Journal of Applied Probability

Couplings for locally branching epidemic processes

A. D. Barbour

Abstract

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.

Article information

Source
J. Appl. Probab., Volume 51A (2014), 43-56.

Dates
First available in Project Euclid: 2 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.jap/1417528465

Digital Object Identifier
doi:10.1239/jap/1417528465

Mathematical Reviews number (MathSciNet)
MR3317348

Zentralblatt MATH identifier
1329.92126

Subjects
Primary: 92H30 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60J85: Applications of branching processes [See also 92Dxx]

Keywords
Coupling epidemic process branching process approximation deterministic approximation

Citation

Barbour, A. D. Couplings for locally branching epidemic processes. J. Appl. Probab. 51A (2014), 43--56. doi:10.1239/jap/1417528465. https://projecteuclid.org/euclid.jap/1417528465


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