  The SIR model is a three-compartment model of the time development of an
epidemic. After normalizing the dependent variables, the model is a system of
two non-linear differential equations for the susceptible proportion $S$ and
the infected proportion $I$. After normalizing the time variable there is only
one remaining parameter. This largely expository article is mainly about
aspects of this model that can be understood with calculus. It also discusses
an alternative exactly solvable model that appeared in early work of Kermack
and McKendrick. This model may be obtained by replacing $SI$ factors by
$\sqrt{2S-1}I$ factors. For a mild epidemic, where $S$ is decreasing from 1 but
remains fairly close to 1, this is a reasonable approximation.

Dynamical Systems