Details

Consider an SIR model in which we divide the population into three parts: susceptible, infected, and recovered, in the proportions , , and , so that . Suppose the birth rate is a constant equal to the death rate. The model is:

,

,

,

where is the infection rate and is the recovery rate, with the initial , , and non-negative. There is an outbreak only if , and the outbreak results in an epidemic only if ; otherwise the infection will die out [1].

The SIR equations are solved and the result presented in a plot in the - plane for various initial values of and , with initial value . You can vary the values of the infection rate and the recovery rate to follow the trajectory of the SIR system.

Reference

[1] Wikipedia. "Compartmental Models in Epidemiology." (Dec 14, 2012) en.wikipedia.org/wiki/Compartmental_models_in _epidemiology.