Thresholds for epidemic spreading in networks

By Claudio Castellano, Romualdo Pastor-Satorras. Physical Review Letters, 2010

612 citations recorded by the source corpus.

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.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f1c0ad767dc23e53daf5d3f8e2097ec81a7772d4

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Citations in the corpus

Analytically Solvable Model of Spreading Dynamics with Non-Poissonian Processes (2013, background): “[10] Claudio Castellano and Romualdo Pastor-Satorras, “Thresholds for epidemic spreading in networks,” Physical Review Letters 105, 218701+ (2010).”
The H-index of a network node and its relation to degree and coreness (2016, background): “According to the heterogeneous mean-ﬁeld theory 47,53,54 , the epidemic threshold of SIR model is approximate to b c (cid:6) k h i = k 2 h i(cid”
Modelling dynamical processes in complex socio-technical systems (2011, methodology): “Following the results obtained with the HMF assumption, a number of rigorous results that link the network topology to the epidemic threshold have been derived 53,57,58 .”
What Stops Social Epidemics? (2011, background): “…disease (Anderson and May 1991; Hethcote 2000) and behaviors (Christakis and Fowler 2007; Christakis and Fowler 2008), computer virus epidemics on the Internet (Castellano and PastorSatorras 2010), word-of-mouth recommendations (Goldenberg, Libai, and Muller 2001), viral marketing…”
Identifying a set of influential spreaders in complex networks (2016, methodology): “5λc is compared with other methods where λc is the threshold [46, 47, 48].”
The Kuramoto model in complex networks (2015, background): “More specifically, in this case, the connections between oscillators are kept constant over different realizations of the network dynamics (networks whose adjacency matrices are fixed over time or over different realizations are also referred as quenched networks [70, 71]).”
Activity driven modeling of time varying networks (2012, background): “…for the definition of interaction processes based on the actual measurement of the activity of the agents forming the system, a task now made possible by the availability of time-resolved, high-quality data on the instantaneous activity of millions of agents in a wide variety of networks [33–37].”