# SIR

## Understanding the SIR model

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.