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Couplings for locally branching epidemic processes

Part of: Special processes Markov processes

Published online by Cambridge University Press:  30 March 2016

A. D. Barbour
A. D. Barbour*
Affiliation:
Universität Zürich and National University of Singapore, Institut für Mathematik, Universität Zürich, Winterthurertrasse 190, CH-8057 Zürich. Email address: [email protected].
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Abstract

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The asymptotic behaviour of many locally branching epidemic models can, at least to first order, be deduced from the limit theory of two branching processes. The first is Whittle's (1955) branching approximation to the early stages of the epidemic, the phase in which approximately exponential growth takes place. The second is the susceptibility approximation; the backward branching process that approximates the history of the contacts that would lead to an individual becoming infected. The simplest coupling arguments for demonstrating the closeness of these branching process approximations do not keep the processes identical for quite long enough. Thus, arguments showing that the differences are unimportant are also needed. In this paper we show that, for some models, couplings can be constructed that are sufficiently accurate for this extra step to be dispensed with.

Keywords

Couplingepidemic processbranching process approximationdeterministic approximation

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory 60J85: Applications of branching processes
Type
Part 3. Biological applications
Information
Journal of Applied Probability , Volume 51 , Issue A: Celebrating 50 Years of The Applied Probability Trust , December 2014 , pp. 43 - 56
Copyright
Copyright © Applied Probability Trust 2014 

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