Analysis of the model of HIV-1 infection of CD4^{+} T-cell with a new approach of fractional derivative

Shahram Rezapour,Hakimeh Mohammadi,Dumitru Baleanu

doi:10.1186/s13662-020-02544-w

Abstract

By using the fractional Caputo–Fabrizio derivative, we investigate a new version for the mathematical model of HIV. In this way, we review the existence and uniqueness of the solution for the model by using fixed point theory. We solve the equation by a combination of the Laplace transform and homotopy analysis method. Finally, we provide some numerical analytics and comparisons of the results.

Highlights

The HIV infection target is CD4+ T cells which are the largest white blood cells of the immune system [1, 2]
6 Numerical results we present a numerical simulation of the results of the HIV-1 infection Tcells system (3)
7 Conclusion In this work, we extend the model of HIV-1 infection of CD4+ T-cell to the concept of Caputo–Fabrizio fractional derivative

Summary

Introduction

The HIV infection target is CD4+ T cells which are the largest white blood cells of the immune system [1, 2]. We use the Caputo and Fabrizio fractional derivative [14] to express the model of HIV and solve the equations by a method that combines the homotopy and Laplace transforms [14, 40,41,42]. The Caputo fractional derivative of order ν for a function f via integrable differentiations is defined by Let b > a, f ∈ H1(a, b), and ν ∈ (0, 1), the Caputo–Fabrizio derivative of order ν for a function f is defined by

Results

Conclusion