Stochastic and deterministic analysis of SIS household epidemics

Neal, Peter John (2006) Stochastic and deterministic analysis of SIS household epidemics. Advances in Applied Probability, 38 (4). pp. 943-968. ISSN 0001-8678

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Abstract

We analyse SIS epidemics among populations partitioned into households. The analysis considers both the stochastic and deterministic models and, unlike in previous analyses, we consider general infectious period distributions. For the deterministic model, we prove the existence of an endemic equilibrium for the epidemic if and only if the threshold parameter, R*, is greater than 1. Furthermore, by utilising Markov chains we show that the total number of infectives converges to the endemic equilibrium as t → ∞. For the stochastic model, we prove a law of large numbers result for the convergence, to the deterministic limit, of the mean number of infectives per household. This is followed by the derivation of a Gaussian limit process for the fluctuations of the stochastic model.

Item Type: Journal Article
Journal or Publication Title: Advances in Applied Probability
Uncontrolled Keywords: /dk/atira/pure/subjectarea/asjc/2600/2613
Subjects:
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 76923
Deposited By: ep_importer_pure
Deposited On: 27 Nov 2015 16:12
Refereed?: Yes
Published?: Published
Last Modified: 14 Feb 2020 03:28
URI: https://eprints.lancs.ac.uk/id/eprint/76923

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