Asymptotic final-size distribution for some chain-binomial processes

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 certainl inear barriero f the imbeddingp rocess.T he asymptoticd istributiono f the final size can be derived from some weak convergence results for the imbedding process. The existence of a distribution determining set of harmonic functionsf or these chain-binomiapl rocesses is also establishe