Approximation of the Basic Reproduction Number R 0 for Vector-Borne Diseases with a Periodic Vector Population

ArticleinBulletin of Mathematical Biology 69(3):1067-91 · April 2007with99 Reads
DOI: 10.1007/s11538-006-9166-9 · Source: PubMed
Abstract
The main purpose of this paper is to give an approximate formula involving two terms for the basic reproduction number R(0) of a vector-borne disease when the vector population has small seasonal fluctuations of the form p(t) = p(0) (1+epsilon cos(omegat - phi)) with epsilon < 1. The first term is similar to the case of a constant vector population p but with p replaced by the average vector population p(0). The maximum correction due to the second term is (epsilon(2)/8)% and always tends to decrease R(0). The basic reproduction number R(0) is defined through the spectral radius of a linear integral operator. Four numerical methods for the computation of R(0) are compared using as example a model for the 2005/2006 chikungunya epidemic in La Réunion. The approximate formula and the numerical methods can be used for many other epidemic models with seasonality.
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    Full-text · Article · Aug 2016
    • "The expressions for R 0 in equations [2.5,2.7,2.8] do not apply in seasonal settings, but can be calculated numerically using Floquet theory [35]—see the electronic supplementary material. "
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    Article · Dec 2015 · Proceedings of the Royal Society B: Biological Sciences
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