包含两种感染方式的非线性感染模型稳定性分析

发布时间：2018-06-24 21:02

本文选题：HIV-1感染模型 + 时滞　；参考：《哈尔滨工业大学》2017年硕士论文

【摘要】：HIV即人类免疫缺陷病毒,是一种具有传染性的病毒。HIV病毒的传播途径很广泛,在之前的研究中,考虑的是无时滞情况或者线性发生率的情况,关于HIV病毒模型的研究工作很多,然而同时考虑细胞干扰细胞及病毒感染细胞的感染机制工作较为少见。在本文中,我们对此进行深入研究。在这篇文章中,我们考虑了一种包含细胞向细胞和病毒向细胞传播的病毒感染模型,包括一般的靶细胞动力学、非线性发生率依赖状态的死亡率、状态依赖去除函数和细胞内无限分布的时滞。首先,定义一个全局动态阈值,它完全由基本再生数(?)_0来描述,如果(?)_0＜1,那么感染消除平衡点是全局渐近稳定的。如果(?)_0＞1,则模型是一致持久的且正平衡点是全局渐近稳定的。数值模拟验证了上述分析结果。
[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.
【学位授予单位】：哈尔滨工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

【参考文献】