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Reproduction numbers for epidemic models with households and other social structures II : comparisons and implications for vaccination
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Ball, Frank, Pellis, Lorenzo and Trapman, Pieter (2016) Reproduction numbers for epidemic models with households and other social structures II : comparisons and implications for vaccination. Mathematical Biosciences, 274 . pp. 108-139. doi:10.1016/j.mbs.2016.01.006 ISSN 0025-5564.
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Official URL: http://dx.doi.org/10.1016/j.mbs.2016.01.006
Abstract
In this paper we consider epidemic models of directly transmissible SIR (susceptible → infective → recovered) and SEIR (with an additional latent class) infections in fully-susceptible populations with a social structure, consisting either of households or of households and workplaces. We review most reproduction numbers defined in the literature for these models, including the basic reproduction number R0 introduced in the companion paper of this, for which we provide a simpler, more elegant derivation. Extending previous work, we provide a complete overview of the inequalities among these reproduction numbers and resolve some open questions. Special focus is put on the exponential-growth-associated reproduction number Rr, which is loosely defined as the estimate of R0 based on the observed exponential growth of an emerging epidemic obtained when the social structure is ignored. We show that for the vast majority of the models considered in the literature Rr ≥ R0 when R0 ≥ 1 and Rr ≤ R0 when R0 ≤ 1. We show that, in contrast to models without social structure, vaccination of a fraction 1−1/R0 of the population, chosen uniformly at random, with a perfect vaccine is usually insufficient to prevent large epidemics. In addition, we provide significantly sharper bounds than the existing ones for bracketing the critical vaccination coverage between two analytically tractable quantities, which we illustrate by means of extensive numerical examples.
Item Type: | Journal Article | ||||||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||
Journal or Publication Title: | Mathematical Biosciences | ||||||||||
Publisher: | Elsevier Science Inc. | ||||||||||
ISSN: | 0025-5564 | ||||||||||
Official Date: | April 2016 | ||||||||||
Dates: |
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Volume: | 274 | ||||||||||
Page Range: | pp. 108-139 | ||||||||||
DOI: | 10.1016/j.mbs.2016.01.006 | ||||||||||
Status: | Peer Reviewed | ||||||||||
Publication Status: | Published | ||||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||||
Open Access Version: |
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