考慮免疫損害和滯后免疫增殖的病毒動力學(xué)模型分析
發(fā)布時間：2018-11-11 09:36
【摘要】： 本文建立了幾個考慮免疫反應(yīng)的病毒感染數(shù)學(xué)模型,研究了這些模型的動力學(xué)性態(tài)并分析了它們的生物意義。對于某些病毒性感染,抗原不但會激發(fā)宿主的免疫調(diào)節(jié)系統(tǒng),產(chǎn)生免疫應(yīng)答,促進免疫細(xì)胞的復(fù)制增殖,還會抑制免疫反應(yīng),當(dāng)抗原數(shù)量足夠大時甚至?xí)茐乃拗鞯拿庖呦到y(tǒng),因此本文的前兩部分分別建立了兩個慢性病毒感染模型來描述這種免疫損害。在第一部分我們考慮了CTL免疫反應(yīng)(細(xì)胞介導(dǎo)的免疫反應(yīng))。證明了當(dāng)病毒的基本再生數(shù)大于1時,病毒將在宿主體內(nèi)持續(xù)存在;當(dāng)系統(tǒng)只存在一個正平衡點時,免疫細(xì)胞能持續(xù)存在;當(dāng)病毒的基本再生數(shù)超過某一閾值時,系統(tǒng)會存在兩個平衡點,導(dǎo)致雙穩(wěn)性態(tài)的出現(xiàn),根據(jù)初始條件的不同,免疫細(xì)胞在宿主體內(nèi)將持續(xù)存在或消失。如果是前者,則此病毒感染終將被免疫系統(tǒng)控制,而如果是后者,則病毒感染將導(dǎo)致疾病進一步升級。理論分析和數(shù)值模擬均表明,通過某段有限時間的治療有可能實現(xiàn)長期的免疫控制,從而避免疾病進一步發(fā)展。在第二部分我們考慮了體液免疫,分析了該系統(tǒng)平衡點的局部以及全局穩(wěn)定性,當(dāng)系統(tǒng)只存在一個正平衡點時,還證明了系統(tǒng)的持久性。這兩個系統(tǒng)有相似的動力學(xué)性態(tài)。 本文的第三部分章建立了一個具有滯后免疫增殖的病毒模型,并從數(shù)學(xué)上分析了該系統(tǒng)的性態(tài)。此模型中,對于CTL免疫細(xì)胞,我們用一種更為合理的飽和免疫增殖方式取代了通常的線性免疫增殖方式;而對于健康宿主細(xì)胞,用滿足某些條件的一般函數(shù)來表示其數(shù)量的增長;同時,引入了反映滯后免疫增殖的時間滯量。如果病毒的基本再生數(shù)小于1,則病毒未感染平衡點是全局穩(wěn)定的;理論分析及數(shù)值模擬均表明,如果病毒的基本再生數(shù)大于1,則免疫反應(yīng)滯后時間將導(dǎo)致復(fù)雜的動力學(xué)性態(tài)。如果將時滯視為分支參數(shù),則隨著此時滯的增加,將會出現(xiàn)一列Hopf分支,并且當(dāng)時滯增至足夠大時,出現(xiàn)了混沌現(xiàn)象。數(shù)學(xué)結(jié)論表明宿主細(xì)胞增長的密度制約性與免疫細(xì)胞增長的飽和性均會對系統(tǒng)的動力學(xué)性態(tài)產(chǎn)生影響。
[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.
【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】：2008
【分類號】：R373
本文編號：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.
【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】：2008
【分類號】：R373
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