Fractal-fractional study of the hepatitis C virus infection model

Abstract

The main purpose of this article is proposed and investigated a new model of fractal-fractional-order model for hepatitis C virus (HCV) infection with immune response, in which the effect of dendritic cells (DC) and cytotoxic T lymphocytes (CTL) on HCV infection is considered. Fractal-Fractional new model is studied by replacing the classic derivative by fractal-fractional derivatives based on Caputo-Fabrizio (CF). By employing the basic theory of fractional calculus, and the Lagrange polynomial interpolation (LGPI) (the Newton polynomial interpolation (NPI)), we can construct an algorithm, through which we obtain the numerical solutions for the new model. We compare the numerical solutions obtained with help of LGPI and NPI with the numerical solutions using finite differences method (FDM). Also, the comparison between the numerical solutions based on LGPI and NPI is presented. We calculated the absolute error of these solutions, the results are very accurate, and the order of the error decreases as we increase the number of the iterations. The chaos of the numerical solutions for the fractal-fractional-order model are obtained for different values of parameters and represented graphically.