Abstract In this paper, we derive and analyze an HIV infection model containing a fixed latent period and both cell-free and cell-to-cell transmissions. The model is described by a spatially non-local reaction-diffusion system with the zero-flux condition on the boundary. We first show that the model admits global solutions and possesses a global attractor. Following the definition of the next infection operator, we obtain the expression of the basic reproduction number ℜ 0 , which is shown as a threshold parameter for the model dynamics. Our results indicate that the clearance/persistence of HIV is governed by the sign of ℜ 0 − 1 . In particular, an explicit formula of ℜ 0 is given in the homogeneous case.

中文翻译：

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具有无细胞和细胞间传播的延迟非局部反应扩散 HIV 感染模型的阈值动态

摘要 在本文中，我们推导出并分析了一个包含固定潜伏期和无细胞和细胞间传播的 HIV 感染模型。该模型由在边界上具有零通量条件的空间非局部反应-扩散系统描述。我们首先证明该模型承认全局解并具有全局吸引子。根据下一个感染算子的定义，我们获得了基本再生数 ℜ 0 的表达式，它被显示为模型动力学的阈值参数。我们的结果表明，HIV 的清除/持久性受 ℜ 0 - 1 的符号控制。特别地，在齐次情况下给出了 ℜ 0 的显式公式。