Global Analysis for an HIV Infection Model with CTL Immune Response and Infected Cells in Eclipse Phase

Karam Allali,Jaouad Danane,Yang Kuang

doi:10.3390/app7080861

Karam Allali, Jaouad Danane + Show 1 more

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https://doi.org/10.3390/app7080861

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Abstract

A modified mathematical model describing the human immunodeficiency virus (HIV) pathogenesis with cytotoxic T-lymphocytes (CTL) and infected cells in eclipse phase is presented and studied in this paper. The model under consideration also includes a saturated rate describing viral infection. First, the positivity and boundedness of solutions for nonnegative initial data are proved. Next, the global stability of the disease free steady state and the endemic steady states are established depending on the basic reproduction number R 0 and the CTL immune response reproduction number R C T L . Moreover, numerical simulations are performed in order to show the numerical stability for each steady state and to support our theoretical findings. Our model based findings suggest that system immunity represented by CTL may control viral replication and reduce the infection.

Highlights

Human immunodeficiency virus (HIV) is known as a pathogen causing the acquired immunodeficiency syndrome (AIDS), which is the end-stage of the infection
It is well known that the cellular immune responses play an indispensable role during the HIV viral infection, especially in people known as elite controllers who are infected by HIV but maintain a normal CD4 count for many years and remain asymptomatic or have a very delayed disease progression over the course of their HIV infection [3,4]
We extend their work by incorporating the cytotoxic T lymphocytes (CTL) immune response

Summary

Introduction

Human immunodeficiency virus (HIV) is known as a pathogen causing the acquired immunodeficiency syndrome (AIDS), which is the end-stage of the infection. It is well known that the cellular immune responses play an indispensable role during the HIV viral infection, especially in people known as elite controllers who are infected by HIV but maintain a normal CD4 count for many years and remain asymptomatic or have a very delayed disease progression over the course of their HIV infection [3,4]. The basic viral infection model with CTLs immune was first studied in [5] and its global stability was studied in [6,7]. In [12], the authors consider the interaction between CTL, viruses and macrophages and study the global stability in a model with a mass action infection term

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