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Epidemics on Random Graphs with Tunable Clustering

Published online by Cambridge University Press:  14 July 2016

Tom Britton*
Affiliation:
Stockholm University
Maria Deijfen*
Affiliation:
Stockholm University
Andreas N. Lagerås*
Affiliation:
Stockholm University
Mathias Lindholm*
Affiliation:
Stockholm University
*
Postal address: Department of Mathematics, Stockholm University, 106 91 Stockholm, Sweden.
Postal address: Department of Mathematics, Stockholm University, 106 91 Stockholm, Sweden.
Postal address: Department of Mathematics, Stockholm University, 106 91 Stockholm, Sweden.
Postal address: Department of Mathematics, Stockholm University, 106 91 Stockholm, Sweden.
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Abstract

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In this paper 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.

Type
Research Article
Copyright
Copyright © Applied Probability Trust 2008 

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