Fractional Dynamics of HIV with Source Term for the Supply of New CD4+ T-Cells Depending on the Viral Load via Caputo–Fabrizio Derivative

Zahir Shah,Meshal Shutaywi,Poom Kumam,Rashid Jan,Wejdan Deebani

doi:10.3390/molecules26061806

Abstract

Human immunodeficiency virus (HIV) is a life life-threatening and serious infection caused by a virus that attacks T-cells, which fight against infections and make a person susceptible to other diseases. It is a global public health problem with no cure; therefore, it is highly important to study and understand the intricate phenomena of HIV. In this article, we focus on the numerical study of the path-tracking damped oscillatory behavior of a model for the HIV infection of T-cells. We formulate fractional dynamics of HIV with a source term for the supply of new CD4+ T-cells depending on the viral load via the Caputo–Fabrizio derivative. In the formulation of fractional HIV dynamics, we replaced the constant source term for the supply of new T-cells from the thymus with a variable source term depending on the concentration of the viral load, and introduced a term that describes the incidence of the HIV infection of T-cells. We present a novel numerical scheme for fractional view analysis of the proposed model to highlight the solution pathway of HIV. We inspect the periodic and chaotic behavior of HIV for the given values of input factors using numerical simulations.

Highlights

Mathematical biology has a wide range of applications in genetics, environmental sciences, population dynamics, medical sciences, etc
Motivated by the above accurate results of the fractional derivative, we opt to explore the fractional dynamics of human immunodeficiency virus (HIV) with a source term for the supply of new CD4+ T-cells depending on the viral load using the Caputo–Fabrizio derivative
We formulated the fractional dynamics of HIV with a source term for the supply of article, new CD4+

Summary

Introduction

Mathematical biology has a wide range of applications in genetics, environmental sciences, population dynamics, medical sciences, etc. The Caputo–Fabrizio operator possess an exponential decay law kernel which produce more accurate results for natural phenomena This new developed fractional operator contains stronger properties as compared to the other fractional operators. We opt to investigate the dynamical behavior of HIV in the framework of the fractional derivative under the Caputo–Fabrizio operator to capture more accurate and more reliable information about the infection. Motivated by the above accurate results of the fractional derivative, we opt to explore the fractional dynamics of HIV with a source term for the supply of new CD4+ T-cells depending on the viral load using the Caputo–Fabrizio derivative. A fractional model is formulated for HIV with a source term for the supply of new CD4+ T-cells depending on the viral load in the framework of Caputo–Fabrizio derivative. Concluding remarks and suggestions are presented in last section

Structure of HIV Dynamics

Fractional Dynamics of HIV Infection

Novel Numerical Scheme for Fractional Model

Illustration of of thethe portrait healthy model

Illustration of the portrait healthy CD4 verses infected

Conclusions