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

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 CTL . 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.

Global stability analysis of a delayed HIV model with saturated infection rate

“…The HIV dynamics involving three densities of the uninfected cells, the infected cells and the HIV virus have been widely studied in different mathematical models [2][3][4][5][6]. In this work, we propose a modified viral dynamics model, using a saturated incidence function with two delays in the generation of infected cells and in the production of viruses.…”

“…With 36.7 million people living with HIV, 2.1 million people becoming newly infected by HIV and more than 1.1 million deaths annually, HIV becomes a major global public health issue [1]. For this reason, several mathematical models describing the dynamics of HIV infection have been developed and studied [2][3][4][5][6]. The basic of them was suggested in [2]:…”

Analysis and optimal control of an HIV model with logistic growth and infected cells in eclipse phase

“…Currently, there exist two main kinds of antiretroviral drugs; Reverse Transcriptase Inhibitors (RTIs) and Protease Inhibitors (PIs) [5]. Many mathematical models have proved their usefulness for describing and understanding the dynamics of HIV infection 1074 SANAA HARRO UDI, JAOUAD DANANE, AND KARAM ALLALI [6,5,7,8,9,10,11,12]. The basic of them was suggested in [6]: 8 > < > :…”

Optimal control of an HIV model with CTL cells and latently infected cells

“…Based on these alarming statistics, HIV becomes a major global public health issue. Hence, mathematical modeling of human immunodeficiency virus (HIV) infection is one of the great current interest [2,4,7,8,[14][15][16][17]20,21,23]. The basic viral infection model with four dynamics components including the uninfected cells, the infected cells, the free viruses and the cytotoxic T-lymphocytes (CTL) immune response was first studied in [14].…”

“…However, upon the virus entry to the uninfected cell, there exists a latent period after that the cell becomes infected. In a recent work, the model describing HIV viral dynamics taking into account this fifth compartment representing the infected cells in latent stage is formulated and studied in [2]. The authors study the global stability of the endemic states and illustrate the numerical simulations in order to show the numerical stability for each problem steady state.…”