A fractional order model for Hepatitis B virus with treatment via Atangana-Baleanu derivative

Hepatitis B infection is a serious public health issue worldwide and can be controlled through proper treatment. Mathematical models can be effectively used to explore the effect of different treatment strategies on hepatitis B patients. In this paper, we illustrate a new epidemic fractional order model of the hepatitis B virus with treatment case via Atangana-Baleanu derivative in Caputo sense. In the beginning, we investigate the non-negativity and uniqueness of the model solution. Then, we evaluate the basic reproduction number and equilibria of the model. Further, an iterative scheme is applied to calculate solution of the proposed model. Finally, to show the influence of fractional order and model parameters, we present a detail numerical simulations for different values of fractional order "gamma". The results show the importance and convincing behavior of the fractional order "gamma" and ensure that by including the memory effects in the model seems very appropriate for such an investigation. (C) 2019 Elsevier B.V. All rights reserved.