关于连续结构种群中的基本繁殖数
On the basic reproduction number in continuously structured populations
AI总结：
本文研究连续结构种群中基本繁殖数的计算方法，通过极限过程定义其为序列模型基本繁殖数的极限，应用于多个结构模型。
摘要：
在种群动力学框架中，基本繁殖数R_0被定义为个体一生中产生的后代的期望数量。在恒定和时间周期性环境中，它被计算为所谓的下一生成算子的谱半径。在定义于Banach空间X中的连续结构种群中，由于出生时集中状态的存在，无法在X中定义下一生成算子。本文提出了一种计算此类模型基本繁殖数的方法，即作为一系列模型基本繁殖数序列的极限。这些结果应用于一些例子：经典的尺寸依赖模型、尺寸结构细胞种群模型、具有结构空间扩散的尺寸结构模型（在某些特定假设下）以及具有结构空间扩散的生理年龄结构模型。
英文摘要：
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.
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