本文選題：宿主體內(nèi)模型 + 基孔肯雅病毒感染��； 參考：《西南大學(xué)》2016年碩士論文

【摘要】：本文根據(jù)基孔肯雅病毒在宿主體內(nèi)的發(fā)病機(jī)制和免疫機(jī)制,在病毒動(dòng)力學(xué)基本模型的基礎(chǔ)上,建立并分析了考慮體液免疫和免疫時(shí)滯的基孔肯雅病毒動(dòng)力學(xué)模型,以及具有飽和感染率的離散時(shí)滯動(dòng)力學(xué)模型.探究了兩個(gè)模型的動(dòng)力學(xué)性態(tài)及生物意義.第一章首先介紹了有關(guān)基孔肯雅病毒的背景知識(shí)、該病毒動(dòng)力學(xué)模型研究進(jìn)展及本文用到的主要理論.第二章建立了雙時(shí)滯的基孔肯雅病毒在宿主體內(nèi)的動(dòng)力學(xué)模型.計(jì)算了模型基本再生數(shù)R0.若R01,無感染平衡點(diǎn)全局漸近穩(wěn)定且疾病消失.若Ro1,沒有免疫時(shí)滯時(shí),唯一的感染平衡點(diǎn)E1全局穩(wěn)定,而免疫時(shí)滯可以改變E1的穩(wěn)定性,導(dǎo)致Hop盼支的存在.而且,通過Hopf分支的方向的計(jì)算公式得到了分支周期解的穩(wěn)定性.最后,給出了一些數(shù)值模擬來驗(yàn)證結(jié)論.第三章建立并分析了考慮基孔肯雅病毒在宿主體內(nèi)的離散時(shí)滯動(dòng)力學(xué)模型.首先,證明了解的正性和有界性,并計(jì)算出基本再生數(shù)Ro.其次,討論了模型平衡點(diǎn)的存在性,無感染平衡點(diǎn)始終存在,而當(dāng)Ro1時(shí),存在唯一的感染平衡點(diǎn).最后,通過構(gòu)造Lyapunov泛函,得到了無感染平衡點(diǎn)的全局穩(wěn)定性及感染平衡點(diǎn)的全局穩(wěn)定性.第四章簡(jiǎn)要回顧了本文的結(jié)論,著重介紹了本文研究內(nèi)容的生物和實(shí)際意義.最后討論了本文的一些不足和需要進(jìn)一步研究的問題.
[Abstract]:Based on the basic model of the virus dynamics, based on the basic model of the virus dynamics, based on the basic model of the virus dynamics, the dynamic model of the base hole Kenya virus, which consider the humoral immunity and the immune time delay, and the discrete time delay dynamic model with the saturated infection rate are established and analyzed. The dynamics of the two models are explored. The first chapter introduces the background knowledge about the base hole Kenya virus, the research progress of the virus dynamic model and the main theory used in this paper. In the second chapter, the dynamic model of the double time-delay base hole Kenya virus in the host is set up. The number of regenerative number R0. of the model, if R01, is calculated, the overall situation of the non infection equilibrium point is calculated. The asymptotically stable and disappearing of the disease. If Ro1 has no immune delay, the only infection equilibrium point E1 is globally stable, and the immune delay can change the stability of the E1 and lead to the existence of the Hop branch. Furthermore, the stability of the bifurcation periodic solution is obtained by the formula of the direction of the Hopf branch. Finally, some numerical simulations are given to verify the conclusion. The third chapter establishes and analyzes the discrete time-delay dynamics model of the base hole Kenya virus in the host. First, it proves the positive and boundedness of the knowledge, and calculates the basic regeneration number Ro. next, and discusses the existence of the equilibrium point of the model, and there is always the existence of the non infection equilibrium point. When Ro1, there is a unique equilibrium point of infection. The global stability of the non infectious equilibrium point and the global stability of the equilibrium point of infection are obtained by constructing the Lyapunov functional. The fourth chapter briefly reviews the conclusions of this paper, and focuses on the biological and practical significance of this study. Finally, some shortcomings of this paper and the problems to be further studied 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】：2016
【分類號(hào)】：O175
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本文編號(hào)：2074780