Hopf bifurcation in a HIV model with a quadratic logistic growth term
Résumé
We consider a model of disease dynamics in the modeling of Human Immunodeficiency Virus (HIV). This model consists of three ODEs for the concentrations of the target T cells, the infected cells and the virus particles. There are two bifurcation parameters, $N$, the total number of virions produced by one infected cell, and $r$, the logistic parameter which controls the growth rate. This paper focuses on the stability of the uninfected and infected steady state. We identify two domains, $\mathscr U$ and $\mathscr I$, where the uninfected equilibrium is respectively asymptotically stable and unstable. The infected equilibrium is asymptotically stable in $\mathscr I$, except in a region $\mathscr P$ where we prove its instability. Hopf bifurcations occur at the interface. Numerical results are presented.
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