The shape of the size distribution of an epidemic in a finite population

Qualitative changes in the shape of the distribution of the final size of the susceptible-->infected-->removed (S-I-R) epidemic are used by Nåsell to define a threshold concept for the stochastic S-I-R epidemic. Numerical evaluations indicate that this threshold depends on the population size N according to the formula R0 approximately 1 + p/N1/3 for large N, where R0 is the basic reproduction ratio for the model. We derive an approximation of the final size distribution that supports this numerical result.