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Threshold behaviour and final outcome of an epidemic on a random network with household structure

  • Frank Ball (a1), David Sirl (a1) and Pieter Trapman (a2)

Abstract

In this paper we consider a stochastic SIR (susceptible→infective→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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Copyright

Corresponding author

Postal address: School of Mathematical Sciences, The University of Nottingham, University Park, Nottingham, NG7 2RD, UK.
∗∗ Email address: frank.ball@nottingham.ac.uk
∗∗∗ Email address: david.sirl@nottingham.ac.uk
∗∗∗∗ Postal address: Stochastics Section, Faculty of Sciences, Vrije Universiteit Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands. Email address: ptrapman@few.vu.nl

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Threshold behaviour and final outcome of an epidemic on a random network with household structure

  • Frank Ball (a1), David Sirl (a1) and Pieter Trapman (a2)

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