| Network epidemic models with two levels of mixing. | |
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MedLine Citation:
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PMID: 18280521 Owner: NLM Status: MEDLINE |
Abstract/OtherAbstract:
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The study of epidemics on social networks has attracted considerable attention recently. In this paper, we consider a stochastic SIR (susceptible-->infective-->removed) model for the spread of an epidemic on a finite network, having an arbitrary but specified degree distribution, in which individuals also make casual contacts, i.e. with people chosen uniformly from the population. The behaviour of the model as the network size tends to infinity is investigated. In particular, the basic reproduction number R(0), that governs whether or not an epidemic with few initial infectives can become established is determined, as are the probability that an epidemic becomes established and the proportion of the population who are ultimately infected by such an epidemic. For the case when the infectious period is constant and all individuals in the network have the same degree, the asymptotic variance and a central limit theorem for the size of an epidemic that becomes established are obtained. Letting the rate at which individuals make casual contacts decrease to zero yields, heuristically, corresponding results for the model without casual contacts, i.e. for the standard SIR network epidemic model. A deterministic model that approximates the spread of an epidemic that becomes established in a large population is also derived. The theory is illustrated by numerical studies, which demonstrate that the asymptotic approximations work well, even for only moderately sized networks, and that the degree distribution and the inclusion of casual contacts can each have a major impact on the outcome of an epidemic. |
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Authors:
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Frank Ball; Peter Neal |
Publication Detail:
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Type: Journal Article; Research Support, Non-U.S. Gov't Date: 2008-01-11 |
Journal Detail:
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Title: Mathematical biosciences Volume: 212 ISSN: 0025-5564 ISO Abbreviation: Math Biosci Publication Date: 2008 Mar |
Date Detail:
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Created Date: 2008-03-03 Completed Date: 2008-05-01 Revised Date: 2009-11-11 |
Medline Journal Info:
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Nlm Unique ID: 0103146 Medline TA: Math Biosci Country: United States |
Other Details:
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Languages: eng Pagination: 69-87 Citation Subset: IM |
Affiliation:
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School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, UK. frank.ball@nottingham.ac.uk |
Export Citation:
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| MeSH Terms | |
Descriptor/Qualifier:
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Basic Reproduction Number Computer Simulation Disease Outbreaks* Humans Models, Biological* Monte Carlo Method Social Support* Stochastic Processes |
From MEDLINE®/PubMed®, a database of the U.S. National Library of Medicine
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