61695 20190709135443.0 doi 10.1103/PhysRevX.7.011014 sideral 99142 ART-2017-99142 eng de Arruda, G.F. Disease localization in multilayer networks 2017 Access copy available to the general public Unrestricted We present a continuous formulation of epidemic spreading on multilayer networks using a tensorial representation, extending the models of monoplex networks to this context. We derive analytical expressions for the epidemic threshold of the susceptible-infected-susceptible (SIS) and susceptibleinfected- recovered dynamics, as well as upper and lower bounds for the disease prevalence in the steady state for the SIS scenario. Using the quasistationary state method, we numerically show the existence of disease localization and the emergence of two or more susceptibility peaks, which are characterized analytically and numerically through the inverse participation ratio. At variance with what is observed in single-layer networks, we show that disease localization takes place on the layers and not on the nodes of a given layer. Furthermore, when mapping the critical dynamics to an eigenvalue problem, we observe a characteristic transition in the eigenvalue spectra of the supra-contact tensor as a function of the ratio of two spreading rates: If the rate at which the disease spreads within a layer is comparable to the spreading rate across layers, the individual spectra of each layer merge with the coupling between layers. Finally, we report on an interesting phenomenon, the barrier effect; i.e., for a three-layer configuration, when the layer with the lowest eigenvalue is located at the center of the line, it can effectively act as a barrier to the disease. The formalism introduced here provides a unifying mathematical approach to disease contagion in multiplex systems, opening new possibilities for the study of spreading processes. info:eu-repo/grantAgreement/ES/MINECO/FIS2014-55867-P info:eu-repo/grantAgreement/EC/FP7/317532/EU/Foundational Research on MULTIlevel comPLEX networks and systems/MULTIPLEX info:eu-repo/semantics/openAccess by http://creativecommons.org/licenses/by/3.0/es/ 14.385 2017 PHYSICS, MULTIDISCIPLINARY 4 / 78 = 0.051 2017 Q1 T1 6.11 2017 Physics and Astronomy (miscellaneous) 2017 Q1 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion (orcid)0000-0002-5655-1587 Cozzo, E. Peixoto, T.P. Rodrigues, F.A. (orcid)0000-0002-0895-1893 Moreno, Y. Universidad de Zaragoza 2004 405 Universidad de Zaragoza Dpto. Física Teórica Área Física Teórica 7, 1 (2017), 011014 [25 pp] Physical review. X Physical review. X 2160-3308 2097033 http://zaguan.unizar.es/record/61695/files/texto_completo.pdf Versión publicada 110530 http://zaguan.unizar.es/record/61695/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:61695 articulos driver 2019-07-09-11:37:00 ARTICLE