Eur. Phys. J. Plus (2018) 133: 313
https://doi.org/10.1140/epjp/i2018-12120-1

Regular Article

Modeling and analysis of the fractional HBV model with Atangana-Baleanu derivative

¹ Department of Mathematics, University of Peshawar, Peshawar, KP, Pakistan
² Department of Mathematics, City University of Science and Information Technology, Peshawar, KP, Pakistan

^* e-mail: altafdir@gmail.com

Received: 23 May 2018
Accepted: 22 June 2018
Published online: 6 August 2018

Abstract

Recently a new fractional derivative with non-local and non-singular kernel was proposed by Atangana and Baleanu. In this paper, a fractional hepatitis B virus model with Atangana-Baleanu derivative (AB derivative) is formulated. Initially, we present the model equilibria and basic reproduction number. The local stability of the disease-free equilibrium point is proved using Matignon’s conditions. The fixed-point theory is applied to show the existence and uniqueness of solutions for the fractional HBV disease model. A numerical scheme using Adams-Bashforth method for solving the proposed fractional model involving the AB derivative is presented. Finally, numerical simulations are performed in order to validate the importance of the arbitrary order derivative. The fractional-order derivative provides more information about the complexity of the dynamics of the proposed HBV model.