Since the analytical solution of the stochastic age-structured human immunodeficiency virus/acquired immune deficiency syndrome model is difficult to solve, establishing an efficient numerical approximation is an important way to predict the dynamic behavior of the model. In this article, a full-discrete scheme is proposed, where the Galerkin finite element method and the positivity preserving truncated Euler–Maruyama scheme are used to discrete the age variable and the time variable, respectively. The error between the numerical solution and the analytical solution is analyzed. Finally, the theoretical results are illustrated by the numerical examples.

中文翻译：

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用于随机年龄结构 HIV/AIDS 模型的正性保留截断 Euler-Maruyama 方案

由于随机年龄结构的人类免疫缺陷病毒/获得性免疫缺陷综合征模型的解析解难以求解，因此建立有效的数值近似是预测模型动态行为的重要途径。本文提出了一种全离散方案，分别采用Galerkin有限元法和保正性截断Euler-Maruyama方案对年龄变量和时间变量进行离散。分析了数值解与解析解的误差。最后通过算例说明了理论结果。