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Epidemics on random graphs with tunable clustering. (English) Zbl 1147.92034

Summary: A branching process approximation for the spread of a Reed-Frost epidemic on a network with tunable clustering is derived. The approximation gives rise to expressions for the epidemic threshold and the probability of a large outbreak in the epidemic. We investigate how these quantities vary with the clustering in the graph and find that, as the clustering increases, the epidemic threshold decreases. The network is modeled by a random intersection graph, in which individuals are independently members of a number of groups and two individuals are linked to each other if and only if there is at least one group that they are both members of.

MSC:

92D30 Epidemiology
05C80 Random graphs (graph-theoretic aspects)
60J85 Applications of branching processes
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