Numerical Assessment of the Hepatitis B Virus Transmission Model Using a Non-standard Finite Difference Scheme and a Feedforward Neural Network

Abstract

Hepatitis B virus (HBV) infection is one of the leading causes of death and is a contagious disease that produces chronic liver infection. The infection of hepatitis B has a complex nature involving multiple and long infectious periods, behavioral changes, and healthcare limitations. The multiple infection phases, immune system, behavioral changes, and healthcare saturation have a
significant impact on the dynamics of hepatitis B virus transmission. Since HBV can persist in the body for years, the number of infectious individuals accumulates, and people take precautionary measures as awareness increases. Considering the multiple stages of the disease and the saturation level, we propose an innovative hybrid approach combining a mathematical model with a saturated incidence rate and a forward neural network to represent the transmission dynamics of the hepatitis B virus. First, we prove the biological and mathematical feasibility to show that the model under consideration is well-posed. We also investigate the dynamics of the model using linear stability analysis to derive the stability conditions. In addition, we perform the numerical assessment of the model using a novel hybrid approach of NSFD–FFNN framework to show the accuracy and large-scale numerical simulations.