Two-dimensional stability analysis in a HIV model with quadratic logistic growth term

TL;DR

This paper analyzes the stability of HIV infection models with quadratic logistic growth in a two-dimensional setting, incorporating viral diffusion and exploring bifurcations and periodic solutions.

Contribution

It extends previous models by including two-dimensional viral diffusion and studies stability, bifurcations, and periodic solutions in this context.

Findings

Stability conditions for uninfected and infected equilibria

Identification of Hopf bifurcation points

Existence of stable periodic solutions

Abstract

We consider a Human Immunodeficiency Virus (HIV) model with a logistic growth term and continue the analysis of the previous article [6]. We now take the viral diffusion in a two-dimensional environment. The model consists of two ODEs for the concentrations of the target T cells, the infected cells, and a parabolic PDE for the virus particles. We study the stability of the uninfected and infected equilibria, the occurrence of Hopf bifurcation and the stability of the periodic solutions.