@article{fdi:010037910,
  title = {{A}pproximation of the basic reproduction number {R}-0 for vector-borne diseases with a periodic vector population},
  author = {{B}acaer, {N}icolas},
  abstract = {{T}he 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. {T}he first term is similar to the case of a constant vector population p but with p replaced by the average vector population p (0). {T}he maximum correction due to the second term is (epsilon(2)/8)% and always tends to decrease {R} (0). {T}he basic reproduction number {R} (0) is defined through the spectral radius of a linear integral operator. {F}our numerical methods for the computation of {R} (0) are compared using as example a model for the 2005/2006 chikungunya epidemic in {L}a {R}eunion. {T}he approximate formula and the numerical methods can be used for many other epidemic models with seasonality.},
  keywords = {epidemics ; basic reproduction number ; seasonality},
  journal = {{B}ulletin of {M}athematical {B}iology},
  volume = {69},
  numero = {3},
  pages = {1067--1091},
  ISSN = {0092-8240},
  year = {2007},
  DOI = {10.1007/s11538-006-9166-9},
  URL = {http://www.documentation.ird.fr/hor/fdi:010037910},
}