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A network with tunable clustering, degree correlation and degree distribution, and an epidemic thereon
Stockholm University, Faculty of Science, Department of Mathematics.
2013 (English)In: Journal of Mathematical Biology, ISSN 0303-6812, E-ISSN 1432-1416, Vol. 66, no 4-5, 979-1019 p.Article in journal (Refereed) Published
Abstract [en]

A random network model which allows for tunable, quite general forms of clustering, degree correlation and degree distribution is defined. The model is an extension of the configuration model, in which stubs (half-edges) are paired to form a network. Clustering is obtained by forming small completely connected subgroups, and positive (negative) degree correlation is obtained by connecting a fraction of the stubs with stubs of similar (dissimilar) degree. An SIR (Susceptible Infective Recovered) epidemic model is defined on this network. Asymptotic properties of both the network and the epidemic, as the population size tends to infinity, are derived: the degree distribution, degree correlation and clustering coefficient, as well as a reproduction number , the probability of a major outbreak and the relative size of such an outbreak. The theory is illustrated by Monte Carlo simulations and numerical examples. The main findings are that (1) clustering tends to decrease the spread of disease, (2) the effect of degree correlation is appreciably greater when the disease is close to threshold than when it is well above threshold and (3) disease spread broadly increases with degree correlation when is just above its threshold value of one and decreases with when is well above one.

Place, publisher, year, edition, pages
2013. Vol. 66, no 4-5, 979-1019 p.
Keyword [en]
Branching process, Configuration model, Epidemic size, Random graph, SIR epidemic, Threshold behaviour
National Category
Biological Sciences Mathematics
URN: urn:nbn:se:su:diva-88699DOI: 10.1007/s00285-012-0609-7ISI: 000315093100015OAI: diva2:612886


Available from: 2013-03-25 Created: 2013-03-25 Last updated: 2013-03-25Bibliographically approved

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