%0 Journal Article
%9 ACL : Articles dans des revues à comité de lecture répertoriées dans les bases internationales
%A Bacaer, Nicolas
%T Approximation of the basic reproduction number R-0 for vector-borne diseases with a periodic vector population
%D 2007
%L fdi:010037910
%J Bulletin of Mathematical Biology
%K epidemics ; basic reproduction number ; seasonality
%M ISI:000245124600011
%N 3
%P 1067-1091
%R 10.1007/s11538-006-9166-9
%U http://www.documentation.ird.fr/hor/fdi:010037910
%> http://www.documentation.ird.fr/intranet/publi/2007/05/010037910.pdf
%V 69
%W Horizon (IRD)
%X 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.