Coupling a branching process to an infinite dimensional epidemic process
ESAIM: Probability and Statistics, Tome 14 (2010), pp. 53-64.

Branching process approximation to the initial stages of an epidemic process 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, in such a way that their paths coincide for as long as possible. In this paper, it is shown, in the context of a markovian model of parasitic infection, that coincidence can be achieved with asymptotically high probability until MN infections have occurred, as long as MN = o(N2/3), where N denotes the total number of hosts.

DOI : 10.1051/ps:2008023
Classification : 92D30, 62E17
Mots-clés : likelihood ratio coupling, branching process approximation, epidemic process 
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     author = {Barbour, Andrew D.},
     title = {Coupling a branching process to an infinite dimensional epidemic process},
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Barbour, Andrew D. Coupling a branching process to an infinite dimensional epidemic process. ESAIM: Probability and Statistics, Tome 14 (2010), pp. 53-64. doi : 10.1051/ps:2008023. http://www.numdam.org/articles/10.1051/ps:2008023/

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