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

Abstract

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 $\mathcal{R}_0 <1$, and instability in all other scenarios. We establish conditions ensuring the existence and uniqueness of solutions for the proposed fractional dynamics model of hepatitis B. In addition to this, we present a new numerical method for analyzing the time series analysis of the system. Through our investigation, we elucidate the impact of input variables on the dynamic behavior of the system and identify the critical factors within the model. Our analysis identifies key parameters of the model that can be targeted for the control and management of hepatitis B infection.