Thresholds for Epidemic Spreading in Networks

Claudio Castellano and Romualdo Pastor-Satorras
Phys. Rev. Lett. 105, 218701 – Published 17 November 2010

Abstract

We study the threshold of epidemic models in quenched networks with degree distribution given by a power-law. For the susceptible-infected-susceptible model the activity threshold λc vanishes in the large size limit on any network whose maximum degree kmax diverges with the system size, at odds with heterogeneous mean-field (HMF) theory. The vanishing of the threshold has nothing to do with the scale-free nature of the network but stems instead from the largest hub in the system being active for any spreading rate λ>1/kmax and playing the role of a self-sustained source that spreads the infection to the rest of the system. The susceptible-infected-removed model displays instead agreement with HMF theory and a finite threshold for scale-rich networks. We conjecture that on quenched scale-rich networks the threshold of generic epidemic models is vanishing or finite depending on the presence or absence of a steady state.

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  • Received 25 June 2010

DOI:https://doi.org/10.1103/PhysRevLett.105.218701

© 2010 The American Physical Society

Authors & Affiliations

Claudio Castellano1 and Romualdo Pastor-Satorras2

  • 1Istituto dei Sistemi Complessi (CNR-ISC), UOS Sapienza and Dip. di Fisica, “Sapienza” Università di Roma, P.le A. Moro 2, I-00185 Roma, Italy
  • 2Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya, Campus Nord B4, 08034 Barcelona, Spain

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Vol. 105, Iss. 21 — 19 November 2010

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