Electronic Journal of Probability
- Electron. J. Probab.
- Volume 18 (2013), paper no. 54, 30 pp.
Approximating the epidemic curve
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.
Electron. J. Probab., Volume 18 (2013), paper no. 54, 30 pp.
Accepted: 16 May 2013
First available in Project Euclid: 4 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60J85: Applications of branching processes [See also 92Dxx]
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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