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

Laurent Decreusefond (1, 2) , Jean-Stephane Dhersin (3, 4) , Pascal Moyal (5) , Viet Chi Tran (6, 7)

1 LTCI - Laboratoire Traitement et Communication de l'Information
2 Télécom ParisTech
3 IG - Institut Galilée
4 LAGA - Laboratoire Analyse, Géométrie et Applications
5 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
6 LPP - Laboratoire Paul Painlevé - UMR 8524
7 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

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).

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

Domaines: Probabilités [math.PR]; Santé publique et épidémiologie

Laurent Decreusefond, Jean-Stephane Dhersin, Pascal Moyal, Viet Chi Tran. Large graph limit for an SIR process in random network with heterogeneous connectivity. 2010. ⟨hal-00505167v2⟩