Asymptotic final-size distribution for some chain-binomial processes

Abstract

The classical Reed-Frost process is generalized by allowing infection probabilities to depend on current epidemic size. Such a process can be imbedded in a simple Markov process derived from i.i.d. waiting times. The final size of the epidemic has the same distribution as the time for the first crossing of a certain linear barrier of the imbedding process. The asymptotic distribution of the final size can be derived from some weak convergence results for the imbedding process. The existence of a distribution determining set of harmonic functions for these chain-binomial processes is also established.