Analysis of a stochastic SIR epidemic on a random network incorporating household structure |
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| Authors: | Frank Ball David Sirl Pieter Trapman |
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| Institution: | 1. School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK;2. Julius Center for Health Sciences and Primary Care, University Medical Center Utrecht, Heidelberglaan 100, 3584 CX Utrecht, The Netherlands;3. Department of Mathematics, Faculty of Sciences, Vrije Universitiet Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands;1. Department of Mathematics, Shanghai University, Shanghai 200444, PR China;2. Department of Electronic Engineering, City University of Hong Kong, Hong Kong SAR, PR China;1. Bruno Kessler Foundation, Trento, Italy;2. School of Social Sciences, University of Trento, Trento, Italy;3. Tomsk Polytechnic University, Tomsk, Russia;1. Warwick Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK;2. School of Life Sciences, University of Warwick, Coventry CV4 7AL, UK;3. School of Mathematics, University of Manchester, Manchester M13 9PL, UK;1. School of Mathematics, University of Manchester, Manchester M13 9PL, United Kingdom;2. Warwick Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom |
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| Abstract: | 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. |
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