考虑免疫损害和滞后免疫增殖的病毒动力学模型分析
发布时间：2018-11-11 09:36
【摘要】： 本文建立了几个考虑免疫反应的病毒感染数学模型,研究了这些模型的动力学性态并分析了它们的生物意义。对于某些病毒性感染,抗原不但会激发宿主的免疫调节系统,产生免疫应答,促进免疫细胞的复制增殖,还会抑制免疫反应,当抗原数量足够大时甚至会破坏宿主的免疫系统,因此本文的前两部分分别建立了两个慢性病毒感染模型来描述这种免疫损害。在第一部分我们考虑了CTL免疫反应(细胞介导的免疫反应)。证明了当病毒的基本再生数大于1时,病毒将在宿主体内持续存在;当系统只存在一个正平衡点时,免疫细胞能持续存在;当病毒的基本再生数超过某一阈值时,系统会存在两个平衡点,导致双稳性态的出现,根据初始条件的不同,免疫细胞在宿主体内将持续存在或消失。如果是前者,则此病毒感染终将被免疫系统控制,而如果是后者,则病毒感染将导致疾病进一步升级。理论分析和数值模拟均表明,通过某段有限时间的治疗有可能实现长期的免疫控制,从而避免疾病进一步发展。在第二部分我们考虑了体液免疫,分析了该系统平衡点的局部以及全局稳定性,当系统只存在一个正平衡点时,还证明了系统的持久性。这两个系统有相似的动力学性态。 本文的第三部分章建立了一个具有滞后免疫增殖的病毒模型,并从数学上分析了该系统的性态。此模型中,对于CTL免疫细胞,我们用一种更为合理的饱和免疫增殖方式取代了通常的线性免疫增殖方式;而对于健康宿主细胞,用满足某些条件的一般函数来表示其数量的增长;同时,引入了反映滞后免疫增殖的时间滞量。如果病毒的基本再生数小于1,则病毒未感染平衡点是全局稳定的;理论分析及数值模拟均表明,如果病毒的基本再生数大于1,则免疫反应滞后时间将导致复杂的动力学性态。如果将时滞视为分支参数,则随着此时滞的增加,将会出现一列Hopf分支,并且当时滞增至足够大时,出现了混沌现象。数学结论表明宿主细胞增长的密度制约性与免疫细胞增长的饱和性均会对系统的动力学性态产生影响。
[Abstract]:In this paper, several mathematical models of viral infection considering immune response were established, the dynamics of these models were studied and their biological significance was analyzed. In some viral infections, antigens not only stimulate the host's immune regulatory system, generate an immune response, promote the replication and proliferation of immune cells, but also inhibit the immune response, and even destroy the host's immune system when the number of antigens is large enough. Therefore, two models of chronic viral infection were established in the first two parts of this paper to describe the immune damage. In the first part, we considered the CTL immune response (cellular mediated immune response). It is proved that the virus will persist in the host when the basic regeneration number of the virus is more than 1, and the immune cells will persist when there is only one positive equilibrium point in the system. When the basic regeneration number of the virus exceeds a certain threshold, there will be two equilibrium points in the system, which will lead to the emergence of bistable state. According to the different initial conditions, the immune cells will persist or disappear in the host. If the former, the virus infection will eventually be controlled by the immune system, and if the latter, the virus infection will lead to further escalation of the disease. Theoretical analysis and numerical simulation show that it is possible to achieve long-term immune control through a limited period of time treatment, thus avoiding the further development of the disease. In the second part, we consider humoral immunity, analyze the local and global stability of the equilibrium point of the system, and prove the persistence of the system when there is only one positive equilibrium point. The two systems have similar dynamics. In the third chapter, a virus model with hysteresis immune proliferation is established, and the properties of the system are analyzed mathematically. In this model, for CTL immune cells, we replace the usual linear immune proliferation with a more reasonable saturated immune proliferation. For healthy host cells, a general function satisfying certain conditions is used to represent the increase of the number of cells, and a time-lag quantity is introduced to reflect the delayed immune proliferation. If the basic regeneration number of the virus is less than 1, the uninfected equilibrium point of the virus is globally stable. Theoretical analysis and numerical simulation show that if the basic regeneration number of the virus is greater than 1, the delay time of the immune reaction will lead to the complex dynamic state. If the delay is regarded as a bifurcation parameter, then with the increase of the lag, there will be a column of Hopf bifurcation, and when the lag increases to large enough, chaos will occur. The mathematical results show that both the density constraint of host cell growth and the saturation of immune cell growth will affect the dynamics of the system.
【学位授予单位】：西南大学
【学位级别】：硕士
【学位授予年份】：2008
【分类号】：R373
本文编号：2324450
[Abstract]:In this paper, several mathematical models of viral infection considering immune response were established, the dynamics of these models were studied and their biological significance was analyzed. In some viral infections, antigens not only stimulate the host's immune regulatory system, generate an immune response, promote the replication and proliferation of immune cells, but also inhibit the immune response, and even destroy the host's immune system when the number of antigens is large enough. Therefore, two models of chronic viral infection were established in the first two parts of this paper to describe the immune damage. In the first part, we considered the CTL immune response (cellular mediated immune response). It is proved that the virus will persist in the host when the basic regeneration number of the virus is more than 1, and the immune cells will persist when there is only one positive equilibrium point in the system. When the basic regeneration number of the virus exceeds a certain threshold, there will be two equilibrium points in the system, which will lead to the emergence of bistable state. According to the different initial conditions, the immune cells will persist or disappear in the host. If the former, the virus infection will eventually be controlled by the immune system, and if the latter, the virus infection will lead to further escalation of the disease. Theoretical analysis and numerical simulation show that it is possible to achieve long-term immune control through a limited period of time treatment, thus avoiding the further development of the disease. In the second part, we consider humoral immunity, analyze the local and global stability of the equilibrium point of the system, and prove the persistence of the system when there is only one positive equilibrium point. The two systems have similar dynamics. In the third chapter, a virus model with hysteresis immune proliferation is established, and the properties of the system are analyzed mathematically. In this model, for CTL immune cells, we replace the usual linear immune proliferation with a more reasonable saturated immune proliferation. For healthy host cells, a general function satisfying certain conditions is used to represent the increase of the number of cells, and a time-lag quantity is introduced to reflect the delayed immune proliferation. If the basic regeneration number of the virus is less than 1, the uninfected equilibrium point of the virus is globally stable. Theoretical analysis and numerical simulation show that if the basic regeneration number of the virus is greater than 1, the delay time of the immune reaction will lead to the complex dynamic state. If the delay is regarded as a bifurcation parameter, then with the increase of the lag, there will be a column of Hopf bifurcation, and when the lag increases to large enough, chaos will occur. The mathematical results show that both the density constraint of host cell growth and the saturation of immune cell growth will affect the dynamics of the system.
【学位授予单位】：西南大学
【学位级别】：硕士
【学位授予年份】：2008
【分类号】：R373
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