## The deterministic Kermack-McKendrick model bounds the general stochastic epidemic

Wilkinson, Robert R. and Ball, Frank G. and Sharkey, Kieran J. (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 $\to$ Infected $\to$ Recovered (SIR) epidemic model of Kermack and McKendrick provides, for any given time $t>0$, a strict lower bound on the expected number of suscpetibles 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 https://nottingham-repository.worktribe.com/output/835942 General stochastic epidemic; deterministic general epidemic; SIR; Kermack-McKendrick; message passing; bound University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences https://doi.org/10.1017/jpr.2016.62 Ball, Prof Frank Granville 08 Feb 2017 14:25 04 May 2020 18:26 https://eprints.nottingham.ac.uk/id/eprint/40422

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