Thresholds for Epidemic Outbreaks in Finite Scale-Free Networks

Dong-Uk Hwang; S. Boccaletti; Y. Moreno; R. López-Ruiz

doi:10.3934/mbe.2005.2.317

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2005, Volume 2, Issue 2: 317-327. Doi: 10.3934/mbe.2005.2.317

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Thresholds for Epidemic Outbreaks in Finite Scale-Free Networks

1.
Istituto Nazionale di Ottica Applicata, Largo E. Fermi, 6 50125 Florence
2.
Istituto Nazionale di Ottica Applicata, Largo E. Fermi, 6, 50125 Florence
3.
Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), Universidad de Zaragoza, Zaragoza 50009
4.
Department of Computer Science, University of Zaragoza, Zaragoza 50009

Received: September 30, 2004

Revised: January 31, 2005

Published: February 2005

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Abstract

We numerically investigate the existence of a threshold for epidemic outbreaks in a class of scale-free networks characterized by a parametrical dependence of the scaling exponent, influencing the convergence of fluctuations in the degree distribution. In finite-size networks, finite thresholds for the spreading of an epidemic are always found. However, both the thresholds and the behavior of the epidemic prevalence are quite different with respect to the type of network considered and the system size. We also discuss agreements and differences with some analytical claims previously reported.

Keywords:

epidemic threshold,
scale-free network.

Mathematics Subject Classification: 92D30.

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