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  本文關(guān)鍵詞：考慮免疫反應(yīng)的病毒動力學(xué)模型的全局性態(tài)　出處：《西南大學(xué)》2006年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 病毒動力學(xué)模型 免疫反應(yīng) 全局穩(wěn)定性 免疫反應(yīng)損害 隨機(jī)穩(wěn)定性

【摘要】：本文主要研究了考慮免疫反應(yīng)的病毒動力學(xué)模型的全局性態(tài)。第一章研究了考慮抗體免疫反應(yīng)的病毒動力學(xué)模型的全局性態(tài)。我們證明了當(dāng)基本再生數(shù)R_0≤1,病毒在體內(nèi)清除;而R_01時,病毒在體內(nèi)持續(xù)生存,并且模型的正解當(dāng)抗體免疫再生數(shù)R_1≤1時趨于無免疫平衡點(diǎn),R_11時趨于正平衡點(diǎn)。 第二章研究了兩個考慮CTL免疫反應(yīng)的病毒動力學(xué)模型性態(tài)。當(dāng)考慮宿主體內(nèi)健康細(xì)胞增長函數(shù)為線性時,我們證明了當(dāng)基本再生數(shù)R_0≤1,病毒在體內(nèi)清除;而R_01時,病毒在體內(nèi)持續(xù)生存,并且模型的正解當(dāng)抗體免疫再生數(shù)R_1≤1時趨于無免疫平衡點(diǎn),R_11時趨于正平衡點(diǎn)。而假設(shè)健康細(xì)胞增長函數(shù)為logistic型時,我們發(fā)現(xiàn)當(dāng)基本再生數(shù)R_0≤1,病毒在體內(nèi)被清除;而R_01時,病毒在體內(nèi)持續(xù)生存。在無免疫平衡點(diǎn)和正平衡點(diǎn)存在的條件下,我們得到了它們漸近穩(wěn)定的充分條件。在這些條件不滿足時,數(shù)值模擬分析出在一定參數(shù)條件下,系統(tǒng)會產(chǎn)生Hopf分支或者復(fù)雜的動力學(xué)性態(tài)。 第三章我們綜合考慮了抗體免疫反應(yīng)和CTL免疫反應(yīng),研究了一個五維ODE模型的全局性態(tài)。我們證明了基本再生數(shù)R_0,CTL免疫再生數(shù)R_1,抗體免疫再生數(shù)R_2,CTL免疫競爭再生數(shù)R_3,抗體免疫競爭再生數(shù)R_4決定了模型的全局性態(tài)。若R_0≤1,病毒在體內(nèi)清除。若R_01,正解在R_1≤1且R_2≤1時趨于無免疫平衡點(diǎn),在R_11且R_4≤1時趨于CTL主導(dǎo)平衡點(diǎn),在R_21且R3≤1時趨于抗體主導(dǎo)平衡點(diǎn),在R_31且R_41時,趨于正平衡點(diǎn)。 第四章我們研究了在免疫反應(yīng)損害情況下的細(xì)胞-細(xì)胞病毒動力學(xué)模型的確定穩(wěn)定性和隨機(jī)穩(wěn)定性。證明了當(dāng)基本再生數(shù)R_0≤1,病毒在體內(nèi)清除;而R_01時,病毒在體內(nèi)持續(xù)生存,并且模型的正平衡點(diǎn)在隨機(jī)擾動下也是穩(wěn)定的。
[Abstract]:This paper mainly studies the global properties of virus dynamics model with immune response. The first chapter studies the virus dynamics model with immune response to the global state. We prove that when the basic reproduction number R_0 is less than 1, the virus clearance in vivo; R_01, viral persistence in vivo survival, and the model is solution when the antibody reproduction number is less than or equal to 1 when R_1 tends to have no immune balance, steady R_11.
The second chapter studies two virus dynamics with CTL immune response model. When considering the health of the host cells in vivo growth function is linear, we prove that when the basic reproduction number R_0 is less than 1, the virus clearance in vivo; R_01, virus persistence, and the model of positive solution of the immune antibody the number of R_1 is less than 1 when the regeneration tends to have no immune balance, steady R_11. And the hypothesis of healthy cells growth of logistic type, we found that when the basic reproduction number R_0 is less than 1, the virus in the body; and R_01, virus persistence. In the presence of immune free equilibrium and positive equilibrium conditions, we obtain sufficient conditions for their asymptotic stability. In these conditions is not satisfied, the numerical simulation analysis under certain parameter conditions, the system produces Hopf bifurcation or complex dynamics.
The third chapter, we consider the immune response and immune response to CTL, the global state of a five dimensional ODE model. We show that the basic reproduction number R_0 CTL number R_1 antibody immune regeneration, regeneration R_2, CTL immune antibody competitive reproduction number R_3, competition R_4 determines the overall number of students state model. If R_0 is less than 1, the virus clearance in vivo. If the R_01 is in R_1 less than or equal to 1 and less than or equal to 1 when R_2 tends to have no immune balance in R_11 and R_4 < 1 CTL leading tends to equilibrium, in R_21 and R3 less than 1 is to dominate equilibrium in the R_31 antibody, and R_41 when tends to an equilibrium point.
The fourth chapter, we study the immune response in the absence of cell damage cell virus dynamics model to determine the stability and stochastic stability. It is proved that if the basic reproduction number R_0 is less than 1, the virus clearance in vivo; R_01, virus persistence, the positive equilibrium point and the model is stable under random perturbation.

【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】：2006
【分類號】：R392

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相關(guān)碩士學(xué)位論文 前1條

1 龐海燕;考慮免疫反應(yīng)的病毒動力學(xué)模型的全局性態(tài)[D];西南大學(xué);2006年

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本文編號：1427503