Large graph limit for an SIR process in random network with heterogeneous connectivity

Laurent Decreusefond; Jean-Stephane Dhersin; Pascal Moyal; Viet Chi Tran

Large graph limit for an SIR process in random network with heterogeneous connectivity

Laurent Decreusefond ^{1, 2} Jean-Stephane Dhersin ³ Pascal Moyal ⁴ Viet Chi Tran ^{5, 6, *}

* Auteur correspondant

1 LTCI - Laboratoire Traitement et Communication de l'Information

2 Télécom ParisTech

3 LAGA - Laboratoire Analyse, Géométrie et Applications

4 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

5 LPP - Laboratoire Paul Painlevé - UMR 8524

6 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

Abstract : 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).

Keywords : large network limit. SIR model mathematical model for epidemiology measure-valued process large network limit Configuration Model graph

Type de document :

Article dans une revue

Domaine :

Mathématiques [math] / Probabilités [math.PR]

Sciences du Vivant [q-bio] / Santé publique et épidémiologie

Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-00505167
Contributeur : Viet Chi Tran <>
Soumis le : samedi 25 juin 2011 - 21:52:27
Dernière modification le : mercredi 27 mars 2019 - 16:08:30
Document(s) archivé(s) le : vendredi 30 septembre 2011 - 11:10:29

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