 |
 |
 |
|
|
|
| HAL: hal-00537467, version 1 |
| Detailed view |  Export this paper |
 |
| Available versions: | v1 (2010-11-19) | v2 (2012-05-27) |
|
|
|
|
| Hopf bifurcation in a HIV model with a quadratic logistic growth term |
|
|
Xinyue Fan 1Claude-Michel Brauner 1, 2 |
|
|
| (2010-11-16) |
|
|
|
| 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. |
|
|
|
|
|
|
|
|
|
|
|
| 1: | School of Mathematical Sciences |
|
|
|
Xiamen University |
|
|
| 2: | Institut de Mathématiques de Bordeaux (IMB) |
|
|
|
CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II |
|
|
|
|
|
|
|
|
|
| Subject | : | Mathematics/Analysis of PDEs Mathematics/Classical Analysis and ODEs |
|
|
| Stability – Hopf bifurcation – HIV modeling |
|
|
|
| Attached file list to this document: | |||||
|
|||||
|
|
|
| hal-00537467, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00537467 | |
| oai:hal.archives-ouvertes.fr:hal-00537467 | |
| From: Claude-Michel Brauner | |
| Submitted on: Thursday, 18 November 2010 21:50:56 | |
| Updated on: Friday, 19 November 2010 08:34:08 | |
