A stochastic age-structured HIV/AIDS model based on parameters estimation and its numerical calculation

Abstract

In this paper, we obtain the expressions of epidemiological parameters using a class of feedforward neural networks (FNNs) based on the data collected from Chinese Center for Disease Control and Prevention (CCDCP), and establish a stochastic age-structured HIV/AIDS model with parameter perturbation. In order to ensure the mathematical and epidemiological rationality of the model, we discuss the existence, uniqueness, and boundedness of its positive solution. Due to the difficulty of solving the true solution for the stochastic age-structured HIV/AIDS model, we propose a full-discrete scheme using the Galerkin finite element method in age discretization and the Euler’s scheme in time discretization. The error estimation between the numerical solution and the true solution is established. The results are justified by computer simulations.