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Collective versus hub activation of epidemic phases on networks

Silvio C. Ferreira, Renan S. Sander, and Romualdo Pastor-Satorras
Phys. Rev. E 93, 032314 – Published 14 March 2016

Abstract

We consider a general criterion to discern the nature of the threshold in epidemic models on scale-free (SF) networks. Comparing the epidemic lifespan of the nodes with largest degrees with the infection time between them, we propose a general dual scenario, in which the epidemic transition is either ruled by a hub activation process, leading to a null threshold in the thermodynamic limit, or given by a collective activation process, corresponding to a standard phase transition with a finite threshold. We validate the proposed criterion applying it to different epidemic models, with waning immunity or heterogeneous infection rates in both synthetic and real SF networks. In particular, a waning immunity, irrespective of its strength, leads to collective activation with finite threshold in scale-free networks with large degree exponent, at odds with canonical theoretical approaches.

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  • Received 20 November 2015

DOI:https://doi.org/10.1103/PhysRevE.93.032314

©2016 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
Networks

Authors & Affiliations

Silvio C. Ferreira1, Renan S. Sander1, and Romualdo Pastor-Satorras2

  • 1Departamento de Física, Universidade Federal de Viçosa, 36570-000 Viçosa, Minas Gerais, Brazil
  • 2Departament de Física, Universitat Politècnica de Catalunya, Campus Nord B4, 08034 Barcelona, Spain

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Issue

Vol. 93, Iss. 3 — March 2016

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