The duration of the closed stochastic epidemic

Abstract

The paper discusses the time between the first infection and the last removal in the closed stochastic epidemic. The method is to prove limit theorems for the distribution of this time, as the population size becomes large, and then to use the limits to provide an approximate distribution: the epidemic is allowed to start either with a large number of immigrant infectives, or with a single case. The accuracy of the approximation in finite populations is illustrated by some examples, and the method of proof also gives s theoretical estimate of the rate of convergence to the limit. The problem is typical of a much wider class of boundary problems, and the method used can be adapted to them without difficulty.