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Research article
First published October 2006

Optimal vaccination schemes for epidemics among a population of households, with application to variola minor in Brazil

Frank Ball and Owen LyneView all authors and affiliations
Volume 15, Issue 5
https://doi.org/10.1177/0962280206071643

Abstract

This paper is concerned with stochastic models for the spread of an epidemic among a community of households, in which individuals mix uniformly within households and, in addition, uniformly at a much lower rate within the population at large. This two-level mixing structure has important implications for the threshold behaviour of the epidemic and, consequently, for both the effectiveness of vaccination strategies for controlling an outbreak and the form of optimal vaccination schemes. A brief introduction to optimal vaccination schemes in this setting is provided by presenting a unified treatment of the simplest and most-studied case, viz. the single-type SIR (susceptible → infective → removed) epidemic.
A reproduction number R*, which determines whether a trace of initial infection can give rise to a major epidemic, is derived and the effect of a vaccination scheme on R* is studied using a general model for vaccine action. In particular, optimal vaccination schemes which reduce R* to its threshold value of one with minimum vaccination coverage are considered. The theory is illustrated by application to data on a variola minor outbreak in São Paulo, which, together with other examples, is used to highlight key issues related to vaccination schemes.

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Published In

Volume 15, Issue 5
Pages: 481 - 497
Article first published: October 2006
Issue published: October 2006

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PubMed: 17089950

Authors

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Frank Ball
School of Mathematical Sciences, University of Nottingham, Nottingham, UK, [email protected]
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Owen Lyne
IMSAS, University of Kent, Canterbury, UK
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