On a general stochastic epidemic model

Abstract

A non-Markovian epidemic model is proposed for which a stochastic epidemic threshold theorem, like that by Whittle (1955) for a simpler model, is shown to hold. The threshold theorem can be a useful guide in determining public health measures aimed at preventing major outbreaks of a communicable disease. Bounds are obtained for the mean size of minor epidemics. A parameter of the model, whose value is crucial to applications of these results, is the product of the infection rate and the mean duration of the infectious period. Estimators are suggested for this parameter by identifying martingales associated with counting processes of the epidemic model and by constructing other martingales which can be written as stochastic integrals.