Interplay Between Spreading and Random Walk Processes in Multiplex Networks

Real networks in our surrounding are usually complex and composite by nature and they consist of many interwoven layers. The commutation of agents (nodes) across layers in these composite multiplex networks heavily influences the underlying dynamical processes, such as information, idea and disease spreading, synchronization, consensus, etc. In order to understand how the agents' dynamics and the compositeness of multiplex networks influence the spreading dynamics, we develop a susceptible-infected-susceptible-based model on the top of these networks, which is integrated with the transition of agents across layers. Moreover, we analytically obtain a critical infection rate for which an epidemic dies out in a multiplex network, and latter show that this rate can be higher compared with the isolated networks. Finally, using numerical simulations we confirm the epidemic threshold and we show some interesting insights into the epidemic onset and the spreading dynamics in several real and generic multiplex networks.