本文選題：HIV-1感染模型 + HBV感染模型��； 參考：《云南師范大學(xué)》2017年碩士論文

【摘要】：艾滋病和乙型肝炎作為目前全世界兩種極具危害的傳染病,己經(jīng)給人類的健康造成了很大程度的威脅.本文則從它們的源頭-病毒入手,通過分析相應(yīng)微分方程平衡點的穩(wěn)定性,探討HIV-1和HBV感染系統(tǒng)的動力學(xué)行為.主要內(nèi)容如下:第一章簡單敘述了傳染病的研究背景和研究意義、HIV-1和HBV感染系統(tǒng)的國內(nèi)外研究狀況、本文的主要研究內(nèi)容和用到的定理、定義等.第二章,我們對一個帶有CTL免疫反應(yīng)、飽和發(fā)生率和三個時滯的五維HIV-1感染系統(tǒng)進(jìn)行了動力學(xué)研究.首先,我們給出了模型的基本性質(zhì),其中包括模型的適定性、基本再生數(shù)以及平衡點的存在性.然后通過分析平衡點的對應(yīng)特征方程,我們確定了每個可行性平衡點的局部穩(wěn)定性和出現(xiàn)Hopf分岔的條件.接下來運用波動引理和構(gòu)造適當(dāng)?shù)睦钛牌罩Z夫泛函,我們驗證了在局部穩(wěn)定的條件下前兩個不動點仍然是全局穩(wěn)定的.最后,我們對系統(tǒng)進(jìn)行數(shù)值計算來檢驗理論結(jié)果.第三章,我們研究一個新的包含空間擴(kuò)散,一般發(fā)生率和三個時滯的慢性HBV感染模型的動力學(xué).首先我們分析了在有界區(qū)域內(nèi)模型初始值問題的適定性,然后我們定義了一個被稱為基本再生數(shù)的閥值參數(shù),并且表明了我們的模型存在兩個可能的平衡點.接下來通過構(gòu)造兩個適當(dāng)?shù)睦钛牌罩Z夫泛函,說明了平衡點的全局動力學(xué)行為完全由系統(tǒng)閾值決定.最終我們給出數(shù)值計算來驗證之前所得結(jié)論的正確性.
[Abstract]:AIDS and hepatitis B are two harmful infectious diseases all over the world, which have posed a great threat to human health.In this paper, the dynamic behavior of HIV-1 and HBV infection systems is discussed by analyzing the stability of the equilibrium point of the corresponding differential equations.The main contents are as follows: in the first chapter, the research background and significance of infectious diseases are briefly described. The main research contents, theorems and definitions of HIV-1 and HBV infection systems are also discussed.In chapter 2, we study the dynamics of a five-dimensional HIV-1 infection system with CTL immune response, saturation incidence and three delays.First, we give the basic properties of the model, including the fitness of the model, the number of basic reproducing and the existence of equilibrium point.Then, by analyzing the corresponding characteristic equations of the equilibrium point, we determine the local stability of each feasible equilibrium point and the conditions for the occurrence of Hopf bifurcation.Then by using wave Lemma and constructing appropriate Lyapunov Functionals we prove that the first two fixed points are globally stable under locally stable conditions.Finally, we verify the theoretical results by numerical calculation of the system.In chapter 3, we study the dynamics of a new chronic HBV infection model with spatial diffusion, general incidence and three delays.First, we analyze the fitness of the initial value problem of the model in a bounded region, then we define a threshold parameter called the basic reproducing number, and show that there are two possible equilibrium points in our model.Then, by constructing two proper Lyapunov Functionals, it is shown that the global dynamical behavior of the equilibrium point is completely determined by the system threshold.Finally, we give a numerical calculation to verify the correctness of the previous conclusions.
【學(xué)位授予單位】：云南師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O175

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本文編號：1740899