Epidemiology: The SIR model

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Simulation of differential equations with turtle graphics.

SIR model without vital dynamics

A single epidemic outbreak is usually far more rapid than the vital dynamics of a population, thus, if the aim is to study the immediate consequences of a single epidemic, one may neglect the birth-death processes. In this case the SIR system described above can be expressed by the following set of differential equations:

   \frac{dS}{dt} = - \beta I S     
   
   \frac{dI}{dt} = \beta I S - \nu I 
   \frac{dR}{dt} = \nu I