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Approximating the epidemic curve


Barbour, A D; Reinert, Gesine (2013). Approximating the epidemic curve. Electronic Journal of Probability, 18(54):1-30.

Abstract

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 include a stochastic version of the Kermack & McKendrick model, the Reed–Frost model, and the Volz configuration model.

Abstract

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 include a stochastic version of the Kermack & McKendrick model, the Reed–Frost model, and the Volz configuration model.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2013
Deposited On:28 Dec 2017 14:53
Last Modified:28 Dec 2017 14:53
Publisher:Institute of Mathematical Statistics
ISSN:1083-6489
Funders:Schweizerischer Nationalfonds
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1214/EJP.v18-2557

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