Coupling a branching process to an infinite dimensional epidemic process

Andrew D. Barbour

Universität Zürich Angewandte Mathematik, Winterthurerstrasse 190, 8057 Zürich, Switzerland

Corresponding author: a.d.barbour@math.uzh.ch

Received: 10 March 2008
Revised: 13 July 2008

Abstract

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 M_N infections have occurred, as long as M_N = o(N^2/3), where N denotes the total number of hosts.