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

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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+ε cos (ωt − φ)) with ε ≪ 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 (ε2/8)% 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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MSC 92D30 ⋅ 45C05 ⋅ 47A55

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Bacaër, N. Approximation of the Basic Reproduction Number R 0 for Vector-Borne Diseases with a Periodic Vector Population. Bull. Math. Biol. 69, 1067–1091 (2007). https://doi.org/10.1007/s11538-006-9166-9

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