Fractional modeling dynamics of HIV and CD4+ T-cells during primary infection

Aam Arafa,M Khalil,Sz Rida

doi:10.1186/1753-4631-6-1

Abstract

In this paper, we introduce fractional-order into a model of HIV-1 infection of CD4+ T cells. We study the effect of the changing the average number of viral particles N with different sets of initial conditions on the dynamics of the presented model. Generalized Euler method (GEM) will be used to find a numerical solution of the HIV-1 infection fractional order model.

Highlights

At the present time there are several countries, in Africa, with up to 35% of their populations between the ages of 15 and 50 years infected by human immunodeficiency virus (HIV) [1]
Mathematical models have been proven valuable in understanding the dynamics of HIV infection [4,5,6]
This model has been important in the field of mathematical modeling of HIV infection, and many other models have been proposed, which take this model as their inspiration

Summary

Introduction

At the present time there are several countries, in Africa, with up to 35% of their populations between the ages of 15 and 50 years infected by human immunodeficiency virus (HIV) [1]. A more complete model of human immunodeficiency virus type 1 (HIV-1) dynamics considers in addition to the uninfected and infected CD4+ T -cells, x and y respectively, the number of virions in plasma, z. In [11], the authors modified the ODE model proposed by Culshaw and Ruan into a system of fractional-order [12] They showed that the model established in this paper possesses non-negative solutions, as desired in any population dynamics. They obtained a restriction on the number of viral particles released per infectious cell, in order for infection to be sustained. One of the basic reasons of using fractional order differential equations is that “Fractional order differential equations are, at least, as stable as their integer order counterpart.”

Fractional-order model derivation

Numerical results

Findings

Conclusion