intro.md

Basic microparasite model

Author: Christopher Davis

Date: 2018-10-02

Description

A basic microparasite model of susceptibles and infecteds with the force of infection density dependent. $\beta_{\text{min}}$ is the minimum value of the transmission rate $\beta$, such that the disease will spread.

Equations

$$ \frac{dS(t)}{dt} = (\nu - \mu)\left(1- \frac{S(t)}{K}\right) S(t)- \beta S(t) I(t)\\ \frac{dI(t)}{dt} = \beta S(t) I(t)- (\mu +\ \alpha) I(t)\\ $$

References

• De Leo GA, Dobson AP (February, 1996). "Allometry and simple epidemic models for microparasites". Nature. 379(6567):720