In this paper, certain delayed virus dynamical models with cell-to-cell infection and density-dependent diffusion are investigated. For the viral model with a single strain, we have proved the well-posedness and studied the global stabilities of equilibria by defining the basic reproductive number [Formula: see text] and structuring proper Lyapunov functional. Moreover, we found that the infection-free equilibrium is globally asymptotically stable if [Formula: see text], and the infection equilibrium is globally asymptotically stable if [Formula: see text]. For the multi-strain model, we found that all viral strains coexist if the corresponding basic reproductive number [Formula: see text], while virus will extinct if [Formula: see text]. As a result, we found that delay and the density-dependent diffusion does not influence the global stability of the model with cell-to-cell infection and homogeneous Neumann boundary conditions.

中文翻译：

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具有细胞间传播和密度依赖性扩散的延迟病毒感染模型的动态分析

在本文中，研究了某些具有细胞间感染和密度依赖性扩散的延迟病毒动力学模型。对于单株病毒模型，我们通过定义基本繁殖数[公式：见正文]和构建适当的Lyapunov泛函，证明了适定性并研究了平衡的全局稳定性。此外，我们发现如果[公式：见文本]，则无感染平衡是全局渐近稳定的，如果[公式：见文本]，则感染平衡是全局渐近稳定的。对于多株模型，我们发现如果对应的基本繁殖数[公式：见正文]，所有病毒株共存，而如果[公式：见正文]，病毒就会灭绝。因此，