## 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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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.