## Abstract

The aim of this paper is to develop a fractional order mathematical model for describing the spread of hepatitis B virus (HBV). We also provide a rigorous mathematical analysis of the stability of the disease-free equilibrium (DFE) and the endemic equilibrium of the system based on the basic reproduction number. Here, the infectious disease HBV model is described mathematically in a nonlinear system of differential equations in a caputo sense, and hence, Jacobi collocation method is used to reduce into a system of nonlinear equations. Finally, Newton Raphson method is used for the systems of nonlinear equations to arrive at an approximate solution and matlab 2018 has helped us to simulate the nature of each compartment and effects of the possible control strategies (i.e., vaccination and isolation).

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