Bulletin of Mathematical Biology

, Volume 69, Issue 3, pp 1067–1091

Approximation of the Basic Reproduction Number R0 for Vector-Borne Diseases with a Periodic Vector Population

  • Nicolas Bacaër
Original Article

DOI: 10.1007/s11538-006-9166-9

Cite this article as:
Bacaër, N. Bull. Math. Biol. (2007) 69: 1067. doi:10.1007/s11538-006-9166-9

Abstract

The main purpose of this paper is to give an approximate formula involving two terms for the basic reproduction number R0 of a vector-borne disease when the vector population has small seasonal fluctuations of the form p(t) = p0 (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 p0. The maximum correction due to the second term is (ε2/8)% and always tends to decrease R0. The basic reproduction number R0 is defined through the spectral radius of a linear integral operator. Four numerical methods for the computation of R0 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.

Keywords

Epidemics Basic reproduction number Seasonality 

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • Nicolas Bacaër
    • 1
  1. 1.Institut de Recherche pour le Développement (I.R.D.)Bondy CedexFrance