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Coupling of Two SIR Epidemic Models with Variable Susceptibilities and Infectivities

Part of: Limit theorems Graph theory

Published online by Cambridge University Press:  14 July 2016

Peter Neal
Peter Neal*
Affiliation:
University of Manchester
*
∗ Postal address: School of Mathematics, University of Manchester, Sackville Street, Manchester M60 1QD, UK. Email address: p.neal-2@manchester.ac.uk
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Abstract

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The variable generalised stochastic epidemic model, which allows for variability in both the susceptibilities and infectivities of individuals, is analysed. A very different epidemic model which exhibits variable susceptibility and infectivity is the random-graph epidemic model. A suitable coupling of the two epidemic models is derived which enables us to show that, whilst the epidemics are very different in appearance, they have the same asymptotic final size distribution. The coupling provides a novel approach to studying random-graph epidemic models.

Keywords

SIR epidemicrandom graphbranching processcentral limit theoremcoupling

MSC classification

Primary: 92D30: Epidemiology
Secondary: 60F05: Central limit and other weak theorems 05C80: Random graphs
Type
Research Article
Information
Journal of Applied Probability , Volume 44 , Issue 1 , March 2007 , pp. 41 - 57
Copyright
Copyright © Applied Probability Trust 2007 

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