Mathematical modeling and computational analysis of hepatitis B virus transmission using the higher-order Galerkin scheme

• Published in: Nonlinear engineering 2024-11, Vol.13 (1), p.165-52
• Main Authors: Attaullah, Boulaaras, Salah, Jan, Aasim Ullah, Hassan, Tahir, Radwan, Taha
• Format: Article
• Language: English
• Subjects: computational analysis; Galerkin technique; hepatitis B virus model; nonlinear equations; RK4 technique
• ISSN: 2192-8029; 2192-8029
• DOI: 10.1515/nleng-2024-0048

Hepatitis B, a liver disease caused by the hepatitis B virus (HBV), poses a significant public health burden. The virus spreads through the exchange of bodily fluids between infected and susceptible individuals. Hepatitis B is a complex health challenge for individuals. In this research, we propose a nonlinear HBV mathematical model comprising seven compartments: susceptible, latent, acutely infected, chronically infected, carrier, recovered, and vaccinated individuals. Our model investigates the dynamics of HBV transmission and the impact of vaccination on disease control. Using the next-generation matrix approach, we derive the basic reproduction number and determine the disease-free equilibrium points. We establish the global and local stability of the model using the Lyapunov function. The model is numerically solved using the higher-order Galerkin time discretization technique, and a comprehensive sensitivity analysis is carried out to investigate the impact of all physical parameters involved in the proposed nonlinear HBV mathematical model. A comparison was made of the accuracy and dependability with the findings produced using the Runge–Kutta fourth-order (RK4) approach. The findings highlight the critical need for vaccination, particularly among the exposed class, to facilitate rapid recovery and mitigate the spread of HBV. The results of this study provide valuable insights for public health policymakers and inform strategies for hepatitis B control and elimination.