Dynamics analysis of a delayed viral infection model with logistic growth and immune impairment

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• 作者：Zhixing Hu ; Jiajia Zhang ; Hui Wang ; Wanbiao Ma ; Fucheng Liao
• 关键词：Lyapunov functional ; LaSalle invariant principle ; Stability ; Immune impairment
• 刊名：Applied Mathematical Modelling
• 出版年：15 January, 2014
• 年：2014
• 卷：38
• 期：2
• 页码：524-534
• 全文大小：753 K

文摘

In this paper, the dynamics behavior of a delayed viral infection model with logistic growth and immune impairment is studied. It is shown that there exist three equilibria. By analyzing the characteristic equations, the local stability of the infection-free equilibrium and the immune-exhausted equilibrium of the model are established. By using suitable Lyapunov functional and LaSalle invariant principle, it is proved that the two equilibria are globally asymptotically stable. In the following, the stability of the positive equilibrium is investigated. Furthermore, we investigate the existence of Hopf bifurcation by using a delay as a bifurcation parameter. Finally, numerical simulations are carried out to explain the mathematical conclusions.