Positivity Preserving Truncated Euler-Maruyama Scheme for the Stochastic Age-Structured HIV/AIDS Model.

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.