title: Rare-region effects in the contact process on networks.
abstract: Networks and dynamical processes occurring on them have become a paradigmatic representation of complex systems. Studying the role of quenched disorder, both intrinsic to nodes and topological, is a key challenge. With this in mind, here we analyze the contact process (i.e., the simplest model for propagation phenomena) with node-dependent infection rates (i.e., intrinsic quenched disorder) on complex networks. We find Griffiths phases and other rare-region effects, leading rather generically to anomalously slow (algebraic, logarithmic, etc.) relaxation, on Erdős-Rényi networks. We predict similar effects to exist for other topologies as long as a nonvanishing percolation threshold exists. More strikingly, we find that Griffiths phases can also emerge--even with constant epidemic rates--as a consequence of mere topological heterogeneity. In particular, we find Griffiths phases in finite-dimensional networks as, for instance, a family of generalized small-world networks. These results have a broad spectrum of implications for propagation phenomena and other dynamical processes on networks, and are relevant for the analysis of both models and empirical data.
authors.affiliation: Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, H-1525 Budapest, P.O. Box 49, Hungary.
authors.forename: Róbert
authors.initials: R
authors.lastname: Juhász
authors.forename: Géza
authors.initials: G
authors.lastname: Ódor
authors.forename: Claudio
authors.initials: C
authors.lastname: Castellano
authors.forename: Miguel A
authors.initials: MA
authors.lastname: Muñoz
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D008954:Models, Biological; D015233:Models, Statistical