December 2013 Acquaintance vaccination in an epidemic on a random graph with specified degree distribution
Frank Ball, David Sirl
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J. Appl. Probab. 50(4): 1147-1168 (December 2013). DOI: 10.1239/jap/1389370105

Abstract

We consider a stochastic SIR (susceptible → infective → removed) epidemic on a random graph with specified degree distribution, constructed using the configuration model, and investigate the `acquaintance vaccination' method for targeting individuals of high degree for vaccination. Branching process approximations are developed which yield a post-vaccination threshold parameter, and the asymptotic (large population) probability and final size of a major outbreak. We find that introducing an imperfect vaccine response into the present model for acquaintance vaccination leads to sibling dependence in the approximating branching processes, which may then require infinite type spaces for their analysis and are generally not amenable to numerical calculation. Thus, we propose and analyse an alternative model for acquaintance vaccination, which avoids these difficulties. The theory is illustrated by a brief numerical study, which suggests that the two models for acquaintance vaccination yield quantitatively very similar disease properties.

Citation

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Frank Ball. David Sirl. "Acquaintance vaccination in an epidemic on a random graph with specified degree distribution." J. Appl. Probab. 50 (4) 1147 - 1168, December 2013. https://doi.org/10.1239/jap/1389370105

Information

Published: December 2013
First available in Project Euclid: 10 January 2014

zbMATH: 1301.92071
MathSciNet: MR3161379
Digital Object Identifier: 10.1239/jap/1389370105

Subjects:
Primary: 92D30
Secondary: 05C80 , 60J80

Keywords: branching process , Epidemic process , final size , network , random graph , threshold behaviour , vaccination

Rights: Copyright © 2013 Applied Probability Trust

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Vol.50 • No. 4 • December 2013
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