In this paper, we study stationarity of an age-structured human immunodeficiency virus (HIV) model with a delay and driven by the Ornstein–Uhlenbeck process. The HIV model involves cell-to-virus infection and cell-to-cell transmission, and the two transmission modes have a short intracellular latency described by the delay. As the death rate and virus production rate of infected cells have an explicit age-dependent feature and may be affected by environmental noises, we formulate a stochastic age-structured HIV model to investigate the impacts of the two transmission modes on viral spread. Utilizing suitable Lyapunov functions, we first establish the existence and uniqueness of the global solution for the HIV model, and then study the th moment boundedness of the solution. Finally, the unique stationary distribution of the solution to the model is obtained. Numerical simulations are presented to demonstrate validity of our theoretical results.

中文翻译：

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由 Ornstein-Uhlenbeck 过程驱动的具有延迟的年龄结构 HIV 模型分布的稳定性

在本文中，我们研究了由 Ornstein-Uhlenbeck 过程驱动的具有延迟的年龄结构人类免疫缺陷病毒 (HIV) 模型的平稳性。HIV模型涉及到细胞到病毒的感染和细胞到细胞的传播，两种传播方式都有以延迟描述的较短的细胞内潜伏期。由于受感染细胞的死亡率和病毒产生率具有明显的年龄依赖性特征，并且可能受环境噪声的影响，我们制定了一个随机年龄结构的 HIV 模型来研究两种传播模式对病毒传播的影响。利用合适的 Lyapunov 函数，我们首先建立 HIV 模型全局解的存在唯一性，然后研究解的第 时刻有界。最后，得到模型解的唯一平稳分布。数值模拟被提出来证明我们的理论结果的有效性。