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EPIDEMIC DYNAMICS ON RANDOM AND SCALE-FREE NETWORKS

Published online by Cambridge University Press:  30 January 2013

J. BARTLETT  and
M. J. PLANK
J. BARTLETT
Affiliation:
Department of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand
M. J. PLANK*
Affiliation:
Department of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand
*
✉[email protected]
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Abstract

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Random networks were first used to model epidemic dynamics in the 1950s, but in the last decade it has been realized that scale-free networks more accurately represent the network structure of many real-world situations. Here we give an analytical and a Monte Carlo method for approximating the basic reproduction number ${R}_{0} $ of an infectious agent on a network. We investigate how final epidemic size depends on ${R}_{0} $ and on network density in random networks and in scale-free networks with a Pareto exponent of 3. Our results show that: (i) an epidemic on a random network has the same average final size as an epidemic in a well-mixed population with the same value of ${R}_{0} $; (ii) an epidemic on a scale-free network has a larger average final size than in an equivalent well-mixed population if ${R}_{0} \lt 1$, and a smaller average final size than in a well-mixed population if ${R}_{0} \gt 1$; (iii) an epidemic on a scale-free network spreads more rapidly than an epidemic on a random network or in a well-mixed population.

Keywords

degree distributionPareto distributionpower lawrandom graphSIR modelsuperspreaders

MSC classification

Secondary: 92D40: Ecology
Type
Research Article
Information
The ANZIAM Journal , Volume 54 , Issue 1-2 , October 2012 , pp. 3 - 22
Copyright
Copyright ©2013 Australian Mathematical Society 

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