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The deterministic Kermack‒McKendrick model bounds the general stochastic epidemic

  • Robert R. Wilkinson (a1), Frank G. Ball (a2) and Kieran J. Sharkey (a1)


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.


Corresponding author

* 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:
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