In this paper, we study a delayed viral infection model with cellular infection and full logistic proliferations for both healthy and infected cells. The global asymptotic stabilities of the equilibria are studied by constructing Lyapunov functionals. Moreover, we investigated the existence of Hopf bifurcation at the infected equilibrium by regarding the possible combination of the two delays as bifurcation parameters. The results show that time delays may destabilize the infected equilibrium and lead to Hopf bifurcation. Finally, numerical simulations are carried out to illustrate the main results and explore the dynamics including Hopf bifurcation and stability switches.

中文翻译：

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具有全逻辑增殖的延迟病毒感染模型的稳定性和分岔分析

在本文中，我们研究了一种延迟病毒感染模型，该模型具有细胞感染和健康细胞和受感染细胞的完全逻辑增殖。通过构造 Lyapunov 泛函来研究平衡的全局渐近稳定性。此外，我们通过将两个延迟的可能组合视为分岔参数来研究感染平衡处 Hopf 分岔的存在。结果表明，时间延迟可能会破坏受感染的平衡并导致 Hopf 分岔。最后，进行数值模拟以说明主要结果并探索包括 Hopf 分岔和稳定性开关在内的动力学。