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 AKi its time of infection), stays infectious for a period of length ri, until it is removed. An initially infected individual i stays infected for a period of length ^ri until it is removed. Removed individuals can no longer be affected by the disease. A deterministic approximation as (as K..) to the empirical measure .K=1K.aKi=1.(0,^ri)+1K.bKi=1.(AKi,AKi+ri), describing the average path behavior, is established using Stein's method.