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

Claude-Michel Brauner; Xinyue Fan; Luca Lorenzi

doi:10.3934/cpaa.2013.12.1813

Article Contents

2013, Volume 12, Issue 5: 1813-1844. Doi: 10.3934/cpaa.2013.12.1813

This issue Previous Article Next Article An infinite dimensional bifurcation problem with application to a class of functional differential equations of neutral type

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

1.
School of Mathematical Sciences, Xiamen University, 361005 Xiamen, China, and Institut de Mathématiques de Bordeaux, Université de Bordeaux, 33405 Talence cedex
2.
College of Science, Guizhou University, 550025 Guiyang
3.
Dipartimento di Matematica e Informatica, Università degli Studi di Parma, Parco Area delle Scienze 53/A, 43124 Parma

Received: June 30, 2012

Revised: October 31, 2012

Published: August 2013

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Abstract

We consider a Human Immunodeciency Virus (HIV) model with a logistic growth term and continue the analysis of the previous article [6]. We now take the viral diusion 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.

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Mathematics Subject Classification: Primary: 35K55; Secondary: 35B35, 92C50.

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