本文選題：EBV感染 + Lyapunov泛函�。� 參考：《西南大學(xué)》2017年碩士論文

【摘要】：本文基于Epstein-Barr病毒(EBV)的發(fā)病原理,在潛伏期的特點(diǎn)及其傳播機(jī)制,建立了兩個(gè)動(dòng)力學(xué)模型,分析并討論了其性態(tài)和生物意義.本文第一章簡(jiǎn)要介紹了 EBV的研究背景、動(dòng)力學(xué)模型的研究進(jìn)展、宿主抗EBV免疫反應(yīng)和本文所涉及到的一些理論基礎(chǔ)知識(shí).本文第二章建立了具有雙線(xiàn)性感染函數(shù)并且?guī)в袧摲跁r(shí)滯的動(dòng)力學(xué)模型.首先,證明了模型解的唯一性、非負(fù)性、有界性,求出無(wú)病平衡點(diǎn)和地方性平衡點(diǎn),并計(jì)算出模型基本再生數(shù)R0.其次,我們通過(guò)構(gòu)造恰當(dāng)?shù)腖yapunov函數(shù),結(jié)合LaSalle不變?cè)碜C明兩個(gè)平衡點(diǎn)的全局穩(wěn)定性,并討論了參數(shù)對(duì)EBV感染的影響.本文第三章建立了考慮細(xì)胞細(xì)胞感染的動(dòng)力學(xué)模型.首先,證明了模型解的唯一性、非負(fù)性、有界性,并給出基本再生數(shù)R2.其次,我們討論了模型平衡點(diǎn)的存在性,通過(guò)構(gòu)造恰當(dāng)?shù)腖yapunov泛函,結(jié)合LaSalle不變?cè)矸治隽藷o(wú)病平衡點(diǎn)及正平衡點(diǎn)的全局穩(wěn)定性.本文第四章簡(jiǎn)要回顧了前面的主要工作和主要結(jié)論,著重介紹了本文動(dòng)力學(xué)模型的生物意義與實(shí)際意義,并對(duì)本文工作的不足之處及進(jìn)一步的研究問(wèn)題和工作進(jìn)行了討論.
[Abstract]:Based on the pathogenesis of Epstein-Barr virus (EBV), the characteristics of latent period and its transmission mechanism, two kinetic models were established, and their sexual state and biological significance were analyzed and discussed. In the first chapter, the research background of EBV, the research progress of kinetic model, the host versus EBV immune response and some basic theoretical knowledge involved in this paper are briefly introduced. In chapter 2, a dynamic model with bilinear infection function with latency delay is established. Firstly, the uniqueness, nonnegativity and boundedness of the model solution are proved, and the disease-free equilibrium points and local equilibrium points are obtained, and the basic reproducing number R _ 0 of the model is calculated. Secondly, by constructing appropriate Lyapunov function and combining LaSalle invariant principle, we prove the global stability of the two equilibrium points, and discuss the influence of parameters on EBV infection. In the third chapter, a dynamic model considering cell infection was established. Firstly, the uniqueness, nonnegativity and boundedness of the solution of the model are proved, and the basic reproducing number R _ 2 is given. Secondly, we discuss the existence of the equilibrium point of the model and analyze the global stability of the disease-free equilibrium point and the positive equilibrium point by constructing the appropriate Lyapunov functional and combining the LaSalle invariant principle. In the fourth chapter, the main work and conclusions are reviewed briefly, the biological significance and practical significance of the kinetic model are emphatically introduced, and the shortcomings of this work and the further research problems and work are discussed.
【學(xué)位授予單位】：西南大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：O175

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