The deterministic Kermack-McKendrick model bounds the general stochastic epidemic
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 exp...
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| Format: | Article |
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Applied Probability Trust
2016
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| Online Access: | https://eprints.nottingham.ac.uk/40422/ |
| _version_ | 1848796052483735552 |
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| author | Wilkinson, Robert R. Ball, Frank G. Sharkey, Kieran J. |
| author_facet | Wilkinson, Robert R. Ball, Frank G. Sharkey, Kieran J. |
| author_sort | Wilkinson, Robert R. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T19:41:51Z |
| format | Article |
| id | nottingham-40422 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:41:51Z |
| publishDate | 2016 |
| publisher | Applied Probability Trust |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-404222020-05-04T18:26:50Z https://eprints.nottingham.ac.uk/40422/ The deterministic Kermack-McKendrick model bounds the general stochastic epidemic Wilkinson, Robert R. Ball, Frank G. Sharkey, Kieran J. 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. Applied Probability Trust 2016-12-09 Article PeerReviewed Wilkinson, Robert R., 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 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 doi:10.1017/jpr.2016.62 doi:10.1017/jpr.2016.62 |
| spellingShingle | General stochastic epidemic; deterministic general epidemic; SIR; Kermack-McKendrick; message passing; bound Wilkinson, Robert R. Ball, Frank G. Sharkey, Kieran J. The deterministic Kermack-McKendrick model bounds the general stochastic epidemic |
| title | The deterministic Kermack-McKendrick model bounds the general stochastic epidemic |
| title_full | The deterministic Kermack-McKendrick model bounds the general stochastic epidemic |
| title_fullStr | The deterministic Kermack-McKendrick model bounds the general stochastic epidemic |
| title_full_unstemmed | The deterministic Kermack-McKendrick model bounds the general stochastic epidemic |
| title_short | The deterministic Kermack-McKendrick model bounds the general stochastic epidemic |
| title_sort | deterministic kermack-mckendrick model bounds the general stochastic epidemic |
| topic | General stochastic epidemic; deterministic general epidemic; SIR; Kermack-McKendrick; message passing; bound |
| url | https://eprints.nottingham.ac.uk/40422/ https://eprints.nottingham.ac.uk/40422/ https://eprints.nottingham.ac.uk/40422/ |