本文選題：非溶解治愈　切入點(diǎn)：全局穩(wěn)定性　出處：《西南大學(xué)》2012年碩士論文

【摘要】：本文建立并分析了考慮具有非溶解自愈,免疫損傷.免疫反應(yīng)時(shí)滯等因素的乙型肝炎病毒感染模型.首先我們建立了一個(gè)三維模型,考慮了健康細(xì)胞、感染細(xì)胞以及CTL免疫細(xì)胞數(shù)量的動(dòng)力學(xué)性態(tài).然后建立了具有免疫反應(yīng)時(shí)滯的模型及同時(shí)考慮抗體免疫和CTL免疫的數(shù)學(xué)模型.隨后討論了平衡點(diǎn)的局部和全局穩(wěn)定性及相應(yīng)的生物意義.全文共分四章. 第一章,簡(jiǎn)述了乙型肝炎的發(fā)病,傳播原理及預(yù)防,治療措施.進(jìn)一步給出了傳染病動(dòng)力學(xué).病毒動(dòng)力學(xué)和微分方程穩(wěn)定性理論和基礎(chǔ)知識(shí). 第二章,我們主要考慮一個(gè)具有免疫損傷和細(xì)胞因子介導(dǎo)的乙肝病毒感染模型.研究了平衡點(diǎn)的全局和局部穩(wěn)定性,得到了只要無(wú)疾病平衡點(diǎn)和無(wú)免疫平衡點(diǎn)是局部穩(wěn)定的.就一定是全局漸近穩(wěn)定的.并得證明了若感染平衡點(diǎn)存在.則系統(tǒng)是一致持續(xù)生存的. 第三章,我們考慮了具有免疫反應(yīng)時(shí)滯的乙肝病毒感染模型.通過對(duì)模型的分析,我們證明了免疫反應(yīng)對(duì)無(wú)感染平衡點(diǎn)和無(wú)免疫平衡點(diǎn)的局部和全局穩(wěn)定性均無(wú)影響.但是會(huì)影響感染平衡點(diǎn)的穩(wěn)定性. 第四章,我們同時(shí)考慮了抗體免疫和CTL免疫反應(yīng)并建立了一個(gè)五維模型.我們研究了平衡點(diǎn)的局部穩(wěn)定性,并且分析了免疫損傷對(duì)乙肝病毒感染的影響. 第五章,我們對(duì)全文的結(jié)論進(jìn)行總結(jié)和討論.本文從數(shù)學(xué)的角度為乙型肝炎控制與治療提供了一個(gè)優(yōu)化合理的策略,為乙肝的治療及預(yù)防提供了一定的理論參考.
[Abstract]:In this paper, a hepatitis B virus infection model with insoluble self-healing, immune damage, immune response delay and other factors was established and analyzed. The dynamic state of the number of infected cells and CTL immune cells is discussed. Then, a model with immune response delay and a mathematical model considering both antibody and CTL immunity are established. Then, the local and global stability of equilibrium point is discussed. Qualitative and corresponding biological significance. The full text is divided into four chapters. In the first chapter, the pathogenesis, transmission principle, prevention and treatment of hepatitis B are briefly introduced. Furthermore, the theory and basic knowledge of infectious disease dynamics, viral dynamics and differential equation stability are given. In the second chapter, we mainly consider a model with immune damage and cytokine mediated hepatitis B virus infection. We study the global and local stability of the equilibrium point. As long as the disease-free equilibrium point and the non-immune equilibrium point are locally stable, it must be globally asymptotically stable, and it is proved that the system is uniformly persistent if the infection equilibrium exists. In the third chapter, we consider the hepatitis B virus infection model with immune response delay. We prove that the immune response has no effect on the local and global stability of the non-infective equilibrium point and the non-immune equilibrium point, but it will affect the stability of the infective equilibrium point. In chapter 4, we consider both antibody immunity and CTL immune response and establish a five-dimensional model. We study the local stability of equilibrium point and analyze the effect of immune injury on hepatitis B virus infection. In the fifth chapter, we summarize and discuss the conclusions of this paper. This paper provides a reasonable strategy for the control and treatment of hepatitis B from the mathematical point of view, and provides a certain theoretical reference for the treatment and prevention of hepatitis B.
【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】：2012
【分類號(hào)】：R311;O19

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本文編號(hào)：1700098