Open Access
2013 Approximating the epidemic curve
Andrew Barbour, Gesine Reinert
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Electron. J. Probab. 18: 1-30 (2013). DOI: 10.1214/EJP.v18-2557


Many models of epidemic spread have a common qualitative structure. The numbers of infected individuals during the initial stages of an epidemic can be well approximated by a branching process, after which the proportion of individuals that are susceptible follows a more or less deterministic course. In this paper, we show that both of these features are consequences of assuming a locally branching structure in the models, and that the deterministic course can itself be determined from the distribution of the limiting random variable associated with the backward, susceptibility branching process. Examples considered includea stochastic version of the Kermack & McKendrick model, the Reed-Frost model, and the Volz configuration model.


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Andrew Barbour. Gesine Reinert. "Approximating the epidemic curve." Electron. J. Probab. 18 1 - 30, 2013.


Accepted: 16 May 2013; Published: 2013
First available in Project Euclid: 4 June 2016

zbMATH: 1301.92072
MathSciNet: MR3065864
Digital Object Identifier: 10.1214/EJP.v18-2557

Primary: 92H30
Secondary: 60J85 , 60K35

Keywords: branching processes , configuration model , deterministic approximation , epidemics , Reed--Frost

Vol.18 • 2013
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