In this paper, a delayed HIV/AIDS epidemic model with treatment and spatial diffusion is introduced. By analyzing the corresponding characteristic equations, the local stability of a disease-free steady state and an endemic steady state is discussed. By using the cross-iteration method and Schauder’s fixed point theorem, we reduce the existence of traveling waves to the existence of a pair of upper–lower solutions. By constructing a pair of upper–lower solutions, we derive the existence of a traveling wave solution connecting the disease-free steady state and the endemic steady state. It is shown that the existence of traveling waves of the proposed HIV/AIDS epidemic model is fully determined by the basic reproduction number and the minimal wave speed. Finally, numerical simulations are performed to show the feasibility and effectiveness of the theoretical results.

中文翻译：

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具有治疗和空间扩散的延迟 HIV/AIDS 流行模型的行波

本文介绍了一种具有治疗和空间扩散的延迟 HIV/AIDS 流行模型。通过分析相应的特征方程，讨论了无病稳态和地方病稳态的局部稳定性。通过使用交叉迭代法和 Schauder 不动点定理，我们将行波的存在简化为一对上下解的存在。通过构造一对上下解，我们推导出连接无病稳态和地方性稳态的行波解的存在。结果表明，所提出的艾滋病病毒/艾滋病流行模型行波的存在完全由基本再生数和最小波速决定。最后，