Author: Simon Frost
Date: 2018-07-12
The susceptible-infected-recovered (SIR) model in a closed population was proposed by Kermack and McKendrick as a special case of a more general model, and forms the framework of many compartmental models. Susceptible individuals, $S$, are infected by infected individuals, $I$, at a per-capita rate $\beta I$, and infected individuals recover at a per-capita rate $\gamma$ to become recovered individuals, $R$.
$$
\frac{dS(t)}{dt} = -\beta S(t) I(t)\\
\frac{dI(t)}{dt} = \beta S(t) I(t)- \gamma I(t)\\
\frac{dR(t)}{dt} = \gamma I(t)
$$
- Kermack WO, McKendrick AG (August 1, 1927). "A Contribution to the Mathematical Theory of Epidemics". Proceedings of the Royal Society A. 115 (772): 700–721
- https://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology