Convergence to a pulsating travelling wave for an epidemic reaction-diffusion system with non-diffusive susceptible population
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | DUCROT, Arnaud | |
| dc.contributor.author | GILETTI, Thomas | |
| dc.date.accessioned | 2024-04-04T02:40:38Z | |
| dc.date.available | 2024-04-04T02:40:38Z | |
| dc.date.issued | 2014-09 | |
| dc.identifier.issn | 0303-6812 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191078 | |
| dc.description.abstractEn | In this work we study the asymptotic behaviour of the Kermack-McKendrick reaction-diffusion system in a periodic environment with nondiffusivesusceptible population. This problem was proposed by Kallenet al. as a model for the spatial spread for epidemics, where it can bereasonable to assume that the susceptible population is motionless. Forarbitrary dimensional space we prove that large classes of solutions of sucha system have an asymptotic spreading speed in large time, and that theinfected population has some pulse-like asymptotic shape. The analysis ofthe one-dimensional problem is more developed, as we are able to uncovera much more accurate description of the profile of solutions. Indeed, wewill see that, for some initially compactly supported infected population,the profile of the solution converges to some pulsating travelling wavewith minimal speed, that is to some entire solution moving at a constantpositive speed and whose profile’s shape is periodic in time. | |
| dc.language.iso | en | |
| dc.publisher | Springer | |
| dc.title.en | Convergence to a pulsating travelling wave for an epidemic reaction-diffusion system with non-diffusive susceptible population | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1007/s00285-013-0713-3 | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| bordeaux.journal | Journal of Mathematical Biology | |
| bordeaux.page | 533-552 | |
| bordeaux.volume | 69 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 3 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-03162052 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-03162052v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20Mathematical%20Biology&rft.date=2014-09&rft.volume=69&rft.issue=3&rft.spage=533-552&rft.epage=533-552&rft.eissn=0303-6812&rft.issn=0303-6812&rft.au=DUCROT,%20Arnaud&GILETTI,%20Thomas&rft.genre=article |
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