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Epidemic spreading and cooperation dynamics on homogeneous small-world networks

F. C. Santos1,2, J. F. Rodrigues2, and J. M. Pacheco3,2

  • 1IRIDIA, Université Libre de Bruxelles, Avenue Franklin Roosevelt 50, Belgium
  • 2GADGET, Apartado 1329, 1009-001 Lisboa, Portugal
  • 3Centro de Física Teórica e Computacional and Departamento de Física da Faculdade de Ciências, Universidad de Lisboa, P-1649-003 Lisboa Codex, Portugal

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Phys. Rev. E 72, 056128 – Published 23 November, 2005

DOI: https://doi.org/10.1103/PhysRevE.72.056128

Abstract

We introduce a class of small-world networks—homogeneous small-worlds—which, in contrast with the well-known Watts-Strogatz small-worlds, exhibit a homogeneous connectivity distribution, in the sense that all nodes have the same number of connections. This feature allows the investigation of pure small-world effects, detached from any associated heterogeneity. Furthermore, we use at profit the remarkable similarity between the properties of homogeneous small worlds and the heterogeneous small-worlds of Watts-Strogatz to assess the separate roles of heterogeneity and small-world effects. We investigate the dependence on these two mechanisms of the threshold for epidemic outbreaks and also of the coevolution of cooperators and defectors under natural selection. With respect to the well-studied regular homogeneous limits, we find a subtle interplay between these mechanisms. While they both contribute to reduce the threshold for an epidemic outburst, they exhibit opposite behavior in the evolution of cooperation, such that the overall results mask the true nature of their individual contribution to this process.

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Phys. Rev. E 72, 056128– Published 23 November, 2005
  • Received 23 April 2005

© 2005 American Physical Society

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