Electronic Journal of Probability

Approximating the epidemic curve

Andrew Barbour and Gesine Reinert

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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.

Article information

Electron. J. Probab., Volume 18 (2013), paper no. 54, 30 pp.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Epidemics Reed--Frost configuration model deterministic approximation branching processes

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Barbour, Andrew; Reinert, Gesine. Approximating the epidemic curve. Electron. J. Probab. 18 (2013), paper no. 54, 30 pp. doi:10.1214/EJP.v18-2557. https://projecteuclid.org/euclid.ejp/1465064279

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