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, t0), where t0 is an identifiable number.