Global stability analysis of a fractional differential system in hepatitis B

Abstract

This paper describes the dynamics of hepatitis B by a fractional-order model in the Caputo sense. The basic results of the fractional hepatitis B model are presented. Two equilibrium point for the model exists, the disease-free point and the infected point. The local and global stability analysis of the system is given in terms of the basic reproductive number. We execute the global stability analysis using the extended Barbalat's lemma to the fractional-order system. The results show that the extension of Barbalat's Lemma is a robust tool for the asymptotic analysis of the fractional dynamic systems. Moreover, numerical simulations by Nonstandard Finite Difference Schemes show that the solutions converge to an equilibrium point as predicted in the stability analysis.