Coupling a branching process to an infinite dimensional epidemic process

2007/10/19 by A. D. Barbour, Barbour, A. D.
Mathematics · Medicine · #60J85 #92D30 #COVID-19 epidemiological studies #FOS: Biological sciences #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Populations and Evolution (q-bio.PE) #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.0710.3697

openalex publication_date 2007/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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

Citations

• THE OUTCOME OF A STOCHASTIC EPIDEMIC—A NOTE ON BAILEY'S PAPER

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