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Extinction times in the subcritical stochastic SIS logistic epidemic

Brightwell, Graham, House, Thomas and Luczak, Malwina J. (2018) Extinction times in the subcritical stochastic SIS logistic epidemic. Journal of Mathematical Biology, 77 (2). pp. 455-493. ISSN 0303-6812

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Identification Number: 10.1007/s00285-018-1210-5


Many real epidemics of an infectious disease are not straightforwardly super- or sub-critical, and the understanding of epidemic models that exhibit such complexity has been identified as a priority for theoretical work. We provide insights into the near-critical regime by considering the stochastic SIS logistic epidemic, a well-known birth-and-death chain used to model the spread of an epidemic within a population of a given size N. We study the behaviour of the process as the population size N tends to infinity. Our results cover the entire subcritical regime, including the “barely subcritical” regime, where the recovery rate exceeds the infection rate by an amount that tends to 0 as N→∞ but more slowly than N−1/2 . We derive precise asymptotics for the distribution of the extinction time and the total number of cases throughout the subcritical regime, give a detailed description of the course of the epidemic, and compare to numerical results for a range of parameter values. We hypothesise that features of the course of the epidemic will be seen in a wide class of other epidemic models, and we use real data to provide some tentative and preliminary support for this theory

Item Type: Article
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Additional Information: © 2018 Springer-Verlag
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 15 Mar 2018 16:11
Last Modified: 20 Oct 2021 00:38

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