Abstract: In this paper, a mathematical model for Hepatitis B Virus（HBV） infection with delay in Cytotoxic T Lymphocytes（CTL） immune response is considered, which is taking into account the effect of role of lytic and non-lytic mechanisms. The local stability and the existence conditions of Hopf bifurcation are discussed, as well as the global stability of the infection-free equilibrium point and the immune-free equilibrium point is analyzed. Some numerical analysis show that the delay has no effect on the stability of the positive equilibrium point if the delay is smaller than one certain threshold value. But if the delay is greater than the certain threshold value, the positive equilibrium point is unstable. Finally a series of Hopf bifurcations and periodic solutions are observed by the numerical analysis.

Key words: Hepatitis B Virus（HBV） infection, delay, stability, Hopf , bifurcation

摘要： 考虑了溶解性和非溶解性机制下的一类具有免疫时滞的HBV感染动力学模型。分析了无感染平衡点及感染无免疫平衡点的全局稳定性，讨论了感染免疫平衡点的局部稳定性和Hopf分支的存在条件。数值模拟结果表明：当易感细胞生成率的取值使得基本再生数满足平衡存在条件且低于某一临界值时，时滞对平衡点的稳定性没有影响；当大于该临界值时，随着时滞增大，平衡点不稳定，出现一系列Hopf分支，最终表现为周期波动模式。

关键词: 乙型肝炎病毒（HBV）感染, 时滞, 稳定性, Hopf分支