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The deterministic Kermack‒McKendrick model bounds the general stochastic epidemic

Wilkinson, RR, Ball, FG and Sharkey, KJ (2016) The deterministic Kermack‒McKendrick model bounds the general stochastic epidemic. Journal of Applied Probability, 53 (4). pp. 1031-1040. ISSN 0021-9002

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Abstract

We prove that, for Poisson transmission and recovery processes, the classic susceptible→infected→recovered (SIR) epidemic model of Kermack and McKendrick provides, for any given time t>0, a strict lower bound on the expected number of susceptibles and a strict upper bound on the expected number of recoveries in the general stochastic SIR epidemic. The proof is based on the recent message passing representation of SIR epidemics applied to a complete graph.

Item Type: Article
Uncontrolled Keywords: 0102 Applied Mathematics, 0104 Statistics
Subjects: Q Science > QA Mathematics
R Medicine > R Medicine (General)
R Medicine > RB Pathology
Divisions: Applied Mathematics
Publisher: Cambridge University Press (CUP)
Date Deposited: 03 Jul 2019 09:32
Last Modified: 03 Jul 2019 09:45
DOI or Identification number: 10.1017/jpr.2016.62
URI: http://researchonline.ljmu.ac.uk/id/eprint/10963

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