1. Large graph limit for an SIR process in random network with heterogeneous connectivity
- Author
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Jean-Stéphane Dhersin, Pascal Moyal, Viet Chi Tran, Laurent Decreusefond, Laboratoire Traitement et Communication de l'Information (LTCI), Télécom ParisTech-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS), Télécom ParisTech, Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Université Paris 13 (UP13)-Institut Galilée-Centre National de la Recherche Scientifique (CNRS), CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS), Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), Chaire Modélisation Mathématique de la Biodiversité of Veolia Environnement-Ecole Polytechnique-Museum National d'Histoire Naturelle-Fondation X, ANR-08-SYSC-0016,VIROSCOPY,Modélisation stochastique et inférence statistique pour la propagation des maladies infectieuses transmissibles: du microscopique au macroscopique(2008), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Institut Galilée-Université Paris 13 (UP13), Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Laboratoire Paul Painlevé - UMR 8524 (LPP), and Centre National de la Recherche Scientifique (CNRS)-Université de Lille
- Subjects
Statistics and Probability ,large network limit ,05C80 ,mathematical model for epidemiology ,01 natural sciences ,Configuration Model graph ,measure-valued process ,010104 statistics & probability ,03 medical and health sciences ,Corollary ,92D30 ,FOS: Mathematics ,Quantitative Biology::Populations and Evolution ,0101 mathematics ,030304 developmental biology ,Mathematics ,Random graph ,Discrete mathematics ,60J80 ,0303 health sciences ,Mathematical and theoretical biology ,Probability (math.PR) ,Rigorous proof ,Degree distribution ,60F99 ,Graph ,[MATH.MATH-PR]Mathematics [math]/Probability [math.PR] ,[SDV.SPEE]Life Sciences [q-bio]/Santé publique et épidémiologie ,Model network ,SIR model ,Statistics, Probability and Uncertainty ,Epidemic model ,Mathematics - Probability - 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 [Mathematical Biology 56 (2008) 293--310]., Comment: Published in at http://dx.doi.org/10.1214/11-AAP773 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
- Published
- 2012