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Computing the epidemic threshold on temporal networks: ananalytical approach.


Dr. Eugenio Valdano

Professor/a organitzador/a

lex Arenas, Sergio Gmez


Universit Pierre et Marie Curie, Paris, France


13-07-2015 12:00


A wide range of physical, social and biological phenomena can be expressed in terms of spreading processes on networked systems. Notable examples include the spread of infectious diseases through direct contacts, the spatial propagation of epidemics driven by mobility networks, the spread of cyber worms along computer connections, or the diffusion of ideas mediated by social interactions. All these phenomena arise from a complex interplay between the spreading process and the networks underlying topology and dynamics, making a full theoretical understanding difficult. In particular, a fundamental property of such phenomena is the presence of a critical transmission probability above which large-scale propagation occurs, as opposed to quick extinction of the epidemic-like process. Computing this threshold is of utmost importance for epidemic containment and control of information diffusion. Previous studies have extensively characterized the epidemic threshold in the regime of timescale separation, i.e. when the spreading process evolves much slower, or much faster, than the timescale characterizing the evolution of the underlying network. In the case of comparable timescales, however, extensive empirical studies in social settings show that the detailed temporal structure of the network often determines how epidemics spread, and cannot be neglected. I will present a new analytical framework for the computation of the epidemic threshold for an arbitrary time-varying network. By reinterpreting the tensor formalism of multi-layer networks, this framework allows the analytical calculation of the epidemic threshold for the Susceptible-Infectious-Susceptible (SIS) model, without making any assumption on contact structure and evolution. Many contagion processes, however, are characterized by a period of latency, i.e. a time lag between being infected and becoming infectious (SEIS model). I will show how the additional timescale induced by latency period has a non-negligible impact on the epidemic threshold, and derive an analytical formula for its computation in this scenario. In order to do that I will introduce a novel mapping of the SEIS model around critical point into an SIS model on a two-layer structure.


Laboratori 231 (a confirmar)