两类具有类年龄结构的细菌感染动力学模型

发布时间：2019-02-09 14:00

【摘要】：根据细菌污染环境在人群中传播特点,本文建立和分析了两类具有类年龄结构的细菌感染动力学模型.一类是考虑带有免疫年龄结构的细菌感染动力学模型,另一类考虑带有接种年龄结构的细菌感染动力学模型.运用微分方程动力学性质理论和知识我们全局分析了所建模型的动力学性质.通过系统地分析,得到了模型基本再生数,以及系统中呈现出的无病平衡态和地方病平衡态的存在性,唯一性；运用特征线理论和方法,我们分析了模型平衡态局部稳定性,得到了当基本再生数R0≤1时,无病平衡态E0局部渐近稳定；当R01时,无病平衡态E0局部不稳定地方性疾病平衡态E*局部稳定；通过运用无穷维动力系统持续生存理论,我们分析了系统的持续生存性.得到了当R01时,系统中疾病持续生存；最后,我们通过构造一类Lyapunov函数,对模型平衡态的全局稳定性进行分析.当基本再生数R0≤1时,无病平衡态E0全局渐近稳定；当Ro1时,地方性疾病平衡态E*全局渐近稳定.
[Abstract]:According to the characteristics of bacterial contamination in the population, two kinds of bacterial infection dynamics models with similar age structure were established and analyzed in this paper. One is to consider the bacterial infection kinetic model with immune age structure, the other is to consider the bacterial infection kinetic model with inoculation age structure. By using the theory of dynamical properties of differential equations and knowledge, the dynamical properties of the model are analyzed globally. Through systematic analysis, the basic regenerative number of the model and the existence and uniqueness of disease-free equilibrium and endemic equilibrium are obtained. Using the characteristic line theory and method, we analyze the local stability of the equilibrium state of the model, and obtain the local asymptotic stability of the disease-free equilibrium state E _ 0 when the basic regenerative number R _ 0 鈮，

本文编号：2419026