Introduction In class we covered the SIR model with births and deaths. As a quick refresher: susceptible individuals (\(S\)) become infected and move into the infected class (\(I\)), and then infected individuals who recover move into the recovored, or immune, class (\(R\)). Assuming the birth rate is equal to the death rate (\(\mu\)) gives:
\[\begin{align*} \frac{dS}{dt} &= \mu N -\beta S I - \mu S\\ \frac{dI}{dt} &= \beta S I - \gamma I - \mu I\\ \frac{dR}{dt} &= \gamma I - \mu R.