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

Moyal, Pascal; Dhersin, Jean-Stéphane; Decreusefond, Laurent; Tran, Viet Chi

Moyal, Pascal; Dhersin, Jean-Stéphane; Decreusefond, Laurent; Tran, Viet Chi (2012), Large graph limit for an SIR process in random network with heterogeneous connectivity, The Annals of Applied Probability, 22, 2, p. 541-575. http://dx.doi.org/10.1214/11-AAP773

Type

Article accepté pour publication ou publié

External document link

http://hal.archives-ouvertes.fr/hal-00505167/fr/

Date

2012

Journal name

The Annals of Applied Probability

Volume

Number

Publisher

Institute of Mathematical Statistics

Pages

541-575

Abstract (EN)

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).

Subjects / Keywords

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