An SIR epidemic model on a population with random network and household structure and several types of individuals
We consider a stochastic SIR (susceptible → infective → removed) epidemic model with several types of individuals. Infectious individuals can make infectious contacts on two levels, within their own ‘household’ and with their neighbours in a random graph representing additional social contacts. This...
| Main Authors: | , |
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| Format: | Article |
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Applied Probability Trust
2010
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| Online Access: | https://eprints.nottingham.ac.uk/1393/ |
| _version_ | 1848790596569792512 |
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| author | Ball, Frank G. Sirl, David J. |
| author_facet | Ball, Frank G. Sirl, David J. |
| author_sort | Ball, Frank G. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | We consider a stochastic SIR (susceptible → infective → removed) epidemic model with several types of individuals. Infectious individuals can make infectious contacts on two levels, within their own ‘household’ and with their neighbours in a random graph representing additional social contacts. This random graph is an extension of the well-known configuration model to allow for several types of individuals. We give a strong approximation theorem which leads to a threshold theorem for the epidemic model and a method for calculating the probability of a major outbreak given few initial infectives. A multitype analogue of a theorem of Ball et al. (2009) heuristically
motivates a method for calculating the expected size of such a major outbreak. We also consider vaccination and give some short numerical illustrations of our results. |
| first_indexed | 2025-11-14T18:15:08Z |
| format | Article |
| id | nottingham-1393 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:15:08Z |
| publishDate | 2010 |
| publisher | Applied Probability Trust |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-13932020-05-04T20:25:17Z https://eprints.nottingham.ac.uk/1393/ An SIR epidemic model on a population with random network and household structure and several types of individuals Ball, Frank G. Sirl, David J. We consider a stochastic SIR (susceptible → infective → removed) epidemic model with several types of individuals. Infectious individuals can make infectious contacts on two levels, within their own ‘household’ and with their neighbours in a random graph representing additional social contacts. This random graph is an extension of the well-known configuration model to allow for several types of individuals. We give a strong approximation theorem which leads to a threshold theorem for the epidemic model and a method for calculating the probability of a major outbreak given few initial infectives. A multitype analogue of a theorem of Ball et al. (2009) heuristically motivates a method for calculating the expected size of such a major outbreak. We also consider vaccination and give some short numerical illustrations of our results. Applied Probability Trust 2010 Article NonPeerReviewed Ball, Frank G. and Sirl, David J. (2010) An SIR epidemic model on a population with random network and household structure and several types of individuals. Advances in Applied Probability . ISSN 0001-8678 (Submitted) http://www.appliedprobability.org/content.aspx?Group=journals&Page=apjournals |
| spellingShingle | Ball, Frank G. Sirl, David J. An SIR epidemic model on a population with random network and household structure and several types of individuals |
| title | An SIR epidemic model on a population with random network and household structure and several types of individuals |
| title_full | An SIR epidemic model on a population with random network and household structure and several types of individuals |
| title_fullStr | An SIR epidemic model on a population with random network and household structure and several types of individuals |
| title_full_unstemmed | An SIR epidemic model on a population with random network and household structure and several types of individuals |
| title_short | An SIR epidemic model on a population with random network and household structure and several types of individuals |
| title_sort | sir epidemic model on a population with random network and household structure and several types of individuals |
| url | https://eprints.nottingham.ac.uk/1393/ https://eprints.nottingham.ac.uk/1393/ |