title: Thresholds for epidemic spreading in networks.
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 λ(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 λ>1/√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.
authors.affiliation: Istituto dei Sistemi Complessi (CNR-ISC), UOS Sapienza and Dip. di Fisica, Sapienza Università di Roma, P.le A. Moro 2, I-00185 Roma, Italy.
authors.forename: Claudio
authors.initials: C
authors.lastname: Castellano
authors.forename: Romualdo
authors.initials: R
authors.lastname: Pastor-Satorras
mesh_terms: D018562:Disease Transmission, Infectious; D058872:Epidemics; D006801:Humans; D008954:Models, Biological; D013997:Time Factors