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Publisher: Applied Probability Trust
Languages: English
Types: Article
Subjects: Quantitative Biology - Populations and Evolution, random graph, 92D30, 60K35, epidemic process, 60J80, households, threshold theorem, 05C80, susceptibility set, coupling, Branching process, final outcome, 92D30, local and global contacts, Mathematics - Probability, 60K35

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arxiv: Quantitative Biology::Populations and Evolution
This paper considers a stochastic SIR (susceptible$\to$infective$\to$removed) epidemic model in which individuals may make infectious contacts in two ways, both within `households' (which for ease of exposition are assumed to have equal size) and along the edges of a random graph describing additional social contacts. Heuristically-motivated branching process approximations are described, which lead to a threshold parameter for the model and methods for calculating the probability of a major outbreak, given few initial infectives, and the expected proportion of the population who are ultimately infected by such a major outbreak. These approximate results are shown to be exact as the number of households tends to infinity by proving associated limit theorems. Moreover, simulation studies indicate that these asymptotic results provide good approximations for modestly sized finite populations. The extension to unequal sized households is discussed briefly.
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