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Coupling a branching process to an infinite dimensional epidemic process* **

Published online by Cambridge University Press:  15 December 2008

Andrew D. Barbour
Andrew D. Barbour*
Affiliation:
Universität Zürich Angewandte Mathematik, Winterthurerstrasse 190, 8057 Zürich, Switzerland
*
a.d.barbour@math.uzh.ch
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Abstract

Branching process approximation to the initial stages of an epidemicprocess has been used since the 1950's as a technique for providing stochastic counterparts to deterministic epidemic threshold theorems.One way of describing the approximation is to construct both branching and epidemic processes on the same probability space, insuch a way that their paths coincide for as long as possible. Inthis paper, it is shown, in the context of a Markovian model of parasiticinfection, that coincidence can be achieved with asymptotically high probability until MN infections have occurred, as long asMN = o(N 2/3), where N denotes the total number of hosts.

Keywords

Likelihood ratio couplingbranching process approximationepidemic process.

Information

Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 14 , 2010 , pp. 53 - 64
Copyright
© EDP Sciences, SMAI, 2010

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Footnotes

*

Work supported in part by Schweizerischer Nationalfonds Projekt No. 20–117625/1.

**

To Cindy Greenwood, for her 70th.

References

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