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Reed–Frost model


The Reed–Frost model is a mathematical model of epidemics put forth in the 1920s by Lowell Reed and Wade Hampton Frost, of Johns Hopkins University. While originally presented in a talk by Frost in 1928 and used in courses at Hopkins for two decades, the mathematical formulation was not published until the 1950s, when it was also made into a TV episode.

This is an example of a "chain binomial" model, a simplified, iterative model of how an epidemic will behave over time.

The Reed-Frost model is one of the simplest stochastic epidemic models. It was formulated by Lowell Reed and Wade Frost in 1928 (in unpublished work) and describes the evolution of an infection in generations. Each infected individual in generation t (t = 1,2,...) independently infects each susceptible individual in the population with some probability p. The individuals that become infected by the individuals in generation t then constitute generation t + 1 and the individuals in generation t are removed from the epidemic process.

The Reed–Frost model is based on the following assumptions:

The following parameters are set initially:

With this information, a simple formula allows the calculation of how many individuals will be infected, and how many immune, in the next time interval. This is repeated until the entire population is immune, or no infective individuals remain. The model can then be run repeatedly, adjusting the initial conditions, to see how these affect the progression of the epidemic.

The probability of adequate contact corresponds roughly with R0, the basic reproduction number—in a large population when the initial number of infecteds is small, an infected individual is expected to cause new cases.


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