A fractional modeling approach to a new Hepatitis B model in light of asymptomatic carriers, vaccination and treatment

Abstract

Hepatitis B virus (HBV) is a much more threatening and prolonged disease than hepatitis A. It can start as an acute disease, but in roughly 5 to 10% of situations, it can progress to a chronic condition that permanently damages the liver. After getting or coming into contact with the Hepatitis B virus (HBV), the said symptoms normally last from 10 days to 6 months. In the present paper, to have a firm understanding of the dynamics of HBV, we derived a new fractional model in the Caputo sense with asymptomatic carriers, vaccination, and treatment classes. We obtain the basic reproduction number R0 for the diagnosis and recurrence of the disease. We determine the stability of the proposed model locally and globally for R0 values less than and greater than 1. We use the Lyapunov function theory in fractional environments to establish the global stability of the fractional Hepatitis B virus (HBV) model. We demonstrate the existence and uniqueness of the fractional-order model. To look at the fractional order model’s solution graphically, we used a useful numerical strategy to get more detailed numerical results for the factors that have a big effect on getting rid of diseases. Additionally, the inclusion of the treatment class in the population allows for the determination of the impact of alternative medicines used to treat infected populations. Numerical simulation of the proposed fractional order (FO) Caputo model is performed, allowing for the analysis of graphical representations and the significance of fractional order derivatives to illustrate the impact of our theoretical findings.

Keywords

• Caputo fractional derivative
• Mathematical modeling
• Hepatitis B virus (HBV)
• Critical Vaccination Coverage (CVC)
• Lyapunov function
• Numerical simulation