Heterogeneous Viral Environment in a HIV Spatial Model
| dc.creator | Brauner, Claude-Michel | |
| dc.creator | Jolly, Danaelle | |
| dc.creator | Lorenzi, Luca | |
| dc.creator | Thiebaut, Rodolphe | |
| dc.date | 2009-05-13 | |
| dc.date.accessioned | 2026-07-07T13:14:26Z | |
| dc.date.available | 2026-07-07T13:14:26Z | |
| dc.description | 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 $λ_0$ as an eigenvalue of some Sturm-Liouville problem, which takes the heterogenous reproductive ratio into account. For $λ_0<0$ the trivial non-infected solution is the only equilibrium. When $λ_0>0$, 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.identifier | https://arxiv.org/abs/0905.2023 | |
| dc.identifier | http://arxiv.org/abs/0905.2023 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/230209 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 35K55 | |
| dc.title | Heterogeneous Viral Environment in a HIV Spatial Model | |
| dc.type | text |