Chaotic spreading of epidemics in complex networks of excitable units

F. S. Vannucchi; S. Boccaletti

doi:10.3934/mbe.2004.1.49

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2004, Volume 1, Issue 1: 49-55. Doi: 10.3934/mbe.2004.1.49

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Chaotic spreading of epidemics in complex networks of excitable units

F. S. Vannucchi^1, and
S. Boccaletti^1,

1.
Istituto Nazionale di Ottica Applicata, Largo E. Fermi, 6, 50125 Florence

Received: January 31, 2004

Revised: January 31, 2004

Published: February 2004

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Abstract

We explore the dynamics of an epidemiological disease spreading within a complex network of individuals. The local behavior of the epidemics is modelled by means of an excitable dynamics, and the individuals are connected in the network through a weighted small-world wiring. The global behavior of the epidemics can have stationary as well as chaotic states, depending upon the probability of substituting short-range with long-range interactions. We describe the bifurcation scenario leading to such latter states, and discuss the relevance of the observed chaotic dynamics for the description of the spreading mechanisms of epidemics inside complex networks.

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Mathematics Subject Classification: 92D30, 34D20.

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