intro.md

SIS model

Author: Simon Frost

Date: 2018-07-12

Description

The susceptible-infected-susceptible (SIS) model is one of the simplest models that has an endemic equilibrium. 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 susceptible again.

Equations

$$ \frac{dS(t)}{dt} = -\beta S(t) I(t)+\gamma I(t)\\ \frac{dI(t)}{dt} = \beta S(t) I(t)- \gamma I(t)\\ $$

References

1. https://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology