具有类年龄结构的传染病模型的全局性态分析
发布时间：2018-07-28 17:50
【摘要】：传染病动力学是理论性定量,定性研究传染病流行规律的一种方法.年龄结构传染病模型及其动力学性质的研究又是传染病动力学研究的一个重要课题.本论文主要分析传染病系统的性质以及建立相应的Lyapunov函数来分析年龄结构模型的全局性态问题,本课题的研究对于传染病发展趋势的估计是重要的且是具有实际意义的工作.本文通过研究两类具有类年龄结构的传染病模型:一类为HIV病毒传染模型,考虑了发生率函数为非线性时,平衡点依赖于阈值(基本再生数)的动力学行为;另一类模型是流行病模型,本文考虑了SVIR以及SVEIR两种流行病模型,研究加入接种疫苗仓室后,平衡点依赖于阈值(基本再生数)的动力学行为.重点考虑模型的适定性以及构造合适的Lyapunov函数去解决平衡点全局稳定性的问题.另外本文构造了一类Lyapunov函数(泛函)方法来解决非线性以及年龄结构模型的稳定性问题,提供了一些简单有效的判定定理,对实际的传染病预防控制工作可以起到决策依据以及理论参考.
[Abstract]:Infectious disease dynamics is a theoretical quantitative, qualitative study of epidemic law of an infectious disease. The study of age-structured infectious disease model and its dynamic properties is also an important subject of infectious disease dynamics research. This paper mainly analyzes the properties of infectious disease system and establishes the corresponding Lyapunov function to analyze the global problem of age structure model. The research in this paper is important and meaningful for the estimation of infectious disease development trend. In this paper, two kinds of age-like infectious disease models are studied: one is HIV virus infection model, and the equilibrium point is dependent on threshold (basic reproduction number) when the incidence function is nonlinear; The other one is epidemic model. In this paper, SVIR and SVEIR epidemic models are considered, and the dynamic behavior of equilibrium point dependent on threshold (basic regeneration number) is studied. The suitability of the model and the construction of appropriate Lyapunov functions are considered to solve the problem of global stability of the equilibrium point. In addition, a class of Lyapunov function (functional) method is constructed to solve the problem of nonlinearity and the stability of age structure model, and some simple and effective decision theorems are provided. To the actual infectious disease prevention and control work can play the decision-making basis and the theory reference.
【学位授予单位】：黑龙江大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O175
，
本文编号：2151129
[Abstract]:Infectious disease dynamics is a theoretical quantitative, qualitative study of epidemic law of an infectious disease. The study of age-structured infectious disease model and its dynamic properties is also an important subject of infectious disease dynamics research. This paper mainly analyzes the properties of infectious disease system and establishes the corresponding Lyapunov function to analyze the global problem of age structure model. The research in this paper is important and meaningful for the estimation of infectious disease development trend. In this paper, two kinds of age-like infectious disease models are studied: one is HIV virus infection model, and the equilibrium point is dependent on threshold (basic reproduction number) when the incidence function is nonlinear; The other one is epidemic model. In this paper, SVIR and SVEIR epidemic models are considered, and the dynamic behavior of equilibrium point dependent on threshold (basic regeneration number) is studied. The suitability of the model and the construction of appropriate Lyapunov functions are considered to solve the problem of global stability of the equilibrium point. In addition, a class of Lyapunov function (functional) method is constructed to solve the problem of nonlinearity and the stability of age structure model, and some simple and effective decision theorems are provided. To the actual infectious disease prevention and control work can play the decision-making basis and the theory reference.
【学位授予单位】：黑龙江大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O175
，
本文编号：2151129
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