English

The deterministic Kermack-McKendrick model bounds the general stochastic epidemic

Populations and Evolution 2017-02-13 v3 Statistical Mechanics Probability Physics and Society

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>0t>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.

Keywords

Cite

@article{arxiv.1602.01730,
  title  = {The deterministic Kermack-McKendrick model bounds the general stochastic epidemic},
  author = {Robert R. Wilkinson and Frank G. Ball and Kieran J. Sharkey},
  journal= {arXiv preprint arXiv:1602.01730},
  year   = {2017}
}
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