Developments of Basic Reproduction Number Theory
Developments of Basic Reproduction Number Theory
复制标题
基本复制数论的发展
DOI：
10.11540/bjsiam.30.1_14
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
稲葉 寿
中科院分区：
文献类型：
--
作者：
Nicolas Bacaer;Hisashi Inaba and Ali Moussaoui;稲葉 寿
结构种群动力学中的基本再生数R 0 被定义为由更新积分方程的积分核导出的世代演化算子的谱半径。如果基本种群动态由与非自治微分方程相关的进化系统描述，则世代进化算子是根据进化系统导出的进化半群的无穷小生成元来计算的。利用世代演化算子定义的基本再生数，可以检验非线性非自治系统总轨道的存在性和稳定性，其中总轨道作为演化半群的不动点给出。因此，R 0 的思想被独特地扩展到时间异质环境中种群灭绝和持续存在的阈值。
The basic reproduction number R 0 in structured population dynamics is defined as the spectral radius of the generation evolution operator induced by the integral kernel of the renewal integral equation. If the basic population dynamics is described by the evolutionary system associated with a nonautonomous differential equation, the generation evolution operator is calculated from the infinitesimal generator of the evolution semigroup induced from the evolutionary system. Using the basic reproduction number defined by the generation evolution operator, we can examine existence and stability of total orbits of nonlinear nonautonomous system, in which the total orbit is given as a fixed point of the evolution semigroup. Thus the idea of R 0 is uniquely extended to the threshold value for extinction and persistence of population in time-heterogeneous environments.