论文标题
关于连续结构化种群的基本繁殖数
On the basic reproduction number in continuously structured populations
论文作者
论文摘要
在人口动态的框架中，根据定义，基本的繁殖数R_0是个人在其一生中具有的后代的预期数。在恒定和时间周期性的环境中，它被计算为所谓的下一代操作员的光谱半径。在具有浓缩状态的Banach晶格X中定义的连续结构化种群中，一个人不能定义X中的下一代操作员。在本文中，我们提出了一种方法来计算一种模型的基本复制数，例如基本复制模型的基本复制数量的限制，可以将R_0计算为下一步的频谱radius的下一个模型的光谱。我们将这些结果应用于一些示例：（经典）尺寸依赖性模型，大小结构化细胞种群模型，一个大小结构化模型，在结构空间中扩散（在某些特定假设下）和一个（生理）年龄结构化模型，并在结构空间中扩散。
In the framework of population dynamics, the basic reproduction number R_0 is, by definition, the expected number of offspring that an individual has during its lifetime. In constant and time periodic environments it is calculated as the spectral radius of the so-called next-generation operator. In continuously structured populations defined in a Banach lattice X with concentrated states at birth one cannot define the next-generation operator in X. In the present paper we present an approach to compute the basic reproduction number of such models as the limit of the basic reproduction number of a sequence of models for which R_0 can be computed as the spectral radius of the next-generation operator. We apply these results to some examples: the (classical) size-dependent model, a size structured cell population model, a size structured model with diffusion in structure space (under some particular assumptions) and a (physiological) age-structured model with diffusion in structure space.
