  Identifying the most influential spreaders is important to understand and
control the spreading process in a network. As many real-world complex systems
can be modeled as multilayer networks, the question of identifying important
nodes in multilayer network has attracted much attention. Existing studies
focus on the multilayer network structure, while neglecting how the structural
and dynamical coupling of multiple layers influence the dynamical importance of
nodes in the network. Here we investigate on this question in an
information-disease coupled spreading dynamics on multiplex networks. Firstly,
we explicitly reveal that three interlayer coupling factors, which are the
two-layer relative spreading speed, the interlayer coupling strength and the
two-layer degree correlation, significantly impact the spreading influence of a
node on the contact layer. The suppression effect from the information layer
makes the structural centrality on the contact layer fail to predict the
spreading influence of nodes in the multiplex network. Then by mapping the
coevolving spreading dynamics into percolation process and using the
message-passing approach, we propose a method to calculate the size of the
disease outbreaks from a single seed node, which can be used to estimate the
nodes' spreading influence in the coevolving dynamics. Our work provides
insights on the importance of nodes in the multiplex network and gives a
feasible framework to investigate influential spreaders in the asymmetrically
coevolving dynamics.
