Research Repository

# The deterministic Kermack‒McKendrick model bounds the general stochastic epidemic

## Authors

Robert R. Wilkinson

FRANK BALL frank.ball@nottingham.ac.uk
Professor of Applied Probability

Kieran J. Sharkey

### 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 $t>0$, 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.

Journal Article Type Article 2016-12 Journal of Applied Probability 0021-9002 Applied Probability Trust Peer Reviewed 53 4 1031-1040 Wilkinson, R. R., Ball, F. G., & Sharkey, K. J. (2016). The deterministic Kermack‒McKendrick model bounds the general stochastic epidemic. Journal of Applied Probability, 53(4), 1031-1040. https://doi.org/10.1017/jpr.2016.62 https://doi.org/10.1017/jpr.2016.62 General stochastic epidemic; deterministic general epidemic; SIR; Kermack-McKendrick; message passing; bound https://www.cambridge.org/core/journals/journal-of-applied-probability/article/div-classtitlethe-deterministic-kermackmckendrick-model-bounds-the-general-stochastic-epidemicdiv/E36C0B8C1A9341F35FA2E0B22CE35946 Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf

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