Mathematical analysis of delayed HIV-1 infection model for the competition of two viruses

Nigar Ali,Muhammad Ikhlaq Chohan,Gul Zaman,Brian Ingalls

doi:10.1080/23311835.2017.1332821

Nigar Ali, Muhammad Ikhlaq Chohan + Show 2 more

Open Access

https://doi.org/10.1080/23311835.2017.1332821

Copy DOI

Abstract

In this research article, a new mathematical delayed human immunodeficiency virus (HIV-1) infection model with two constant intracellular delays, is investigated. The analysis of the model is thoroughly discussed by the basic reproduction numbers R0 and Rs. For R0<1, the infection-free equilibrium (E0) is shown to be locally as well as globally stable. Similarly, the single-infection equilibrium (Es) is proved to be locally as well as globally asymptotically stable if 1<R0<Rs. Our derived results show that the incorporation of even small intracellular time delay can control the spread of HIV-1 infection and can better the quality of the life of the patient. Finally, numerical simulations are used to illustrate the derived theoretical results.

Highlights

Human immunodeficiency virus (HIV-1) is a lentivirus that causes acquired immunodeficiency syndrome (AIDS)
We discuss some numerical results and simulations by using dde23 from the software MATLAB R2010a. These results show that delays play an important role in determining the dynamic behavior of the HIV-1 modeling
It has been shown that our proposed model with delay has three equilibrium solutions: the disease-free equilibrium E0, single-infection equilibrium Es, Figure 3

Summary

Introduction

Human immunodeficiency virus (HIV-1) is a lentivirus that causes acquired immunodeficiency syndrome (AIDS). HIV attacks CD4 cells and weakens the immune system. This infection passes though three different phases: the primary infection, the chronic infection and AIDS is the last stage of HIV-1 infection. To control this infection, many scientists and researchers have been focusing on it but in spite of this, there is no effective way to cure AIDS. Recombinant virus is used for controlling the infection of HIV-1 (see for example, Nolan, 1997; Wagner & Hewlett, 1999). Recombinant virus is used for controlling the infection of HIV-1 (see for example, Nolan, 1997; Wagner & Hewlett, 1999). Revilla and Garcya-Ramos (2003) established a five-dimensional ordinary differential equation system to

PUBLIC INTEREST STATEMENT

The modula of the above equation result in

Proof Let us consider the following Lyapunov functional

Proof Let us construct the Lyapunove functional

Infected cells

Pathogen virus