Evaluation of vaccination strategies for SIR epidemics on random networks incorporating household structure

Ball, Frank and Sirl, David J. (2017) Evaluation of vaccination strategies for SIR epidemics on random networks incorporating household structure. Journal of Mathematical Biology . pp. 1-48. ISSN 1432-1416

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Abstract

This paper is concerned with the analysis of vaccination strategies in a stochastic SIR (susceptible → infected → 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. Under various vaccine action models, we consider both household-based vaccination schemes, in which the way in which individuals are chosen for vaccination depends on the size of the households in which they reside, and acquaintance vaccination, which targets individuals of high degree in the social network. For both types of vaccination scheme, assuming a large population with few initial infectives, we derive a threshold parameter which determines whether or not a large outbreak can occur and also the probability and fraction of the population infected by such an outbreak. The performance of these schemes is studied numerically, focusing on the influence of the household size distribution and the degree distribution of the social network. We find that acquaintance vaccination can significantly outperform the best household-based scheme if the degree distribution of the social network is heavy-tailed. For household-based schemes, when the vaccine coverage is insufficient to prevent a major outbreak and the vaccine is imperfect, we find situations in which both the probability and size of a major outbreak under the scheme which minimises the threshold parameter are \emph{larger} than in the scheme which maximises the threshold parameter.

Item Type: Article
Keywords: Branching process, con_guration model, epidemic process, final size, random graph, threshold behaviour, vaccination
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: 10.1007/s00285-017-1139-0
Depositing User: Eprints, Support
Date Deposited: 17 May 2017 14:16
Last Modified: 29 Jun 2017 23:45
URI: http://eprints.nottingham.ac.uk/id/eprint/42915

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