The Annals of Applied Probability

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

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

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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 [Mathematical Biology 56 (2008) 293–310].

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Ann. Appl. Probab., Volume 22, Number 2 (2012), 541-575.

First available in Project Euclid: 2 April 2012

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Zentralblatt MATH identifier

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 05C80: Random graphs [See also 60B20] 92D30: Epidemiology 60F99: None of the above, but in this section

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


Decreusefond, Laurent; Dhersin, Jean-Stéphane; Moyal, Pascal; Tran, Viet Chi. Large graph limit for an SIR process in random network with heterogeneous connectivity. Ann. Appl. Probab. 22 (2012), no. 2, 541--575. doi:10.1214/11-AAP773.

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