Approximation of the Basic Reproduction Number R 0 for Vector-Borne Diseases with a Periodic Vector Population
Institut de Recherche pour le Développement (IRD), 32 avenue Henri Varagnat, 93143 Bondy Cedex, France.Bulletin of Mathematical Biology (Impact Factor: 1.39). 04/2007; 69(3):1067-91. DOI: 10.1007/s11538-006-9166-9
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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