Abstract This paper considers an impulsive switching human immunodeficiency virus (HIV) infection model incorporating the mean-reverting Ornstein–Uhlenbeck process. The model involve the virus-to-cell infection and cell-to-cell transmission and has an explicit age-dependent structure. Due to the exact solution of this system can not be expressed explicitly, it is necessary to give a suitable numerical method to discuss the numerical solution. In this paper, we apply the truncated Euler–Maruyama (EM) method to investigate the explicit numerical approximation for the impulsive stochastic age-structured HIV infection model with Markovian switching. We study the p th moment boundedness of the numerical solution, and the corresponding strong convergence of such algorithm. Numerical simulations are presented to demonstrate the validity of our findings.

中文翻译：

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具有马尔可夫转换的脉冲随机年龄结构 HIV 感染模型的显式数值近似

摘要 本文考虑了一种包含均值回复 Ornstein-Uhlenbeck 过程的脉冲转换人类免疫缺陷病毒 (HIV) 感染模型。该模型涉及病毒到细胞的感染和细胞到细胞的传播，并具有明确的年龄依赖性结构。由于该系统的精确解不能明确表达，有必要给出合适的数值方法来讨论数值解。在本文中，我们应用截断的 Euler-Maruyama (EM) 方法来研究具有马尔可夫转换的脉冲随机年龄结构 HIV 感染模型的显式数值近似。我们研究了数值解的p阶矩有界性，以及该算法对应的强收敛性。提供了数值模拟来证明我们发现的有效性。