The deterministic Kermack‒McKendrick model bounds the general stochastic epidemic

Wilkinson, Robert R.; Ball, Frank G.; Sharkey, Kieran J.

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
• Publication Date: 2016-12
• Journal: Journal of Applied Probability
• Print ISSN: 0021-9002
• Publisher: Applied Probability Trust
• Peer Reviewed: Peer Reviewed
• Volume: 53
• Issue: 4
• Pages: 1031-1040
• APA6 Citation: 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
• DOI: https://doi.org/10.1017/jpr.2016.62
• Keywords: General stochastic epidemic; deterministic general epidemic; SIR; Kermack-McKendrick; message passing; bound
• Publisher URL: https://www.cambridge.org/core/journals/journal-of-applied-probability/article/div-classtitlethe-deterministic-kermackmckendrick-model-bounds-the-general-stochastic-epidemicdiv/E36C0B8C1A9341F35FA2E0B22CE35946
• Copyright Statement: Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf