Numerical Investigation of the Dynamical Behavior of Hepatitis B Virus via Caputo-Fabrizio Fractional Derivative (European Journal of Pure and Applied Mathematics, 2025)
Hepatitis B is a viral infection that primarily targets the liver, potentially causing acute or chronic liver diseases with severe complications, such as cirrhosis and liver cancer. Its persistent prevalence underscores its status as a noteworthy global health issue. In this research, we construct a mathematical model for the progression of  hepatitis B through fractional derivative, accounting for a two-dose vaccine regimen. The basic results and concepts of the Caputo-Fabrizio (CF) derivative has been presented for the analysis of the model. We investigate the infection-free equilibrium of the model and determine the endemic indicator of the system with the help of next-generation matrix method, indicated by $\mathcal{R}_0$.  We demonstrate that the infection-free equilibrium of the model exhibits local asymptotic stability when $\mathcal{R}_0