Numerical Investigation of the Dynamical Behavior of Hepatitis B Virus via Caputo-Fabrizio Fractional Derivative

Hepatitis B is a viral infection that primarily targets the liver, potentially leading to acute or chronic liver diseases with severe complications, such as cirrhosis and liver cancer. Its persistent prevalence underscores its status as a significant global health issue. This research constructs a mathematical model for the progression of Hepatitis B using fractional derivatives, accounting for a two-dose vaccine regimen. The basic concepts of the Caputo-Fabrizio (CF) derivative are presented for the model’s analysis. The infection-free equilibrium is investigated, and the endemic indicator of the system, R₀, is determined using the next-generation matrix method. The model exhibits local asymptotic stability at the infection-free equilibrium when R₀ < 1, and instability otherwise. Conditions ensuring the existence and uniqueness of solutions for the proposed fractional dynamics model are established. A new numerical method for analyzing the time series of the system is also presented. The study elucidates the impact of input variables on the system’s dynamic behavior and identifies critical factors within the model, highlighting key parameters that can be targeted for the control and management of Hepatitis B infection.