具有阶段结构和免疫逃避的传染病模型研究

发布时间：2018-08-09 13:19

【摘要】：本文主要依据传染病模型免疫反应中的“仓室模型”,针对易感人群预防接种后仍会感染乙肝病毒这一现象,我们在此建立了三类具有阶段结构和免疫逃避的SIRS传染病动力学模型。进而研究模型的动力学性态,并给出其生物学意义,全文主要分为以下五章。第一章,本章为全文的绪论。首先简单介绍了传染病的发展简况和本文选题依据,进而总结了传染病的发病机理、传播途径的相关知识和本文的研究意义。其次,陈述了涉及阶段结构和免疫逃避的传染病动力学模型中经典“仓室模型”的国内外研究现状,以及本文主要工作。最后,给出与传染病模型动力学研究相关的一些重要定义和定理。第二章,根据乙肝病毒性肝炎(HBV)的传播规律和医学现状,新生儿不一定均是易感者,存在遗传现象,建立了一个具有垂直传染和连续预防接种的SIRS传染病动力学模型。为研究这种模型的渐近性态,这里综合运用了 Routh-Hurwitz准则、LaSalle不变集原理和广义Dulac函数等方法,得到了关于无病平衡点和正平衡点全局渐近稳定的充分条件。最后,选取合适的参数进行数值模拟。第三章,由于在“仓室模型”中,对疾病发生率的估计是传染病流行趋势预测和预防工作中最重要的。根据传染病发生率的多样性,考虑了易感者与染病者具有非线性发生率,建立了一个具有非线性发生率的SIRS传染病动力学模型。给出此传染病动力学模型的基本再生数R0,综合利用Routh-Hurwitz定理、LaSalle不变集原理、微分方程轨道稳定和复合矩阵的相关理论,得到无病平衡点和正平衡点全局稳定的充分条件,进而分析模型的生物学意义。最后,选取合适的参数进行数值模拟。第四章,最新医学研究数据表明,易感者接种乙肝疫苗后再次感染乙肝病毒的概率即免疫失去率,因易感者的年龄阶段不同而出现差异。因此,基于不同年龄结构免疫逃避的差异性,把易感人群分为幼年和成年两个阶段结构,考虑疾病在幼年和成年群体中均可传播,且只考虑对幼年群体进行连续预防接种,建立了一个具有阶段结构和免疫逃避的S1S2IR传染病模型。为了研究这种模型的渐近性态,我们给出模型的基本再生数R0,进而利用Routh-Hurwitz准则和微分方程比较定理,分别得到疾病消亡和最终成为地方病的充分条件。最后,选取合适的参数进行数值模拟,并分析此传染病模型的生物学意义。第五章,全文总结与展望。
[Abstract]:According to the "storeroom model" in the immune response of infectious disease model, this article aims at the phenomenon that the susceptible population will still be infected with hepatitis B virus after inoculation. Here we establish three SIRS epidemic dynamics models with phase structure and immune escape. Then the dynamic behavior of the model is studied and its biological significance is given. The full text is divided into five chapters. The first chapter, this chapter is the introduction of the full text. First, the development of infectious diseases and the basis of this paper are briefly introduced, and then the pathogenesis of infectious diseases, the relevant knowledge of transmission routes and the significance of this paper are summarized. Secondly, the research status of the classical "warehouse model" in infectious disease dynamics models involving phase structure and immune escape is presented, and the main work of this paper is also presented. Finally, some important definitions and theorems related to the dynamics of infectious disease models are given. In the second chapter, according to the law of (HBV) transmission and the current medical situation of hepatitis B virus hepatitis, the newborns are not all susceptible and have genetic phenomenon. A dynamic model of SIRS infectious disease with vertical transmission and continuous inoculation is established. In order to study the asymptotic behavior of the model, the Routh-Hurwitz criterion and the generalized Dulac function are used to obtain the sufficient conditions for the global asymptotic stability of the disease-free and positive equilibrium points. Finally, the appropriate parameters are selected for numerical simulation. In Chapter 3, the estimation of the incidence of disease is the most important in the prediction and prevention of epidemic trend of infectious diseases. According to the diversity of the incidence of infectious diseases, a dynamic model of SIRS infectious diseases with nonlinear incidence was established by considering the nonlinear incidence between susceptible and infected individuals. In this paper, the basic reproducing number R _ 0 of the dynamic model of infectious disease is given. The sufficient conditions for global stability of disease-free equilibrium point and positive equilibrium point are obtained by synthetically using Routh-Hurwitz theorem and LaSalle invariant set principle, the stability of differential equation orbit and the theory of compound matrix. Then the biological significance of the model is analyzed. Finally, the appropriate parameters are selected for numerical simulation. In the fourth chapter, the latest medical research data show that the probability of reinfection of hepatitis B virus after inoculating hepatitis B vaccine, that is, the rate of immune loss, varies with the age of susceptible person. Therefore, based on the difference of immune evasion in different age structure, the susceptible population was divided into two stages: early childhood and adult. A S1S2IR epidemic model with stage structure and immune escape was established. In order to study the asymptotic behavior of the model, we give the basic reproduction number R _ 0 of the model, and then by using the Routh-Hurwitz criterion and the comparison theorem of differential equations, we obtain the sufficient conditions for the disease to die out and finally become endemic. Finally, the appropriate parameters are selected for numerical simulation, and the biological significance of the epidemic model is analyzed. Chapter V, the full text summary and prospect.
【学位授予单位】：温州大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

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