Threshold behaviour in stochastic epidemics among households

A very general model for the spread of an epidemic among a population consisting of m households, each of size n, is presented. The asymptotic situation in which the number of households in tends to infinity, whilst the household size n remains fixed, is analysed. For large m the process of infected households can be approximated by a branching process. A coupling argument is used to make this approximation precise as in tends to ∞, thus enabling a threshold theorem to be developed. Specialisation to the case where infective individuals during their infectious period make infectious contacts within their own group with rate λ_w and outside their own group with rate λ_Bis briefly considered. Generalisations to populations with unequal household sizes and different types of individuals are outlined.