具有免疫反应的乙肝病毒时滞动力学模型研究

发布时间：2018-10-10 18:07

【摘要】：病毒感染的免疫反应是普遍的,它是消除和控制疾病的必要途径。吞噬细胞、自然杀伤细胞、干扰素、抗体、T细胞等等是对病毒的普通免疫反应的必要组成部分。事实上,在大部分病毒感染中细胞毒性T淋巴细胞(CTL),通过袭击病毒感染细胞,在病毒防御中起着关键作用。同时在病毒感染和宿主机体产生免疫应答的过程中,即健康细胞被感染后,感染细胞分离游离病毒,病毒被清除以及机体建立免疫防线等行为都依据不同的病毒存在不同的时间滞后。由于事实上这些不规则的时间序列的存在,可能对免疫状态的患者造成一定的影响。在数学上显示为周期解或者混沌状态。从而在研究病毒动力学模型时引入免疫反应和时滞将能更好地刻画相应的病毒传播和免疫应答等动力学特征。因此本文针对乙肝病毒做了研究。全文共分三章。在第一章中,简要介绍了传染病动力学的研究意义,乙肝病毒的国内外研究概况及本文的主要工作. 在第二章中,建立了具有时滞的乙肝病毒动力学模型,考虑了CTL对染病细胞的免疫反应。证明了当基本再生数小于1时,无病平衡点的局部渐近稳定性。同时,利用比较定理得到了无病平衡点的全局渐近稳定性。由单调迭代法得到了正平衡点全局稳定的条件。并由数值模拟说明了主要结论。在第三章中,研究了一类具有溶胞、非溶胞途径的乙肝病毒动力学模型。研究了模型的基本性质、平衡点及其稳定性情况。另外,分析了模型发生Hopf分支的条件。并且做了数值模拟证明了该章的主要结论。
[Abstract]:The immune response to viral infection is widespread and is an essential way to eliminate and control disease. Phagocytes, natural killer cells, interferon, antibodies, T cells and so on are essential components of the general immune response to viruses. In fact, cytotoxic T lymphocyte (CTL), plays a key role in virus defense by attacking virus infected cells in most viral infections. At the same time, in the process of virus infection and host body producing immune response, that is, after the healthy cells are infected, the infected cells isolate the free virus. Virus clearance and the establishment of immune defences are based on different viruses with different time lag. In fact, the existence of these irregular time series may have an effect on immune patients. It is mathematically presented as a periodic solution or chaotic state. Therefore, the introduction of immune response and time delay in the study of virus dynamics model can better describe the dynamic characteristics of virus transmission and immune response. Therefore, this paper studies hepatitis B virus. The full text is divided into three chapters. In the first chapter, the research significance of infectious disease dynamics, the domestic and foreign research situation of hepatitis B virus and the main work of this paper are briefly introduced. In chapter 2, a dynamic model of hepatitis B virus with time delay is established, and the immune response of CTL to infected cells is considered. It is proved that the local asymptotic stability of the disease-free equilibrium point is obtained when the basic reproducing number is less than 1. At the same time, the global asymptotic stability of disease-free equilibrium is obtained by comparison theorem. The condition of global stability of positive equilibrium point is obtained by monotone iterative method. The main conclusions are illustrated by numerical simulation. In chapter 3, a class of hepatitis B virus kinetic models with cytolytic and non-lysocytic pathways are studied. The basic properties, equilibrium points and their stability of the model are studied. In addition, the conditions for the Hopf bifurcation of the model are analyzed. The main conclusions of this chapter are proved by numerical simulation.
【学位授予单位】：中北大学
【学位级别】：硕士
【学位授予年份】：2011
【分类号】：R392.1

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