本文選題：HIV治療 + 免疫因子��； 參考：《南華大學》2014年碩士論文

【摘要】：關于HIV感染及其治療數(shù)學模型的研究已有將近30年的歷史,其中,絕大部分模型的研究都是基于連續(xù)動力系統(tǒng)的方法進行的.然而,相比較而言,脈沖動力系統(tǒng)則能更準確地解釋和模擬現(xiàn)實生活中的一些生物學現(xiàn)象.因此,本文主要運用脈沖微分方程的理論知識,結(jié)合輸注免疫因子的HIV治療方法,研究了兩類脈沖輸注免疫因子的HIV治療模型,分別得到了其相應的一些動力學性質(zhì). 本文共三章.其中,第一章概述了艾滋病問題研究的歷史背景和意義、HIV感染和免疫因子治療模型的研究現(xiàn)狀以及本文所做的一些主要工作. 第二章研究了一類關于脈沖輸注免疫因子的HIV治療模型,運用常微分方程穩(wěn)定性理論和脈沖微分方程理論知識中的比較定理和Floquent乘子理論,分析了模型的平衡點的穩(wěn)定性、無病周期解的存在性和穩(wěn)定性；并對脈沖輸注的周期長度進行了估計；最后,通過數(shù)值模擬更直觀地展示了脈沖微分系統(tǒng)周期解的全局漸近穩(wěn)定性. 第三章是在第二章模型的基礎上進行了改進、完善,一方面考慮了在隱蔽期這一特殊時期內(nèi)疾病的發(fā)病機理,另一方面也考慮了免疫因子對健康細胞和有效感染細胞的影響,建立起來的一類隱蔽期脈沖輸注免疫因子的HIV治療模型.本章運用了脈沖微分方程的有關理論知識,分析了模型平衡點的穩(wěn)定性、無病脈沖周期解的存在性及其全局穩(wěn)定的條件,最后進行了相關的數(shù)值模擬.
[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.
【學位授予單位】：南華大學
【學位級別】：碩士
【學位授予年份】：2014
【分類號】：R512.91

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