脉冲输注免疫因子的HIV治疗模型的动力学性质研究

发布时间：2018-04-19 03:01

本文选题：HIV治疗 + 免疫因子　；参考：《南华大学》2014年硕士论文

【摘要】：关于HIV感染及其治疗数学模型的研究已有将近30年的历史,其中,绝大部分模型的研究都是基于连续动力系统的方法进行的.然而,相比较而言,脉冲动力系统则能更准确地解释和模拟现实生活中的一些生物学现象.因此,本文主要运用脉冲微分方程的理论知识,结合输注免疫因子的HIV治疗方法,研究了两类脉冲输注免疫因子的HIV治疗模型,分别得到了其相应的一些动力学性质. 本文共三章.其中,第一章概述了艾滋病问题研究的历史背景和意义、HIV感染和免疫因子治疗模型的研究现状以及本文所做的一些主要工作. 第二章研究了一类关于脉冲输注免疫因子的HIV治疗模型,运用常微分方程稳定性理论和脉冲微分方程理论知识中的比较定理和Floquent乘子理论,分析了模型的平衡点的稳定性、无病周期解的存在性和稳定性；并对脉冲输注的周期长度进行了估计；最后,通过数值模拟更直观地展示了脉冲微分系统周期解的全局渐近稳定性. 第三章是在第二章模型的基础上进行了改进、完善,一方面考虑了在隐蔽期这一特殊时期内疾病的发病机理,另一方面也考虑了免疫因子对健康细胞和有效感染细胞的影响,建立起来的一类隐蔽期脉冲输注免疫因子的HIV治疗模型.本章运用了脉冲微分方程的有关理论知识,分析了模型平衡点的稳定性、无病脉冲周期解的存在性及其全局稳定的条件,最后进行了相关的数值模拟.
[Abstract]:The research on the mathematical model of HIV infection and its treatment has been carried out for nearly 30 years, most of which are based on the method of continuous dynamic system.However, the pulse power system can more accurately explain and simulate some biological phenomena in real life.Therefore, this paper mainly uses the theoretical knowledge of impulsive differential equation, combined with the HIV therapy method of infusion of immune factors, to study two kinds of HIV models of pulsed infusion of immune factors, and obtain some corresponding kinetic properties respectively.There are three chapters in this paper.The first chapter summarizes the historical background and significance of AIDS research.In the second chapter, we study a kind of HIV treatment model about impulsive infusion immune factor. By using the comparison theorem of ordinary differential equation stability theory and the theory of impulsive differential equation and Floquent multiplier theory, we analyze the stability of equilibrium point of the model.The existence and stability of disease-free periodic solutions and the estimation of the period length of impulsive infusion are given. Finally, the global asymptotic stability of periodic solutions of impulsive differential systems is demonstrated more intuitively by numerical simulation.The third chapter is improved on the basis of the second chapter model. On the one hand, it considers the pathogenesis of the disease during the special period of concealment, on the other hand, it also considers the influence of immune factors on healthy cells and effective infected cells.A model of HIV therapy for concealed pulse infusion of immune factors was established.In this chapter, the stability of equilibrium points, the existence of disease-free impulsive periodic solutions and the conditions of global stability are analyzed by using the theoretical knowledge of impulsive differential equations.
【学位授予单位】：南华大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：R512.91

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