School of Mathematics and Statistics, Ningxia University, Yinchuan, P.R. China.
School of Information Engineering, Ningxia University, Yinchuan, P.R. China.
J Comput Biol. 2023 Mar;30(3):293-322. doi: 10.1089/cmb.2022.0032. Epub 2023 Jan 27.
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.
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逼近是预测模型动态行为的重要途径。在本文中，提出了一种完全离散方案，其中使用 Galerkin 有限元方法和保持正定性的截断 Euler-Maruyama 方案分别离散年龄变量和时间变量。分析了数值解与解析解之间的误差。最后，通过数值实例说明了理论结果。
