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December 2016 The deterministic Kermack‒McKendrick model bounds the general stochastic epidemic
Robert R. Wilkinson, Frank G. Ball, Kieran J. Sharkey
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J. Appl. Probab. 53(4): 1031-1040 (December 2016).

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.

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Robert R. Wilkinson. Frank G. Ball. Kieran J. Sharkey. "The deterministic Kermack‒McKendrick model bounds the general stochastic epidemic." J. Appl. Probab. 53 (4) 1031 - 1040, December 2016.

Information

Published: December 2016
First available in Project Euclid: 7 December 2016

zbMATH: 1353.92105
MathSciNet: MR3581239

Subjects:
Primary: 92D30
Secondary: 05C80 , 60J22 , 60J27

Keywords: bound , deterministic general epidemic , general stochastic epidemic , Kermack‒McKendrick , message passing , SIR

Rights: Copyright © 2016 Applied Probability Trust

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Vol.53 • No. 4 • December 2016
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