Threshold dynamics and threshold analysis of HIV infection model with treatment

Zhimin Chen,Liling Zeng,Xiuxiang Liu

doi:10.1186/s13662-020-03057-2

Abstract

In this paper, a human immunodeficiency virus (HIV) infection model that includes a protease inhibitor (PI), two intracellular delays, and a general incidence function is derived from biologically natural assumptions. The global dynamical behavior of the model in terms of the basic reproduction number mathcal{R}_{0} is investigated by the methods of Lyapunov functional and limiting system. The infection-free equilibrium is globally asymptotically stable if mathcal{R}_{0}leq 1. If mathcal{R}_{0}>1, then the positive equilibrium is globally asymptotically stable. Finally, numerical simulations are performed to illustrate the main results and to analyze thre effects of time delays and the efficacy of the PI on mathcal{R}_{0}.

Highlights

Human immunodeficiency virus (HIV) is one of the most dangerous viruses that continues to be a major contributor to the global burden of disease [13]
We have carried out complete analysis for a delayed HIV infection model with a protease inhibitor (PI) mono-therapy and a general incidence function, system (1.2)
The numerical simulation results demonstrate that the value of the basic reproductive number R0 is dominated by the efficacy of the PI drug and is very weakly dependent on the intracellular delays

Summary

Introduction

Human immunodeficiency virus (HIV) is one of the most dangerous viruses that continues to be a major contributor to the global burden of disease [13]. Culshaw and Ruan [3] developed a delay-differential equation model of HIV infection of CD4+ T-cells with discrete intracellular delay and bilinear incidence rate and investigated the effect of the time delay on local stability of the endemically infected equilibrium. Nelson and Perelson [19] generalized the basic ordinary differential model of HIV-1 infection with a PI by allowing the intracellular delay that varied according to a probability distribution and obtained the local stability results of two steady states. A PI mono-therapy is considered; the PI is assumed to have variable efficacy and the drug is less than completely efficacious, i.e., p ∈ (0, 1); the T cells are allowed to vary; the function f (T(t), VI(t)) under some prescribed condition indicates the rate of uninfected target cells becoming infected by the infectious HIV viral particles.

Global threshold dynamics

Simulation of the basic results

Conclusions