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The deterministic Kermack‒McKendrick model bounds the general stochastic epidemic

Part of: Markov processes Graph theory

Published online by Cambridge University Press:  09 December 2016

Robert R. Wilkinson ,
Frank G. Ball  and
Kieran J. Sharkey
Robert R. Wilkinson*
Affiliation:
The University of Liverpool
Frank G. Ball*
Affiliation:
The University of Nottingham
Kieran J. Sharkey*
Affiliation:
The University of Liverpool
*
* Postal address: Department of Mathematical Sciences, The University of Liverpool, Liverpool L69 7ZL, UK.
*** Postal address: School of Mathematical Sciences, The University of Nottingham, University Park, Nottingham NG7 2RD, UK. Email address: frank.ball@nottingham.ac.uk
* Postal address: Department of Mathematical Sciences, The University of Liverpool, Liverpool L69 7ZL, UK.
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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.

Keywords

General stochastic epidemicdeterministic general epidemicSIRKermack‒McKendrickmessage passingbound

MSC classification

Primary: 92D30: Epidemiology
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces 60J22: Computational methods in Markov chains 05C80: Random graphs
Type
Research Papers
Information
Journal of Applied Probability , Volume 53 , Issue 4 , December 2016 , pp. 1031 - 1040
Copyright
Copyright © Applied Probability Trust 2016 

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