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 susceptible-infected-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.

Disease Localization in Multilayer Networks
Guilherme Ferraz de Arruda, Emanuele Cozzo, Tiago P. Peixoto, Francisco A. Rodrigues, and Yamir Moreno
Phys. Rev. X 7, 011014

Source: journals.aps.org

Social media are transforming global communication and coordination and provide unprecedented opportunities for studying socio-technical domains. Here we study global dynamical patterns of communication on Twitter across many scales. Underlying the observed patterns is both the diurnal rotation of the earth, day and night, and the synchrony required for contingency of actions between individuals. We find that urban areas show a cyclic contraction and expansion that resembles heartbeats linked to social rather than natural cycles. Different urban areas have characteristic signatures of daily collective activities. We show that the differences detected are consistent with a new emergent global synchrony that couples behavior in distant regions across the world. Although local synchrony is the major force that shapes the collective behavior in cities, a larger-scale synchronization is beginning to occur.

 

Alfredo J. Morales, Vaibhav Vavilala, Rosa M. Benito, Yaneer Bar-Yam, Global patterns of synchronization in human communications, Journal of the Royal Society (2017).

Source: www.necsi.edu