Mathematical analysis of a HIV model with quadratic logistic growth term
| hal.structure.identifier | School of Mathematical Sciences | |
| dc.contributor.author | FAN, Xinyue | |
| hal.structure.identifier | School of Mathematical Sciences | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | BRAUNER, Claude-Michel | |
| hal.structure.identifier | Epidémiologie et Biostatistique [Bordeaux] | |
| dc.contributor.author | WITTKOP, Linda | |
| dc.date.accessioned | 2024-04-04T02:25:08Z | |
| dc.date.available | 2024-04-04T02:25:08Z | |
| dc.date.created | 2010-11-16 | |
| dc.date.issued | 2012-10 | |
| dc.identifier.issn | 1531-3492 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189862 | |
| dc.description.abstractEn | We consider a model of disease dynamics in the modeling of Human Immunodeficiency Virus (HIV). The system consists of three ODEs for the concentrations of the target T cells, the infected cells and the virus particles. There are two main parameters, $N$, the total number of virions produced by one infected cell, and $r$, the logistic parameter which controls the growth rate. The equilibria corresponding to the infected state are asymptotically stable in a region $(\mathcal I)$, but unstable in a region $(\mathcal P)$. In the unstable region, the levels of the various cell types and virus particles oscillate, rather than converging to steady values. Hopf bifurcations occurring at the interfaces are fully investigated via several techniques including asymptotic analysis. The Hopf points are connected through a ''snake" of periodic orbits. Numerical results are presented. | |
| dc.language.iso | en | |
| dc.publisher | American Institute of Mathematical Sciences | |
| dc.subject.en | HIV modeling | |
| dc.subject.en | stability | |
| dc.subject.en | Hopf bifurcation | |
| dc.subject.en | orbits | |
| dc.subject.en | snakes | |
| dc.title.en | Mathematical analysis of a HIV model with quadratic logistic growth term | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.3934/dcdsb.2012.17.2359 | |
| dc.subject.hal | Mathématiques [math]/Systèmes dynamiques [math.DS] | |
| dc.subject.hal | Sciences du Vivant [q-bio] | |
| bordeaux.journal | Discrete and Continuous Dynamical Systems - Series B | |
| bordeaux.page | 27 | |
| bordeaux.volume | 17 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 7 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00537467 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Non spécifiée | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00537467v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Discrete%20and%20Continuous%20Dynamical%20Systems%20-%20Series%20B&rft.date=2012-10&rft.volume=17&rft.issue=7&rft.spage=27&rft.epage=27&rft.eissn=1531-3492&rft.issn=1531-3492&rft.au=FAN,%20Xinyue&BRAUNER,%20Claude-Michel&WITTKOP,%20Linda&rft.genre=article |
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