User:Hannes Röst/Evolutionary dynamics/Kermack-McKendrick Model

The Kermack-McKendrick Model is a mathematical model that is used in epidemiology. It models the spreading of infectious diseases. In the model, the host population is divided into three classes: susceptible (S), infected (I) and recovered (R). Only the susceptible population can get infected while the recovered population is immune to the pathogen. These kinds of models are also called SRI models.

The model can be discribed by the following differential equations:

${\begin{aligned}{\frac {dS}{dt}}&=-\beta \cdot S\cdot I\\{\frac {dI}{dt}}&=\beta \cdot S\cdot I-\gamma \cdot I\\{\frac {dR}{dt}}&=\gamma \cdot I\end{aligned}}$

where the parameter $\beta$ desrcibes the efficiency of the infection and the parameter $\gamma$ desrcibes the recovery rate.

Literature

• Nowak, Martin A: Evolutionary Dynamics: Exploring the Equations of Life. Belknap Press (2006) ISBN 978-0674023383

External links

• Kermack-McKendrick Model at Wolfram