Abstract:
Mathematical modeling is a vast field that has interdisciplinary implications for research. These models help to investigate the basic dynamics and quantitative behavior of infectious diseases that affect human beings, such as COVID-19, hepatitis B virus (HBV), and human immunodeficiency virus (HIV). The current study investigates the spread of HBV by using the basic virus model. In order to determine the stability of disease-free and endemic equilibria, the basic reproduction number is determined. The convergence and divergence of disease-free and endemic equilibria are demonstrated by using standard finite difference (SFD) and non-standard finite difference (NSFD) schemes. Arguably, SFD schemes, namely Euler and Runge-Kutta order four (RK-4) schemes, converge for lower step sizes, while the NSFD scheme converges for all step sizes. The latter is a strong, efficient, and reliable method that shows a clear picture of the continuous model. All the results are validated using numerical simulations in order to better comprehend the dynamics of the disease. The theoretical and numerical findings in this work can be applied as a useful tool for tracking the prevalence of HBV infectious disease.
Keywords:
Convergence
,
local and global stability
,
numerical schemes
,
HBV model
,
Divergence