Critical behavior of propagation on small-world networks

We report numerical evidence that an epidemiclike model, which can be interpreted as the propagation of a rumor, exhibits critical behavior at a finite randomness of the underlying small-world network. The transition occurs between a regime where the rumor "dies" in a small neighborhood of...

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Bibliographic Details
Published in:Physical review. E, Statistical, nonlinear, and soft matter physics Statistical, nonlinear, and soft matter physics, 2001-11, Vol.64 (5 Pt 1), p.050901-050901
Main Author: Zanette, D H
Format: Article
Language:English
Subjects:
Biophysical Phenomena
Biophysics
Disease Outbreaks
Epidemiologic Methods
Humans
Models, Biological
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Summary:We report numerical evidence that an epidemiclike model, which can be interpreted as the propagation of a rumor, exhibits critical behavior at a finite randomness of the underlying small-world network. The transition occurs between a regime where the rumor "dies" in a small neighborhood of its origin, and a regime where it spreads over a finite fraction of the whole population. Critical exponents are evaluated through finite-size scaling analysis, and the dependence of the critical randomness with the network connectivity is studied. The behavior of this system as a function of the small-network randomness bears noticeable similarities with an epidemiological model reported recently [M. Kuperman and G. Abramson, Phys. Rev. Lett. 86, 2909 (2001)], in spite of substantial differences in the respective dynamical rules.
ISSN:1539-3755
DOI:10.1103/physreve.64.050901