Journal
PHYSICAL REVIEW LETTERS
Volume 105, Issue 21, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.105.218701
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Funding
- Spanish MEC [FIS2007-66485-C02-01, FIS2010-21781-C02-01]
- Generalitat de Catalunya
- Junta de Andalucia [P09-FQM4682]
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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 lambda(c) vanishes in the large size limit on any network whose maximum degree k(max) 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 lambda > 1/root k(max) 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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