In this paper, we propose and analyze a delayed diffusive viral dynamic model incorporating cell-mediated immunity and both cell-free and cell-to-cell transmission. After discussing the well-posedness, we provide some preliminary results on solutions. Then we study the existence and uniqueness of homogeneous steady states, which turned out to be completely determined by the basic reproduction number of infection R₀ and the basic reproduction number of immunity R₁. Note that when R₁ is defined, it is necessary that R₀ > 1. The main result is a threefold dynamics. Roughly speaking, when R₀ < 1 the infection-free steady state is globally asymptotically stable; when R₁ ≤ 1 < R₀ the immunity-free infected steady state is globally asymptotically stable; when R₁ > 1 the infected-immune steady state is globally asymptotically stable. The approaches are linearization technique and the Lyapunov functional method. The theoretical results are also illustrated with numerical simulations.

中文翻译：

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具有细胞介导的免疫和细胞间传播的延迟扩散病毒感染模型的全局动力学

在本文中，我们提出并分析了包含细胞介导的免疫力以及无细胞和细胞间传播的延迟扩散病毒动力学模型。在讨论完好性之后，我们提供了一些初步的解决方案结果。然后，我们研究了均质稳态的存在和唯一性，结果完全取决于感染的基本繁殖数R ₀和免疫力R ₁的基本繁殖数。注意，当定义R ₁时，R ₀ > 1是必要的。主要结果是三重动力学。大致来说，当R _0时<1，无感染稳态是全局渐近稳定的；当[R ₁ ≤1 < - [R ₀无免疫感染稳态是全局渐近稳定; 当R ₁ > 1时，被感染的免疫稳态是全局渐近稳定的。这些方法是线性化技术和Lyapunov函数方法。理论结果也用数值模拟说明。