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Remarks about spatially structured SI model systems with cross diffusion

hal.structure.identifierUniversidad del Bio Bio [Concepción] [UBB]
dc.contributor.authorANAYA, Veronica
hal.structure.identifierModélisation et calculs pour l'électrophysiologie cardiaque [CARMEN]
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorBENDAHMANE, Mostafa
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorLANGLAIS, Michel
hal.structure.identifierDepartamento de Ingeniería Matemática [Santiago] [DIM]
dc.contributor.authorSEPULVEDA, Mauricio
dc.contributor.editorB. N. Chetverushki
dc.contributor.editorW. Fitzgibbon
dc.contributor.editorY.A. Kuznetsov
dc.contributor.editorP. Neittaanmäki
dc.contributor.editorJ. Periaux
dc.contributor.editorO. Pironneau
dc.date.accessioned2024-04-04T03:00:57Z
dc.date.available2024-04-04T03:00:57Z
dc.date.created2019
dc.date.issued2019
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/192858
dc.description.abstractEnOne of the simplest deterministic mathematical model for the spread of an epidemic disease is the so-called SI system made of two Ordinary Differential Equations. It exhibits simple dynamics: a bifurcation parameter T0 yielding persistence of the disease when T0>1, else extinction occurs. A natural question is whether this gentle dynamic can be disturbed by spatial diffusion. It is straightforward to check it is not feasible for linear/nonlinear diffusions. When cross diffusion is introduced for suitable choices of the parameter data set this persistent state of the ODE model system becomes linearly unstable for the resulting initial and no-flux boundary value problem. On the other hand “natural” weak solutions can be defined for this initial and no-flux boundary value problem and proved to exist provided nonlinear and cross diffusivities satisfy some constraints. These constraints are not fully met for the parameter data set yielding instability. A remaining open question is: to which solutions does this apply? Periodic behaviors are observed for a suitable range of cross diffusivities.
dc.language.isoen
dc.publisherSpringer
dc.source.titleContributions to Partial Differential Equations and Applications
dc.title.enRemarks about spatially structured SI model systems with cross diffusion
dc.typeChapitre d'ouvrage
dc.identifier.doi10.1007/978-3-319-78325-3_5
dc.subject.halMathématiques [math]
dc.subject.halMathématiques [math]/Analyse numérique [math.NA]
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
dc.subject.halMathématiques [math]/Combinatoire [math.CO]
dc.subject.halSciences du Vivant [q-bio]
bordeaux.page21
bordeaux.volume47
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.title.proceedingContributions to Partial Differential Equations and Applications
hal.identifierhal-02142018
hal.version1
hal.popularoui
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-02142018v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.btitle=Contributions%20to%20Partial%20Differential%20Equations%20and%20Applications&rft.date=2019&rft.volume=47&rft.spage=21&rft.epage=21&rft.au=ANAYA,%20Veronica&BENDAHMANE,%20Mostafa&LANGLAIS,%20Michel&SEPULVEDA,%20Mauricio&rft.genre=unknown


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