On the normal convergence of a class of simple batch epidemics

A group of n susceptible individuals exposed to a contagious disease is considered. It is assumed that at each instant in time one or more susceptible individuals can contract the disease. The progress of this epidemic is modeled by a stochastic process Xn (t), t in [0,∞) representing the number of infective individuals at time t. It is shown that Xn (t), with the suitable standardization and under a mild condition, converges in distribution as n → ∞to a normal random variable for all t in (0, t 0), where t 0 is an identifiable number.