000061695 001__ 61695 000061695 005__ 20190709135443.0 000061695 0247_ $$2doi$$a10.1103/PhysRevX.7.011014 000061695 0248_ $$2sideral$$a99142 000061695 037__ $$aART-2017-99142 000061695 041__ $$aeng 000061695 100__ $$ade Arruda, G.F. 000061695 245__ $$aDisease localization in multilayer networks 000061695 260__ $$c2017 000061695 5060_ $$aAccess copy available to the general public$$fUnrestricted 000061695 5203_ $$aWe 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. 000061695 536__ $$9info:eu-repo/grantAgreement/ES/MINECO/FIS2014-55867-P$$9info:eu-repo/grantAgreement/EC/FP7/317532/EU/Foundational Research on MULTIlevel comPLEX networks and systems/MULTIPLEX 000061695 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/ 000061695 590__ $$a14.385$$b2017 000061695 591__ $$aPHYSICS, MULTIDISCIPLINARY$$b4 / 78 = 0.051$$c2017$$dQ1$$eT1 000061695 592__ $$a6.11$$b2017 000061695 593__ $$aPhysics and Astronomy (miscellaneous)$$c2017$$dQ1 000061695 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000061695 700__ $$0(orcid)0000-0002-5655-1587$$aCozzo, E. 000061695 700__ $$aPeixoto, T.P. 000061695 700__ $$aRodrigues, F.A. 000061695 700__ $$0(orcid)0000-0002-0895-1893$$aMoreno, Y.$$uUniversidad de Zaragoza 000061695 7102_ $$12004$$2405$$aUniversidad de Zaragoza$$bDpto. Física Teórica$$cÁrea Física Teórica 000061695 773__ $$g7, 1 (2017), 011014 [25 pp]$$pPhysical review. X$$tPhysical review. X$$x2160-3308 000061695 8564_ $$s2097033$$uhttps://zaguan.unizar.es/record/61695/files/texto_completo.pdf$$yVersión publicada 000061695 8564_ $$s110530$$uhttps://zaguan.unizar.es/record/61695/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000061695 909CO $$ooai:zaguan.unizar.es:61695$$particulos$$pdriver 000061695 951__ $$a2019-07-09-11:37:00 000061695 980__ $$aARTICLE