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Biometrika 1968 55(1):199-209; doi:10.1093/biomet/55.1.199
© 1968 by Biometrika Trust
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A perturbation approximation to the simple stochastic epidemic in a large population

NORMAN T. J. BAILEY

World Health Organization Geneva

An asymptotically valid approximation is obtained for the simple stochastic epidemic in a large population of size N, using the following approach. For suitably defined variables, the stochastic process tends to a deterministic limit as N{uparrow}{propto}. The moment-generating function of the deterministic process satisfies an easily soluble partial differential equation and can be represented by an eigenfunction expansion. The solution of the corresponding stochastic equation can accordingly be obtained by standard perturbation theory, and the paper presents various results for the first-order perturbations of order N–1.


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