Roles of the spreading scope and effectiveness in spreading dynamics on   multiplex networks
  Comparing with single networks, the multiplex networks bring two main effects on the spreading process among individuals. First, the pathogen or information can be transmitted to more individuals through different layers at one time, which enlarges the spreading scope. Second, through different layers, an individual can also transmit the pathogen or information to the same individuals more than once at one time, which makes the spreading more effective. To understand the different roles of the spreading scope and effectiveness, we propose an epidemic model on multiplex networks with link overlapping, where the spreading effectiveness of each interaction as well as the variety of channels (spreading scope) can be controlled by the number of overlapping links. We find that for Poisson degree distribution, increasing the epidemic scope (the first effect) is more efficient than enhancing epidemic probability (the second effect) to facilitate the spreading process. However, for power-law degree distribution, the effects of the two factors on the spreading dynamics become complicated. Enhancing epidemic probability makes pathogen or rumor easier to outbreak in a finite system. But after that increasing epidemic scopes is still more effective for a wide spreading. Theoretical results along with reasonable explanation for these phenomena are all given in this paper, which indicates that the epidemic scope could play an important role in the spreading dynamics. 
Ming Li, Run-Ran Liu, Dan Peng, Chun-Xiao Jia, and Bing-Hong Wang
physics.soc-ph cond-mat.dis-nn cond-mat.stat-mech