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| HAL : hal-00505167, version 3 |
| arXiv : 1007.3958 |
| DOI : 10.1214/11-AAP773 |
| Fiche détaillée |  Récupérer au format |
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| Annals of Applied Probability 22, 2 (2012) 541-575 |
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| Versions disponibles : | v1 (22-07-2010) | v2 (05-02-2011) | v3 (26-06-2011) |
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| Large graph limit for an SIR process in random network with heterogeneous connectivity |
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| Laurent Decreusefond 1, 2Jean-Stephane Dhersin 3, 4 |
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| (2012) |
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| We consider an SIR epidemic model propagating on a Configuration Model network, where the degree distribution of the vertices is given and where the edges are randomly matched. The evolution of the epidemic is summed up into three measure-valued equations that describe the degrees of the susceptible individuals and the number of edges from an infectious or removed individual to the set of susceptibles. These three degree distributions are sufficient to describe the course of the disease. The limit in large population is investigated. As a corollary, this provides a rigorous proof of the equations obtained by Volz (2008). |
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| 1 : | Laboratoire Traitement et Communication de l'Information [Paris] (LTCI) |
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Télécom ParisTech – CNRS : UMR5141 |
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| 2 : | Institut Télécom - Télécom ParisTech |
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Télécom ParisTech |
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| 3 : | Institut Galilée (IG) |
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Université Paris XIII - Paris Nord |
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| 4 : | Laboratoire Analyse, Géométrie et Application (LAGA) |
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CNRS : UMR7539 – Université Paris XIII - Paris Nord – Université Paris VIII - Vincennes Saint-Denis |
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| 5 : | CEntre de REcherches en MAthématiques de la DEcision (CEREMADE) |
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CNRS : UMR7534 – Université Paris IX - Paris Dauphine |
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| 6 : | Laboratoire Paul Painlevé (LPP) |
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CNRS : UMR8524 – Université Lille I - Sciences et technologies |
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| 7 : | Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP) |
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Polytechnique - X – CNRS : UMR7641 |
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| Domaine | : | Mathématiques/Probabilités Sciences du Vivant/Santé publique et épidémiologie |
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| Configuration Model graph – SIR model – mathematical model for epidemiology – measure-valued process – large network limit. |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00505167, version 3 | |
| http://hal.archives-ouvertes.fr/hal-00505167 | |
| oai:hal.archives-ouvertes.fr:hal-00505167 | |
| Contributeur : Viet Chi Tran | |
| Soumis le : Samedi 25 Juin 2011, 21:52:27 | |
| Dernière modification le : Mercredi 18 Avril 2012, 19:29:39 | |
