Approximation of the basic reproduction number R0 for vector-borne diseases with a periodic vector population

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 (omega t - 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 Reunion. The approximate formula and the numerical methods can be used for many other epidemic models with seasonality.