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

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).
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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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Laurent Decreusefond, Jean-Stephane Dhersin, Pascal Moyal, Viet Chi Tran. Large graph limit for an SIR process in random network with heterogeneous connectivity. Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2012, 22 (2), pp.541-575. ⟨10.1214/11-AAP773⟩. ⟨hal-00505167v3⟩

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