Analysis of a stochastic SIR epidemic on a random network incorporating household structure
This paper is concerned with a stochastic SIR (susceptible-infective-removed) model for the spread of an epidemic amongst a population of individuals, with a random network of social contacts, that is also partitioned into households. The behaviour of the model as the population size tends to infini...
| Main Authors: | , , |
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| Format: | Article |
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Elsevier
2010
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| Online Access: | https://eprints.nottingham.ac.uk/1292/ |
| _version_ | 1848790578659065856 |
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| author | Ball, Frank G. Sirl, David J. Trapman, Pieter |
| author_facet | Ball, Frank G. Sirl, David J. Trapman, Pieter |
| author_sort | Ball, Frank G. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | This paper is concerned with a stochastic SIR (susceptible-infective-removed) model for the spread of an epidemic amongst a population of individuals, with a random network of social contacts, that is also partitioned into households. The behaviour of the model as the population size tends to infinity in an appropriate fashion is investigated. A threshold parameter which determines whether or not an epidemic with few initial infectives can become established and lead to a major outbreak is obtained, as are the probability that a major outbreak occurs and the expected proportion of the population that are ultimately infected by such an outbreak, together with methods for calculating these quantities. Monte Carlo simulations demonstrate that these asymptotic quantities accurately reflect the behaviour of finite populations, even for only moderately sized finite populations. The model is compared and contrasted with related models previously studied in the literature. The effects of the amount of clustering present in the overall population structure and the infectious period distribution on the outcomes of the model are also explored. |
| first_indexed | 2025-11-14T18:14:51Z |
| format | Article |
| id | nottingham-1292 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:14:51Z |
| publishDate | 2010 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-12922020-05-04T20:25:18Z https://eprints.nottingham.ac.uk/1292/ Analysis of a stochastic SIR epidemic on a random network incorporating household structure Ball, Frank G. Sirl, David J. Trapman, Pieter This paper is concerned with a stochastic SIR (susceptible-infective-removed) model for the spread of an epidemic amongst a population of individuals, with a random network of social contacts, that is also partitioned into households. The behaviour of the model as the population size tends to infinity in an appropriate fashion is investigated. A threshold parameter which determines whether or not an epidemic with few initial infectives can become established and lead to a major outbreak is obtained, as are the probability that a major outbreak occurs and the expected proportion of the population that are ultimately infected by such an outbreak, together with methods for calculating these quantities. Monte Carlo simulations demonstrate that these asymptotic quantities accurately reflect the behaviour of finite populations, even for only moderately sized finite populations. The model is compared and contrasted with related models previously studied in the literature. The effects of the amount of clustering present in the overall population structure and the infectious period distribution on the outcomes of the model are also explored. Elsevier 2010 Article PeerReviewed Ball, Frank G., Sirl, David J. and Trapman, Pieter (2010) Analysis of a stochastic SIR epidemic on a random network incorporating household structure. Mathematical Biosciences, 224 (2). pp. 53-73. ISSN 0025-5564 http://www.elsevier.com/wps/find/journaldescription.cws_home/505777/description#description doi:10.1016/j.mbs.2009.12.003 doi:10.1016/j.mbs.2009.12.003 |
| spellingShingle | Ball, Frank G. Sirl, David J. Trapman, Pieter Analysis of a stochastic SIR epidemic on a random network incorporating household structure |
| title | Analysis of a stochastic SIR epidemic on a random network incorporating household structure |
| title_full | Analysis of a stochastic SIR epidemic on a random network incorporating household structure |
| title_fullStr | Analysis of a stochastic SIR epidemic on a random network incorporating household structure |
| title_full_unstemmed | Analysis of a stochastic SIR epidemic on a random network incorporating household structure |
| title_short | Analysis of a stochastic SIR epidemic on a random network incorporating household structure |
| title_sort | analysis of a stochastic sir epidemic on a random network incorporating household structure |
| url | https://eprints.nottingham.ac.uk/1292/ https://eprints.nottingham.ac.uk/1292/ https://eprints.nottingham.ac.uk/1292/ |