具有Beddington-DeAngelis发生率和免疫损害项的带时滞的病毒感染模型的稳定性分析

Stability analysis of a delayed viral infection model with Beddington-DeAngelis incidence rate and immune impairment

研究一类具有Beddington-De Angelis发生率和免疫损害项的带时滞的病毒感染模型的动力学性质。通过分析相应的特征方程,分别证明无病平衡点和染病无免疫平衡点E1的局部渐近稳定性以及在正平衡点处Hopf分支的存在性;利用适当的Lyapunov泛函和La Salle不变原理,证明无病平衡点及染病无免疫平衡点的全局渐近稳定性;数值模拟验证了以上结论。

Dynamic properties of a delayed viral infection model with Beddington-DeAngelis incidence rate and immune impairment are investigated. By analyzing corresponding characteristic equations, the lo- cal stabilities of the uninfected equilibrium, the infected equilibrium without immunity and the existence of Hopf bifurcation at the infected equilibrium with immunity are established, respectively. Then, apply- ing suitable Lyapunov functional and the LaSalle＇ s invariance principle, the global stabilities of the unin- fected equilibrium and the infected equilibrium without immunity are proved. Finally, numerical simula-tions are carried out to support the main results.