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Acquaintance Vaccination in an Epidemic on a Random Graph with Specified Degree Distribution

  • Frank Ball (a1) and David Sirl (a2)

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.

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Copyright

Corresponding author

Postal address: School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK. Email address: frank.ball@nottingham.ac.uk
∗∗ Postal address: Mathematics Education Centre, Loughborough University, Loughborough LE11 3TU, UK. Email address: d.sirl@lboro.ac.uk

References

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Acquaintance Vaccination in an Epidemic on a Random Graph with Specified Degree Distribution

  • Frank Ball (a1) and David Sirl (a2)

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