression":"0.0083","annotation":"Rate at which a Susceptible species becomes infected\n"},{"compID":5,"name":"gamma","expression":"0.3","annotation":"Rate at which an Infected species recovers from the infection.\n\n"}],"reactions":[{"compID":6,"name":"r1","reactionType":"custom-massaction","summary":"Susceptible+Infected \\rightarrow 2Infected","massaction":true,"propensity":"","annotation":"","subdomains":["subdomain 1:","subdomain 2:"],"rate":{"compID":4,"name":"beta","expression":"8.3","annotation":""},"reactants":[{"ratio":1,"specie":{"compID":1,"name":"Susceptible","value":999,"mode":"discrete","switchTol":0.03,"switchMin":100,"isSwitchTol":true,"annotation":"Initial population of a species that are\n susceptible to infection\n","diffusionCoeff":0,"subdomains":["subdomain 1:","subdomain 2:"]}},{"ratio":1,"specie":{"compID":2,"name":"Infected","value":1,"mode":"discrete","switchTol":0.03,"switchMin":100,"isSwitchTol":true,"annotation":"Initial population of a species that are infected\n","diffusionCoeff":0,"subdomains":["subdomain 1:","subdomain 2:"]}}],"products":[{"ratio":2,"specie":{"compID":2,"name":"Infected","value":1,"mode":"discrete","switchTol":0.03,"switchMin":100,"isSwitchTol":true,"annotation":"Initial population of a species that are infected\n","diffusionCoeff":0,"subdomains":["subdomain 1:","subdomain 2:"]}}]},{"compID":7,"name":"r2","reactionType":"change","summary":"Infected \\rightarrow Recovered","massaction":true,"propensity":"","annotation":"","subdomains":["subdomain 1:","subdomain 2:"],"rate":{"compID":5,"name":"gamma","expression":"0.3","annotation":""},"reactants":[{"ratio":1,"specie":{"compID":2,"name":"Infected","value":1,"mode":"discrete","switchTol":0.03,"switchMin":100,"isSwitchTol":true,"annotation":"Initial population of a species that are infected\n","diffusionCoeff":0,"subdomains":["subdomain 1:","subdomain 2:"]}}],"products":[{"ratio":1,"specie":{"compID":3,"name":"Recovered","value":0,"mode":"discrete","switchTol":0.03,"switchMin":100,"isSwitchTol":true,"annotation":"Initial population of a species that have recovered from infection\n","diffusionCoeff":0,"subdomains":["subdomain 1:","subdomain 2:"]}}]}],"rules":[],"eventsCollection":[],"functionDefinitions":[]} |
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public_models/Gene_Regulatory_Network/GeneRegulatoryNetwork1.smdl
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public_models/Gene_Regulatory_Network/GeneRegulatoryNetwork2.smdl
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public_models/Lotkavolterra_Oscillator/Lotkavolterra_Oscillator.mdl
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