On the asymptotic distribution of the size of a stochastic epidemic

For a stochastic epidemic of the type considered by Bailey 1 and Kendall 3, Daniels 2 showed that ‘when the threshold is large but the population size is much larger, the distribution of the number remaining uninfected in a large epidemic has approximately the Poisson form.' A simple, intuitive proof is given for this result without use of Daniels's assumption that the original number of infectives is ‘small'. The proof is based on a construction of the epidemic process which is more explicit than the usual description.