Discrete-Time System of an Intracellular Delayed HIV Model with CTL Immune Response

TL;DR

This paper develops a discrete-time HIV model with CTL immune response and intracellular delay, analyzing its stability and confirming results through numerical simulations.

Contribution

It introduces a novel discrete-time version of a continuous HIV-CTL model with delay, and proves its global stability properties.

Findings

Global stability of disease-free equilibrium

Stability of endemic equilibrium points

Numerical simulations confirm theoretical results

Abstract

In [Math. Comput. Sci. 12 (2018), no. 2, 111--127], a delayed model describing the dynamics of the Human Immunodeficiency Virus (HIV) with Cytotoxic T Lymphocytes (CTL) immune response is investigated by Allali, Harroudi and Torres. Here, we propose a discrete-time version of that model, which includes four nonlinear difference equations describing the evolution of uninfected, infected, free HIV viruses, and CTL immune response cells and includes intracellular delay. Using suitable Lyapunov functions, we prove the global stability of the disease free equilibrium point and of the two endemic equilibrium points. We finalize by making some simulations and showing, numerically, the consistence of the obtained theoretical results.