Numerical technique based on the interpolation with Lagrange polynomials to analyze the fractional variable-order mathematical model of the hepatitis C with different types of virus genome

Abstract

The basic objective of this work is to present and study an effective and cost-efficient numerical technique for analyzing the fractional variable order mathematical model for hepatitis C having various types of the virus genome. Here, we give this model via the most commonly used non-singular Caputo–Fabrizio fractional derivative (CF) depending upon the exponential-kernel. The Hepatitis C virus (HCV) is an RNA virus that is single-stranded. The HCV genomes show substantial variability in sequence and are categorized into both types and subtypes. Those types in the range from 1 to 11 are recognized so far (every kind with a specific number of sub-kinds). It is reported that around 90% of the isolated HCV infections occurring in Egypt goes into only a single subtype (4a). The numerical methodology proposed is established on the fractional calculus basic theorem with the interpolation of the Lagrange polynomial. The effectiveness of the proposed procedure are satisfied. The findings indicate that the technique considered is a simple and successful method for investigating the solution of such models. The 4th-order Runge–Kutta method (RK4), is utilized to compare the numerical solutions and show the excellent agreement that has been found out via applying the CFC-derivatives. The obtained solutions of the suggested model illustrate the simple usage and the effectiveness of the presented method and are in agreement with the characteristics of the virus.