本文選題：HIV-1感染模型 + 時(shí)滯�。� 參考：《哈爾濱工業(yè)大學(xué)》2017年碩士論文

【摘要】：HIV即人類免疫缺陷病毒,是一種具有傳染性的病毒。HIV病毒的傳播途徑很廣泛,在之前的研究中,考慮的是無時(shí)滯情況或者線性發(fā)生率的情況,關(guān)于HIV病毒模型的研究工作很多,然而同時(shí)考慮細(xì)胞干擾細(xì)胞及病毒感染細(xì)胞的感染機(jī)制工作較為少見。在本文中,我們對此進(jìn)行深入研究。在這篇文章中,我們考慮了一種包含細(xì)胞向細(xì)胞和病毒向細(xì)胞傳播的病毒感染模型,包括一般的靶細(xì)胞動力學(xué)、非線性發(fā)生率依賴狀態(tài)的死亡率、狀態(tài)依賴去除函數(shù)和細(xì)胞內(nèi)無限分布的時(shí)滯。首先,定義一個(gè)全局動態(tài)閾值,它完全由基本再生數(shù)(?)_0來描述,如果(?)_0＜1,那么感染消除平衡點(diǎn)是全局漸近穩(wěn)定的。如果(?)_0＞1,則模型是一致持久的且正平衡點(diǎn)是全局漸近穩(wěn)定的。數(shù)值模擬驗(yàn)證了上述分析結(jié)果。
[Abstract]:HIV, the human immunodeficiency virus (human immunodeficiency virus), is a kind of infectious virus.HIV virus, which is widely spread. In the previous study, there was no delay or linear incidence. There was a lot of research on the HIV virus model. However, the infection mechanism of cell and virus infected cells was considered at the same time. In this article, we consider a virus infection model that contains cells to cells and viruses to cells, including the general target cell dynamics, the mortality of the nonlinear incidence dependent state, the state dependent removal function and the infinite distribution within the cell. First, a global dynamic threshold is defined, which is completely described by the basic regeneration number (?) _0. If (?) _0 < 1, the infection elimination equilibrium point is globally asymptotically stable. If (?) _0 > 1, the model is uniformly persistent and the positive equilibrium point is globally asymptotically stable. The numerical simulation verifies the above analysis results.
【學(xué)位授予單位】：哈爾濱工業(yè)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O175

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本文編號：2062940