Modeling Epidemic Spreading in Complex Networks: Concurrency and Traffic

  • Sandro Meloni
  • Alex Arenas
  • Sergio Gómez
  • Javier Borge-Holthoefer
  • Yamir Moreno
Chapter
Part of the Springer Optimization and Its Applications book series (SOIA, volume 57)

Abstract

The study of complex networks sheds light on the relation between the structure and function of complex systems. One remarkable result is the absence of an epidemic threshold in infinite-size scale-free networks, which implies that any infection will perpetually propagate regardless of the spreading rate. However, real-world networks are finite and experience indicates that infections do have a finite lifetime. In this chapter, we will provide with two new approaches to cope with the problem of concurrency and traffic in the spread of epidemics. We show that the epidemic incidence is shaped by contact flow or traffic conditions. Contrary to the classical assumption that infections are transmitted as a diffusive process from nodes to all neighbors, we instead consider the scenario in which epidemic pathways are defined and driven by flows. Extensive numerical simulations and theoretical predictions show that whether a threshold exists or not depends directly on contact flow conditions. Two extreme cases are identified. In the case of low traffic, an epidemic threshold shows up, while for very intense flow, no epidemic threshold appears. In this way, the classical mean-field theory for epidemic spreading in scale free networks is recovered as a particular case of the proposed approach. Our results explain why some infections persist with low prevalence in scale-free networks, and provide a novel conceptual framework to understand dynamical processes on complex networks.

Keywords

Transportation 

Notes

Acknowledgements

We acknowledge the group of Prof. L. A. N. Amaral for sharing the airports data set. This work was supported by Spanish MICINN FIS2009-13730-C02-02, FIS2008-01240 and FIS2009-13364-C02-01, and the Generalitat de Catalunya 2009-SGR-838. A. A. acknowledges partial support by the Director, Office of Science, Computational and Technology Research, U.S. Department of Energy under Contract DE-AC02-05CH11231. Y. M. acknowledges support from the DGA through Project PI038/08 and a grant to FENOL.

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Sandro Meloni
    • 1
  • Alex Arenas
    • 2
    • 3
  • Sergio Gómez
    • 2
  • Javier Borge-Holthoefer
    • 2
    • 3
  • Yamir Moreno
    • 3
    • 4
  1. 1.Department of Informatics and AutomationUniversity of Rome “Roma Tre”RomeItaly
  2. 2.Departament d’Enginyeria Informàtica i MatemàtiquesUniversitat Rovira i VirgiliTarragonaSpain
  3. 3.Instituto de Biocomputación y Física de Sistemas Complejos (BIFI)Universidad de ZaragozaZaragozaSpain
  4. 4.Departamento de Física TeóricaUniversidad de ZaragozaZaragozaSpain

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