  Using the SIS model on unweighted and weighted networks, we consider the
disease localization phenomenon. In contrast to the well-recognized point of
view that diseases infect a finite fraction of vertices right above the
epidemic threshold, we show that diseases can be localized on a finite number
of vertices, where hubs and edges with large weights are centers of
localization. Our results follow from the analysis of standard models of
networks and empirical data for real-world networks.
