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| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | BRAUNER, Claude-Michel | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | JOLLY, Danaelle | |
| hal.structure.identifier | Dipartimento di Matematica | |
| dc.contributor.author | LORENZI, Luca | |
| hal.structure.identifier | Equipe de Biostatistique | |
| dc.contributor.author | THIÉBAUT, Rodolphe | |
| dc.date.accessioned | 2024-04-04T02:39:53Z | |
| dc.date.available | 2024-04-04T02:39:53Z | |
| dc.date.created | 2009-05-12 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191015 | |
| dc.description.abstractEn | We consider the basic model of virus dynamics in the modeling of Human Immunodeficiency Virus (HIV), in a $2D$ heterogenous environment. It consists of two ODEs for the non-infected and infected $CD_4^+$ $T$ lymphocytes, $T$ and $I$, and a parabolic PDE for the virus $V$. We define a new parameter $\lambda_0$ as an eigenvalue of some Sturm-Liouville problem, which takes the heterogenous reproductive ratio into account. For $\lambda_0<0$ the trivial non-infected solution is the only equilibrium. When $\lambda_0>0$, the former becomes unstable whereas there is only one positive infected equilibrium. Considering the model as a dynamical system, we prove the existence of a universal attractor. Finally, in the case of an alternating structure of viral sources, we define a homogenized limiting environment. The latter justifies the classical approach via ODE systems. | |
| dc.language.iso | en | |
| dc.subject.en | Mathematical models | |
| dc.subject.en | HIV-host interaction | |
| dc.subject.en | Diffusion | |
| dc.subject.en | Equilibrium solutions | |
| dc.subject.en | Stability | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Systèmes dynamiques [math.DS] | |
| dc.identifier.arxiv | 0905.2023 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-00383320 | |
| hal.version | 1 | |
| hal.audience | Non spécifiée | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00383320v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=BRAUNER,%20Claude-Michel&JOLLY,%20Danaelle&LORENZI,%20Luca&THI%C3%89BAUT,%20Rodolphe&rft.genre=preprint |
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