Robert R. Wilkinson
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.
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
Journal Article Type | Article |
---|---|
Acceptance Date | Feb 17, 2016 |
Online Publication Date | Dec 9, 2016 |
Publication Date | 2016-12 |
Deposit Date | Feb 8, 2017 |
Publicly Available Date | Feb 8, 2017 |
Journal | Journal of Applied Probability |
Print ISSN | 0021-9002 |
Publisher | Applied Probability Trust |
Peer Reviewed | Peer Reviewed |
Volume | 53 |
Issue | 4 |
Pages | 1031-1040 |
DOI | https://doi.org/10.1017/jpr.2016.62 |
Keywords | General stochastic epidemic; deterministic general epidemic; SIR; Kermack-McKendrick; message passing; bound |
Public URL | https://nottingham-repository.worktribe.com/output/835942 |
Publisher URL | https://www.cambridge.org/core/journals/journal-of-applied-probability/article/div-classtitlethe-deterministic-kermackmckendrick-model-bounds-the-general-stochastic-epidemicdiv/E36C0B8C1A9341F35FA2E0B22CE35946 |
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