具有时滞的HBV病毒动力学模型稳定性分析

HBV（HePatitis B virus）是一种具有严重传染性的肝炎病毒，迄今为止，人们对它的免疫和慢性化的机制等方面还不甚了解。本文基于相关的病理知识，对应的建立了具有时滞的微分方程数学模型，系统地探讨了肝炎B病毒与宿主细胞之间的关系，利用Lyapunov函数方法研究了病毒动力学模型感染平衡点的局部稳定性和未感染平衡点全局稳定性，并利用数学模拟验证了理论分析。结果表明时滞的存在不会影响到感染平衡点的局部稳定性，但能影响平衡点到达的时间跨度，对于药物治疗的疗程和治疗时机的确定有参考意义。

Stability Analysis of HBV virus Dynamics model with delay

Hepatitis B virus（HBV） has serious infection and has little been known about the mechanism of its immunity and chronicity. In this paper, Basing on the relative knowledge of its pathology, the delay differential equation model of the HBV infection was constructed. Systematically examines the relationship among the HBV and the host cells, By means of Lyapunov ftmctions, We investigate the local stability of the equilibria, the global stability of the infection - free equilibrium is established. By numerical simulation, we con？ rm our theoretical analysis. The results show that the delay has not influenced the local stability of the equilibria, but has affected on the times of arrival equilibrium point. It has clinical significance to determine the treatment and opportunity of drug therapy.