In this paper, the dynamical behaviors for a five-dimensional virus infection model with Latently Infected Cells and Beddington–DeAngelis incidence are investigated. In the model, four delays which denote the latently infected delay, the intracellular delay, virus production period and CTL response delay are considered. We define the basic reproductive number and the CTL immune reproductive number. By using Lyapunov functionals, LaSalle’s invariance principle and linearization method, the threshold conditions on the stability of each equilibrium are established. It is proved that when the basic reproductive number is less than or equal to unity, the infection-free equilibrium is globally asymptotically stable; when the CTL immune reproductive number is less than or equal to unity and the basic reproductive number is greater than unity, the immune-free infection equilibrium is globally asymptotically stable; when the CTL immune reproductive number is greater than unity and immune response delay is equal to zero, the immune infection equilibrium is globally asymptotically stable. The results show that immune response delay may destabilize the steady state of infection and lead to Hopf bifurcation. The existence of the Hopf bifurcation is discussed by using immune response delay as a bifurcation parameter. Numerical simulations are carried out to justify the analytical results.

中文翻译：

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具有潜伏感染细胞和 Beddington-DeAngelis 发生率的延迟病毒感染模型的稳定性和 Hopf 分岔

在本文中，研究了具有潜在感染细胞和 Beddington-DeAngelis 发病率的五维病毒感染模型的动力学行为。在该模型中，考虑了四种延迟，即潜在感染延迟、细胞内延迟、病毒产生期和 CTL 反应延迟。我们定义了基本再生数和 CTL 免疫再生数。利用Lyapunov泛函、LaSalle不变原理和线性化方法，建立了各平衡点稳定性的阈值条件。证明了当基本再生数小于等于1时，无感染平衡是全局渐近稳定的；当CTL免疫再生数小于等于一且基本再生数大于一时，无免疫感染平衡是全局渐近稳定的；当CTL免疫再生数大于1且免疫反应延迟为零时，免疫感染平衡是全局渐近稳定的。结果表明，免疫反应延迟可能会破坏感染的稳定状态并导致Hopf分叉。以免疫反应延迟作为分岔参数讨论了 Hopf 分岔的存在。进行数值模拟以证明分析结果的合理性。结果表明，免疫反应延迟可能会破坏感染的稳定状态并导致Hopf分叉。以免疫反应延迟作为分岔参数讨论了 Hopf 分岔的存在。进行数值模拟以证明分析结果的合理性。结果表明，免疫反应延迟可能会破坏感染的稳定状态并导致Hopf分叉。以免疫反应延迟作为分岔参数讨论了 Hopf 分岔的存在。进行数值模拟以证明分析结果的合理性。