title: Approximation of the basic reproduction number R0 for vector-borne diseases with a periodic vector population.
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.
authors.affiliation: Institut de Recherche pour le Développement (IRD), 32 avenue Henri Varagnat, 93143 Bondy Cedex, France. bacaer@bondy.ird.fr
authors.forename: Nicolas
authors.initials: N
authors.lastname: Bacaër
mesh_terms: D000330:Aedes / Q000821:virology; D018354:Alphavirus Infections / Q000453:epidemiology* / Q000821:virology; D000818:Animals; D050936:Basic Reproduction Number; D002646:Chikungunya virus / Q000254:growth & development*; D004196:Disease Outbreaks; D006801:Humans; D007303:Insect Vectors / Q000821:virology*; D012621:Seasons