On the simple stochastic epidemic

Abstract

SUMMARY For the simple stochastic epidemic, in which X(t) is the number of infectives at time t and N is the population size, it is shown that the process N½{X(t)/N - m(t)), for suitable m(t), approaches an Ornstein- Uhlenbeck process as N ↑∞. Certain drawbacks in this model for large populations suggest an alternative model, in which the infection rate is the square root of the product of infectives and susceptibles. The asymptotic theory of this model is also investigated.