Covid 19 - Simple Math Model (SIR)

Hi everyone,


I want to use this article to provide a brief description on a basic epidemic model, the SIR and then describe why the need for effective vaccines and movement restrictions.


So the SIR model splits the population to into three groups:

S - susceptible - people who have not been infected

I - Infected - people who are infected

R - Removed - people who were infected and have passed away or recovered


* A key assumption is that someone who has recovered will not catch the virus again.


Without going through the details, two important parameters underline the model.

a) The infection rate of the virus itself (how fast/well does the virus spreads)

b) The interaction rate of the population (the average number of interactions a subject has across the population)


Different societies will have different values of (b), and one definitely need that and (a) to model the spread of the virus effectively. But looking at the Tracetogether app one can see the approximate number "exchanges" we have on a daily basis.


So what can we say for sure?

  • Movement and dining restrictions helps to lower (b)

  • Wearing masks helps to lower (a)

  • Having effective vaccines helps to lower (a)


And that's why the numbers are moving in waves (as observed worldwide). When restrictions are lifted the interaction rates shoots up, lending weight to the transition from stage S to I (in other countries we can even take into consideration the weather (winter flu season). I have not studied the effectiveness of the vaccines we take so I can't really comment much on that, but let's suppose the efficacy of the vaccines do wear out after a few months, then clearly it adds to the problem.


So wear your mask properly when indoors and when at populated areas (malls, public transport).


All these will help to lower the growth rate (r) and the reproduction rate (R) of the virus, yes they are different - I will be addressing them in the next article.


Alvin


#acesmath #covid #SIRmodel #MathIA #Mathmodels #epidemicmodels

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