Added variant frequency and further questions

notes/Work_documented.Expected_immunity.md

@@ -2,7 +2,7 @@
 id: drw8w7u2kcr0z6nl2ekgoea
 title: Expected_immunity
 desc: 'Work done to compute expected immunity'
-updated: 1714594275357
+updated: 1715068525419
 created: 1712142695419
 ---
 ## **Objective:**
@@ -15,6 +15,7 @@ Finding the expected immunity towards an amino acid substitution. This can hint
 2. But in lab's work x,y denotes prevalent variants of SARS_Cov2
 3. In the present work x,y denote amino acid substitutions like "Spike_A344T", "Spike_A344A" - can be assumed like covid variant harbouring only one of the aa_substitutions at a time.
 4. Assumption of point 3 is followed throughout.
+5. Currently the work is studies the immunity against a single infection happended at the start of tthe time horizon.
 
 ## **Calculation of probability of neutralisation:**
 
@@ -101,4 +102,20 @@ All the scripts are present in ```"/Users/vishnushirishyamsaisundar/Documents/Ma
 - The trend of the variant having the high immunity has three distinct crests; Few positions have slight variation in this,  the trend that has has only 2 crests.
 - These positions include 493, 446, 346, 490, 486, 445. ![493 immunity](assets/plots/493_immunity.png) ![446 immunity](assets/plots/446_immunity.png) ![346 immunity](assets/plots/346_immunity.png) ![490 immunity](assets/plots/490_immunity.png) ![486 immunity](assets/plots/486_immunity.png) ![445 immunity](assets/plots/445_immunity.png).
 - In all the above cases, except for position 493, wildtype has the highest immunity among people.
-- 180 positions out of 199 positions have high immunity against the wildtype variant.
+- 180 positions out of 199 positions have high immunity against the wildtype variant.
+- To see what sets the immunity of one variant appart, the frequency of the variants of a position is plotted.
+- It is observed that the variant with high frequency records high immunity against aswell.
+- For an instance if we consider position 493, ![493_imm_freq](assets/plots/493_imm_freq.png) variant Spike_Q493R has high frequency and high immunity against too until Nov22.  While calculating the expected immunnity against the variant, the case when x=y=Spike_Q493R will have the heighest value because p1 will be higher than p2, frequency of Spike_Q493R is higher anyways, so the expected immunity against Spike_Q493R is high
+- My inference from the plot is that, since the frequency is high, more people are infected and so more people are immune against the same variant.
+- Immunity against variants that has higher frequecy after a period in the observation period doesn't have peaks high like the former one. This can be because we consider the infection to happen on the first day of the observation horizon.
+
+## **Further questions:**
+
+- The next question would be how to incorporate multiple infections.
+
+  - By applying weights to reduce the probability of neutralisation?
+  - Or By multiplying the probability of neutralisation combinations
+
+- At what time stamps should another infection be introduced
+  - End of immunity waning period
+  - Or Periods where the freequqency of multiple variants are higher