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

Claude-Michel Brauner (1, 2) , Xinyue Fan (2) , Luca Lorenzi (3)

1 IMB - Institut de Mathématiques de Bordeaux
2 School of Mathematical Sciences
3 Dipartimento di Matematica

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.

Mots clés: HIV; stability; Hopf bifurcation; analytic semigroups; center manifold

Domaines: Equations aux dérivées partielles [math.AP]; Sciences du Vivant [q-bio]

Claude-Michel Brauner, Xinyue Fan, Luca Lorenzi. Two-dimensional stability analysis in a HIV model with quadratic logistic growth term. Communications on Pure and Applied Analysis, 2013, 12 (5), pp.32. ⟨10.3934/cpaa.2013.12.1813⟩. ⟨hal-01261114⟩