BalSirTra2009Preprint[1].pdf (415.4 kB)
Threshold behaviour and final outcome of an epidemic on a random network with household structure
journal contribution
posted on 2011-09-28, 10:53 authored by Frank Ball, David Sirl, Pieter TrapmanIn 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.
History
School
- Science
Department
- Mathematics Education Centre
Citation
BALL, F., SIRL, D. and TRAPMAN, P., 2009. Threshold behaviour and final outcome of an epidemic on a random network with household structure. Advances in Applied Probability, 41(3), pp. 765-796.Publisher
© Applied Probability TrustVersion
- AM (Accepted Manuscript)
Publication date
2009Notes
This article was published in the journal, Advances in Applied Probability [© Applied Probability Trust] and the definitive version is available at http://dx.doi.org/10.1239/aap/1253281063ISSN
0001-8678Publisher version
Language
- en