Mathematical Analysis and Clinical Implications of an HIV Model with Adaptive Immunity.

Jaouad Danane,Karam Allali

doi:10.1155/2019/7673212

Abstract

In this paper, a mathematical model describing the human immunodeficiency virus (HIV) pathogenesis with adaptive immune response is presented and studied. The mathematical model includes six nonlinear differential equations describing the interaction between the uninfected cells, the exposed cells, the actively infected cells, the free viruses, and the adaptive immune response. The considered adaptive immunity will be represented by cytotoxic T-lymphocytes cells (CTLs) and antibodies. First, the global stability of the disease-free steady state and the endemic steady states is established depending on the basic reproduction number R0, the CTL immune response reproduction number R1z, the antibody immune response reproduction number R1w, the antibody immune competition reproduction number R2w, and the CTL immune response competition reproduction number R3z. On the other hand, different numerical simulations are performed in order to confirm numerically the stability for each steady state. Moreover, a comparison with some clinical data is conducted and analyzed. Finally, a sensitivity analysis for R0 is performed in order to check the impact of different input parameters.

Highlights

CTLs expand in response to viral antigen derived from infected cells at a rate cyz and decay in the absence of antigenic stimulation at a rate bz
Rz1 represents the mean of CTL immune cells activated by an infected cell when the viral infection is successful in the absence of the antibody immune response. e second endemic equilibrium is
We have presented and studied a mathematical model describing human immunodeficiency virus (HIV) viral infection with saturated rate in the presence of the adaptive immune response. is adaptive immunity is represented by CTL immune response and antibodies

Summary

Introduction

CTLs expand in response to viral antigen derived from infected cells at a rate cyz and decay in the absence of antigenic stimulation at a rate bz. Rw1 represents the average number of the antibodies activated by virus when the viral infection is successful in the absence of CTL immune response. Rz1 represents the mean of CTL immune cells activated by an infected cell when the viral infection is successful in the absence of the antibody immune response.

Results

Conclusion