本文選題：結(jié)核分枝桿菌 + 后向分支��； 參考：《西南大學(xué)》2017年碩士論文

【摘要】：本文根據(jù)結(jié)核分枝桿菌在體內(nèi)的感染過程免疫機(jī)制,分別建立了一般發(fā)生率下包含結(jié)核分枝桿菌兩種增殖方式的體內(nèi)結(jié)核分枝桿菌動力學(xué)模型,及宿主體內(nèi)包含離散時滯的結(jié)核分枝桿菌動力學(xué)模型,并討論了兩個模型的動力學(xué)性態(tài)和生物意義.第一章,介紹了結(jié)核病的疫情、結(jié)核分枝桿菌的背景知識、國內(nèi)外結(jié)核分枝桿菌動力學(xué)模型的研究進(jìn)展及本文所需的基本理論知識.第二章,建立了一個一般發(fā)生率下包含結(jié)核分枝桿菌兩種增殖方式的宿主體內(nèi)結(jié)核分枝桿菌動力學(xué)模型.首先,給出了結(jié)核分枝桿菌的基本再生數(shù)R0和免疫基本再生數(shù)R1;其次,借助基本再生數(shù)探究了無免疫平衡點(diǎn)的存在性及穩(wěn)定性,并得到在無病平衡點(diǎn)處出現(xiàn)后向分支的充要條件,同時研究了該條件和發(fā)生率函數(shù)及胞內(nèi)增殖所產(chǎn)生的裂解釋放量的關(guān)系;最后,給出了 一些數(shù)值模擬以驗(yàn)證結(jié)論.第三章,建立了一個包含離散時滯與CTL飽和免疫發(fā)生率的宿主體內(nèi)結(jié)核分枝桿菌動力學(xué)模型,并對其進(jìn)行了分析.首先,證明了模型解的非負(fù)性和有界性,并計(jì)算出結(jié)核分枝桿菌的基本再生數(shù)R0和免疫基本再生數(shù)R1;其次,分析了平衡點(diǎn)的存在性和局部穩(wěn)定性;最后,通過構(gòu)造合適的Lyapunov泛函,得到了無病平衡點(diǎn)、無免疫平衡點(diǎn)和正平衡點(diǎn)的全局穩(wěn)定的條件.第四章,對本文的主要工作進(jìn)行了簡要總結(jié),著重介紹了模型的生物意義和實(shí)際價值,并討論了本文的一些不足和需要進(jìn)一步研究的問題.
[Abstract]:According to the immune mechanism of the infection process of Mycobacterium tuberculosis in vivo, a dynamic model of Mycobacterium tuberculosis in vivo containing two modes of mycobacterium tuberculosis proliferation was established in this paper. And the dynamic model of Mycobacterium tuberculosis with discrete time delay in the host is discussed. The dynamic behavior and biological significance of the two models are discussed. The first chapter introduces the epidemic situation of tuberculosis, the background knowledge of Mycobacterium tuberculosis, the research progress of dynamics model of Mycobacterium tuberculosis at home and abroad and the basic theoretical knowledge needed in this paper. In chapter 2, a dynamic model of Mycobacterium tuberculosis in host is established, which contains two modes of mycobacterium tuberculosis proliferation. Firstly, the basic regeneration number R _ 0 and the immune basic regeneration number R _ 1 of Mycobacterium tuberculosis are given. Secondly, the existence and stability of the non-immune equilibrium point are explored with the help of the basic regeneration number. The necessary and sufficient conditions for backward bifurcation at the disease-free equilibrium point are obtained, and the relationship between the condition and the incidence function and the amount of cracking release produced by intracellular proliferation is studied. Finally, some numerical simulations are given to verify the conclusions. In chapter 3, a dynamic model of Mycobacterium tuberculosis in host with discrete delay and CTL saturation immunity is established and analyzed. Firstly, the nonnegative and boundedness of the model solution are proved, and the basic regeneration number R0 and the immune basic regeneration number R1 of Mycobacterium tuberculosis are calculated. Secondly, the existence and local stability of the equilibrium point are analyzed. By constructing appropriate Lyapunov functional, the conditions for global stability of disease-free equilibrium, non-immune equilibrium and positive equilibrium are obtained. In the fourth chapter, the main work of this paper is briefly summarized, the biological significance and practical value of the model are introduced, and some shortcomings and problems need further study are discussed.
【學(xué)位授予單位】：西南大學(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：2109955