Mathematical theory of structured population dynamics and its applications to mathematical models for infectious diseases

我们建立了传染病的结构化种群动力学模型，分析了它们的数学结构，并提出了作为基本复制数及其导数的数学流行病学的关键思想。特别地，我们给出了稳定种群中基于年龄结构传染病动力学模型的基本繁殖数的估计方法以及基本繁殖数与宿主种群增长之间的关系。此外，我们还发展了状态-再生数理论，通过对有症状的感染者进行病例隔离，清除了根除条件。随后，我们给出了一种新的方法来描述异质环境中感染者的基本繁殖数和内在增长率。

We formulated structured population dynamics models for infectious diseases to analyse their mathematical structures, and developed key ideas in mathematical epidemiology as the basic reproduction number and its derivatives. In particular, we have shown the estimation methods of the basic reproduction number and relations between the basic reproduction number and the host population growth based on an age-structured infectious disease dynamics model in a stable population. Moreover, we developed the state-reproduction number theory, by which we cleared the eradication condition by case isolation of symptomatic infecteds. Subsequently, we have shown a new approach to formulate the basic reproduction number and the intrinsic growth rate of infecteds in a heterogeneous environment.