Bacaër Nicolas
Institut de Recherche pour le Développement (IRD), 32 avenue Henri Varagnat, 93143 Bondy Cedex, France.
Bull Math Biol. 2007 Apr;69(3):1067-91. doi: 10.1007/s11538-006-9166-9. Epub 2007 Jan 30.
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.
本文的主要目的是给出一个包含两项的近似公式，用于计算媒介传播疾病的基本再生数(R(0))，其中媒介种群具有形式为(p(t) = p(0) (1 + \epsilon \cos(\omega t - \phi)))的小季节性波动，且(\epsilon << 1)。第一项类似于恒定媒介种群(p)的情况，但(p)被平均媒介种群(p(0))所取代。第二项引起的最大修正为((\epsilon^2 / 8)%)，并且总是倾向于降低(R(0))。基本再生数(R(0))是通过线性积分算子的谱半径来定义的。以留尼汪岛2005/2006年基孔肯雅热疫情的模型为例，比较了四种计算(R(0))的数值方法。该近似公式和数值方法可用于许多其他具有季节性的流行病模型。
