Journal of Applied Probability

Acquaintance vaccination in an epidemic on a random graph with specified degree distribution

Frank Ball and David Sirl

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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.

Article information

J. Appl. Probab., Volume 50, Number 4 (2013), 1147-1168.

First available in Project Euclid: 10 January 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 92D30: Epidemiology
Secondary: 05C80: Random graphs [See also 60B20] 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

Branching process epidemic process final size network random graph threshold behaviour vaccination


Ball, Frank; Sirl, David. Acquaintance vaccination in an epidemic on a random graph with specified degree distribution. J. Appl. Probab. 50 (2013), no. 4, 1147--1168. doi:10.1239/jap/1389370105.

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