# SIR model

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Applied maths
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Wikipedia

## Simplest form

The SIR model is defined for a population $$N$$, $$S$$ the number of susceptible persons, $$I$$ the number of infected people and $$R$$ the number of poeple who have recovered. The following system of differential equations governs the evolution of those three variables:

$\frac{dS}{dt} = - \frac{\beta I S}{N}$ $\frac{dI}{dt} = \frac{\beta I S }{N}- \gamma I$ $\frac{dR}{dt} = \gamma I$

The basic reproduction number $$R_0$$ is defined by $R_0 = \frac{\beta}{\gamma}$