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There has been growing interest in exploring the dynamical interplay of epidemic spreading and awareness diffusion within the multiplex network framework. Recent studies have demonstrated that pairwise interactions are not enough to characterize social contagion processes, but the complex mechanisms of influence and reinforcement should be considered. Meanwhile, the physical social interaction of individuals is not static but time-varying. Therefore, we propose a novel sUAU-tSIS model to characterize the interplay of simplicial awareness contagion and epidemic spreading on time-varying multiplex networks, in which one layer with 2-simplicial complexes is considered the virtual information layer to address the complex contagion mechanisms in awareness diffusion and the other layer with time-varying and memory effects is treated as the physical contact layer to mimic the temporal interaction pattern among population. The microscopic Markov chain approach based theoretical analysis is developed, and the epidemic threshold is also derived. The experimental results show that our theoretical method is in good agreement with the Monte Carlo simulations. Specifically, we find that the synergistic reinforcement mechanism coming from the group interactions promotes the diffusion of awareness, leading to the suppression of the spreading of epidemics. Furthermore, our results illustrate that the contact capacity of individuals, activity heterogeneity, and memory strength also play important roles in the two dynamics; interestingly, a crossover phenomenon can be observed when investigating the effects of activity heterogeneity and memory strength. [ABSTRACT FROM AUTHOR]

Identifying influential nodes in social networks has drawn significant attention in the field of network science. However, most of the existing works request to know the complete structural information about networks, indeed, this information is usually sensitive, private and hard to obtain. Therefore, how to identify the influential nodes in networks without disclosing privacy is especially important. In this paper, we propose a privacy-preserving (named as HE-ranking) framework to identify influential nodes in networks based on homomorphic encryption (HE) protocol. The HE-ranking method collaboratively computes the nodes' importance and protects the sensitive information of each private network by using the HE protocol. Extensive experimental results indicate that the method can effectively identify the influential nodes in the original networks than the baseline methods which only use each private network to identify influential nodes. More importantly, the HE-ranking method can protect the privacy of each private network in different parts. [ABSTRACT FROM AUTHOR]