# Compartmental SIR model in epidemiology (basic reproduction number)

## Description

In order to model the progress of an epidemic in a large population, the population diversity must be reduced to a few key characteristics which are relevant to the infection under consideration. For example, for most common childhood diseases that confer long-lasting immunity, it makes sense to divide the population into those who are susceptible to the disease, those who are infected and those who have recovered and are immune. These subdivisions of the population are called compartments. The SIR model labels three compartments : number susceptible, number infectious and number recovered (immune). The basic reproduction number (or ratio) is the expected number of new infections from a single infection in a population where all subjects are susceptible.

Related formulas## Variables

R_{0} | The basic reproduction number (dimensionless) |

S_{t} | Number susceptible (dimensionless) |

I_{t} | Number infectious (dimensionless) |

R_{t} | Number recovered (dimensionless) |

T_{r} | Typical time until recovery (dimensionless) |

T_{c} | Typical time between contacts (dimensionless) |