一类具时滞的肿瘤免疫模型的动力学研究

发布时间：2018-03-23 13:12

本文选题：肿瘤免疫系统　切入点：时滞　出处：《哈尔滨工业大学》2015年硕士论文

【摘要】：肿瘤免疫治疗是生物医学领域的一个重要的分支。早在八十年代初,生物数学家对肿瘤免疫机制产生了浓烈的兴趣并进行了广泛的实验和深入的研究。主要研究不同免疫环境下,先天性免疫和适应性免疫保护生物体的动力学机制。随着生物数学科学的发展,Kuznetsov提出了经典的肿瘤免疫模型——Kuznetsov模型。近二十年,对此肿瘤免疫时滞系统的稳定性和Hopf分支性质研究已在肿瘤医学治疗得到广泛应用。人体内的效应细胞对于潜伏的肿瘤细胞的攻击有一定的时间延迟(时滞),这一复杂的免疫过程可以用时滞免疫系统加以描述和刻画。分支分析方法是研究带有时滞参数的系统动力学性质主要采用的方法和途径。所谓分支,就是一类具参数的动力学系统,当参数在临界值附近发生微小变动的的情况下,系统的动力学性质发生改变的现象。局部Hopf分支是微分方程动力系统分支研究中较常见的分支类型,它的产生对应于系统的线性化方程的特征方程有一对纯虚根的情形,主要研究系统随参数改变情况下平衡点处的稳定性情况和出现周期解的现象。本文主要研究了一类肿瘤免疫时滞模型的稳定性和Hopf分支性质。首先引入了一类具时滞反馈的肿瘤免疫模型,分析了模型的平衡点的存在性及其稳定性。然后定性地研究了Hopf分支性质。最后运用MATLAB软件进行相应的数值模拟,分析验证了在一段时期内,随着时间的增长,肿瘤细胞与免疫细胞在生物体竞争波动存在的这一生物现象。
[Abstract]:Tumor immunotherapy is an important branch of biomedicine. As early as the early 1980s, Biological mathematicians have developed a strong interest in tumor immune mechanisms and conducted extensive experiments and in-depth studies. With the development of biological mathematics science, Kuznetsov put forward a classical tumor immune model, Kuznetsov model. Studies on the stability of tumor immune delay systems and the properties of Hopf branching have been widely used in the medical treatment of cancer. There is a time delay in the response of effector cells to latent tumor cells in the human body. A complex immune process can be described and characterized by a time-delay immune system. Bifurcation analysis is the main method and approach to study the dynamical properties of a system with time-delay parameters. Is a kind of dynamic system with parameters, when the parameters change slightly near the critical value, Local Hopf bifurcation is one of the most common bifurcation types in the study of dynamical system bifurcation of differential equations. It produces a pair of pure imaginary roots corresponding to the characteristic equations of the linear equations of the system. In this paper, the stability and Hopf bifurcation of a class of tumor immune delay models are studied. Delayed feedback tumor immune model, The existence and stability of equilibrium point of the model are analyzed, and the properties of Hopf bifurcation are studied qualitatively. Finally, the corresponding numerical simulation is carried out by using MATLAB software. This biological phenomenon in which tumor cells and immune cells compete in biological fluctuations.
【学位授予单位】：哈尔滨工业大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O175

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