THE ASYMPTOTIC EVOLUTION OF THE GENERAL STOCHASTIC EPIDEMIC

Generalizing Sellke's construction, a general stochastic epidemic with non-Markovian transition behavior is considered. At time t = 0, the population of total size K consists of aK individuals that are infected by a certain disease (and infectious); the remaining bK individuals are susceptible with respect to that disease. An initially susceptible individual i, when infected (call A(i)(K) its time of infection), stays infectious for a period of length r(i), until it is removed. An initially infected individual i stays infected for a period of length Pi until it is removed. Removed individuals can no longer be affected by the disease. A deterministic approximation as (as K -> infinity) to the empirical measure xi(K) = 1/K Sigma(aK)(i=1) delta((0, fi)) + 1/K Sigma(bK)(i=1) delta((AiK,AiK+ri)), describing the average path behavior, is established using Stein's method.