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This study extends the SIS epidemic model for single virus propagation over an arbitrary graph to an SI1SI2S epidemic model of two exclusive, competitive viruses over a two-layer network with generic structure, where network layers represent the distinct transmission routes of the viruses. We find analytical results determining extinction, mutual exclusion, and coexistence of the viruses by introducing the concepts of survival threshold and winning threshold. Furthermore, we show the possibility of coexistence in SIS-type competitive spreading over multilayer networks. Not only do we rigorously prove a region of coexistence, we quantitate it via interrelation of central nodes across the network layers. Little to no overlapping of layers central nodes is the key determinant of coexistence. Specifically, we show coexistence is impossible if network layers are identical yet possible if the network layers have distinct dominant eigenvectors and node degree vectors. For example, we show both analytically and numerically that positive correlation of network layers makes it difficult for a virus to survive while in a network with negatively correlated layers survival is easier but total removal of the other virus is more difficult. We believe our methodology has great potentials for application to broader classes of multi-pathogen spreading over multi-layer and interconnected networks.
In spite of the extensive previous efforts on traffic dynamics and epidemic spreading in complex networks, the problem of traffic-driven epidemic spreading on {em correlated} networks has not been addressed. Interestingly, we find that the epidemic t
Social interactions are stratified in multiple contexts and are subject to complex temporal dynamics. The systematic study of these two features of social systems has started only very recently mainly thanks to the development of multiplex and time-v
We study SIS epidemic spreading processes unfolding on a recent generalisation of the activity-driven modelling framework. In this model of time-varying networks each node is described by two variables: activity and attractiveness. The first, describ
Time-varying network topologies can deeply influence dynamical processes mediated by them. Memory effects in the pattern of interactions among individuals are also known to affect how diffusive and spreading phenomena take place. In this paper we ana
Dynamic networks exhibit temporal patterns that vary across different time scales, all of which can potentially affect processes that take place on the network. However, most data-driven approaches used to model time-varying networks attempt to captu