title: Analysis of a stochastic SIR epidemic on a random network incorporating household structure.
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.
authors.affiliation: School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK. frank.ball@nottingham.ac.uk
authors.forename: Frank
authors.initials: F
authors.lastname: Ball
authors.forename: David
authors.initials: D
authors.lastname: Sirl
authors.forename: Pieter
authors.initials: P
authors.lastname: Trapman
mesh_terms: D000465:Algorithms; D050936:Basic Reproduction Number; D016000:Cluster Analysis; D003141:Communicable Diseases / Q000453:epidemiology*; D003198:Computer Simulation; D005191:Family Characteristics; D006801:Humans; D008954:Models, Biological; D009010:Monte Carlo Method; D011156:Population Density; D011336:Probability; D016008:Statistical Distributions; D013269:Stochastic Processes