Large graph limit for an SIR process in random network with heterogeneous connectivity
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
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00505167/fr/
Journal nameThe Annals of Applied Probability
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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 / Keywordsmathematical model for epidemiology; measure-valued process; large network limit; Configuration Model graph; SIR model
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