# Epidemiology: The SIR model

From JSXGraph Wiki

Simulation of differential equations with turtle graphics using JSXGraph.

### 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:

- [math]\displaystyle{ \frac{dS}{dt} = - \beta I S }[/math]

- [math]\displaystyle{ \frac{dR}{dt} = \gamma I }[/math]

- [math]\displaystyle{ \frac{dI}{dt} = -(dS+dR) }[/math]

The lines in the JSXGraph-simulation below have the following meaning:

* Blue: Rate of susceptible population * Red: Rate of infected population * Green: Rate of recovered population (which means: immune, isolated or dead)