Susceptibility sets and the final outcome of collective Reed–Frost epidemics
This paper is concerned with exact results for the final outcome of stochastic SIR (susceptible → infective → recovered) epidemics among a closed, finite and homogeneously mixing population. The factorial moments of the number of initial susceptibles who ultimately avoid infection by such an epidemi...
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| Format: | Article |
| Language: | English |
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Springer
2018
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| Online Access: | https://eprints.nottingham.ac.uk/50538/ |
| _version_ | 1848798277114265600 |
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| author | Ball, Frank |
| author_facet | Ball, Frank |
| author_sort | Ball, Frank |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | This paper is concerned with exact results for the final outcome of stochastic SIR (susceptible → infective → recovered) epidemics among a closed, finite and homogeneously mixing population. The factorial moments of the number of initial susceptibles who ultimately avoid infection by such an epidemic are shown to be intimately related to the concept of a susceptibility set. This connection leads to simple, probabilistically illuminating proofs of exact results concerning the total size and severity of collective Reed–Frost epidemic processes, in terms of Gontcharoff polynomials, first obtained in a series of papers by Claude Lef`evre and Philippe Picard. The proofs extend easily to include general final state random variables defined on SIR epidemics, and also to multitype epidemics. |
| first_indexed | 2025-11-14T20:17:13Z |
| format | Article |
| id | nottingham-50538 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T20:17:13Z |
| publishDate | 2018 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-505382018-06-14T16:31:42Z https://eprints.nottingham.ac.uk/50538/ Susceptibility sets and the final outcome of collective Reed–Frost epidemics Ball, Frank This paper is concerned with exact results for the final outcome of stochastic SIR (susceptible → infective → recovered) epidemics among a closed, finite and homogeneously mixing population. The factorial moments of the number of initial susceptibles who ultimately avoid infection by such an epidemic are shown to be intimately related to the concept of a susceptibility set. This connection leads to simple, probabilistically illuminating proofs of exact results concerning the total size and severity of collective Reed–Frost epidemic processes, in terms of Gontcharoff polynomials, first obtained in a series of papers by Claude Lef`evre and Philippe Picard. The proofs extend easily to include general final state random variables defined on SIR epidemics, and also to multitype epidemics. Springer 2018-04-04 Article PeerReviewed application/pdf en cc_by https://eprints.nottingham.ac.uk/50538/8/s11009-018-9631-6.pdf Ball, Frank (2018) Susceptibility sets and the final outcome of collective Reed–Frost epidemics. Methodology and Computing in Applied Probability . ISSN 1573-7713 Total size; Severity; Susceptibility set; Symmetric sampling procedure; Gontcharoff polynomial; General final state random variables https://link.springer.com/article/10.1007%2Fs11009-018-9631-6 doi:10.1007/s11009-018-9631-6 doi:10.1007/s11009-018-9631-6 |
| spellingShingle | Total size; Severity; Susceptibility set; Symmetric sampling procedure; Gontcharoff polynomial; General final state random variables Ball, Frank Susceptibility sets and the final outcome of collective Reed–Frost epidemics |
| title | Susceptibility sets and the final outcome of collective Reed–Frost epidemics |
| title_full | Susceptibility sets and the final outcome of collective Reed–Frost epidemics |
| title_fullStr | Susceptibility sets and the final outcome of collective Reed–Frost epidemics |
| title_full_unstemmed | Susceptibility sets and the final outcome of collective Reed–Frost epidemics |
| title_short | Susceptibility sets and the final outcome of collective Reed–Frost epidemics |
| title_sort | susceptibility sets and the final outcome of collective reed–frost epidemics |
| topic | Total size; Severity; Susceptibility set; Symmetric sampling procedure; Gontcharoff polynomial; General final state random variables |
| url | https://eprints.nottingham.ac.uk/50538/ https://eprints.nottingham.ac.uk/50538/ https://eprints.nottingham.ac.uk/50538/ |