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Biometrika 1972 59(2):494-497; doi:10.1093/biomet/59.2.494
© 1972 by Biometrika Trust
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MISCELLANEA

On the simple stochastic epidemic

DONALD R. MoNEIL

Princeton University

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 N1/2{X(t)/N - m(t)), for suitable m(t), approaches an Ornstein- Uhlenbeck process as N {uparrow}{infty}. 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.

Key Words: Asymptotic distribution • Brownian motion • Diffusion • Deterministic epidemic model • Stochastic epidemic


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