The deterministic Kermack‒McKendrick model bounds the general stochastic epidemic



Wilkinson, RR, Ball, FG and Sharkey, KJ ORCID: 0000-0002-7210-9246
(2016) The deterministic Kermack‒McKendrick model bounds the general stochastic epidemic. Journal of Applied Probability, 53 (4). pp. 1031-1040.

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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: General stochastic epidemic, Deterministic general epidemic, SIR, Kermack‒McKendrick, Message passing, Bound
Depositing User: Symplectic Admin
Date Deposited: 11 Dec 2017 09:09
Last Modified: 19 Jan 2023 06:48
DOI: 10.1017/jpr.2016.62
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3013518

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