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.
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