A multi-layer neural network approach for the stability analysis of the Hepatitis B model

Abstract

In the present study, we explore the dynamics of Hepatitis B virus infection, a significant global health issue, through a newly developed dynamics system. This model is distinguished by its inclusion of asymptomatic carriers and the impact of vaccination and treatment strategies. Compared to Hepatitis A, Hepatitis B poses a more serious health risk, with some cases progressing from acute to chronic. To diagnose and predict disease recurrence, the basic reproduction number ($R_0$) is calculated. We investigate the stability of the disease’s dynamics under different conditions, using the Lyapunov function to confirm our model’s global stability. Our findings highlight the relevance of vaccination and early treatment in reducing Hepatitis B virus spread, making them a useful tool for public health efforts aiming at eradicating Hepatitis B virus. In our research, we investigate the dynamics of a specific model that is characterized by a system of differential equations. This work uses deep neural networks (DNNs) technique to improve model accuracy, proving the use of DNNs in epidemiological modeling. Additionally, we want to find the curves that suit the target solutions with the minimum residual errors. The simulations we conducted demonstrate our methodology’s capability to accurately predict the behavior of systems across various conditions. We rigorously test the solutions obtained via the DNNs by comparing them to benchmark solutions and undergoing stages of testing, validation, and training. To determine the accuracy and reliability of our approach, we perform a series of analyses, including convergence studies, error distribution evaluations, regression analyses, and detailed curve fitting for each equation.