SIR Model

The SIR model is a compartmental mathematical model used in epidemiology to describe the spread of an infectious disease through a population, dividing that population into three compartments, those Susceptible to infection, those currently Infected, and those who have Recovered and gained immunity, and tracking the flow between the compartments over time with a system of ordinary differential equations. It was introduced in 1927 by the Scottish biochemist William Ogilvy Kermack and the Scottish military physician Anderson Gray McKendrick as part of a broader theory of epidemics. A central quantity derived from the model is the basic reproduction number, the average number of new infections a single infected individual produces in an entirely susceptible population, which determines whether an outbreak will grow or die out. The SIR model and its many extensions remain the foundation of modern mathematical epidemiology and were widely cited in public discussion of infectious disease spread during the COVID-19 pandemic.