Layer-crossing overhead and information spreading in multiplex social networks

Many real-world systems consist of multiple different layers of networks and interplay between them. Taking such multiplexity into account is important to a complete understanding of the structure and dynamics of complex systems. In this respect, we propose and study a model of information or disease spreading on multiplex social networks, in which agents interact or communicate through multiple channels (layers), and there exists a layer-switching overhead for transmission across the interaction layers. The model is characterized by the path-dependent transmissibility over a contact, which is dynamically determined, dependent on both incoming and outgoing transmission layers due to the switching overhead. We formulate a generalized theory with a mapping to deal with such a path-dependent transmissibility, and demonstrate dependency of epidemic threshold and epidemic outbreak size with respect to multiplexity characteristics such as the densities of network layers, layer-crossing costs, and type of seed infections. Our results suggest that explicit consideration of multiplexity can be crucial in realistic modeling of spreading processes on social networks.