Human awareness plays an important role in the spread of infectious diseases and the control of propagation patterns. The dynamic process with human awareness is called awareness cascade, during which individuals exhibit herd-like behavior because they are making decisions based on the actions of other individuals [Borge-Holthoefer et al., J. Complex Networks 1, 3 (2013)]. In this paper, to investigate the epidemic spreading with awareness cascade, we propose a local awareness controlled contagion spreading model on multiplex networks. By theoretical analysis using a microscopic Markov chain approach and numerical simulations, we find the emergence of an abrupt transition of epidemic threshold β(c) with the local awareness ratio α approximating 0.5, which induces two-stage effects on epidemic threshold and the final epidemic size. These findings indicate that the increase of α can accelerate the outbreak of epidemics. Furthermore, a simple 1D lattice model is investigated to illustrate the two-stage-like sharp transition at α(c)≈0.5. The results can give us a better understanding of why some epidemics cannot break out in reality and also provide a potential access to suppressing and controlling the awareness cascading systems.

Matrix metalloproteinases (MMPs) are known to play important roles in extracellular matrix remodeling during the process of tumor invasion and metastasis. However, little is known about their role in esophageal squamous cell carcinoma (ESCC). Expression of MMP-2 and MMP-9 in ESCC was detected in our research. Tissue microarray chip was prepared, consisting of 58 cases of ESCC and corresponding esophageal epithelium tissues. MMP-2 and MMP-9 were examined by immunohistochemistry. Overexpression of MMP-2 and MMP-9 was found in ESCC (42.1 and 60.3%, respectively), compared with paired distal normal esophageal tissues (22.9 and 8.9%, respectively). Expression of MMP-2 in ESCC was significantly associated with the tumor invasion depth, tumor-node-metastasis stages, and lymph node metastasis. MMP-2 and MMP-9 may play important roles in carcinogenesis, and MMP-2 may act as a biological marker of invasion and lymph node metastasis in ESCC.

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Random walks constitute a fundamental mechanism for many dynamics taking place on complex networks. Besides, as a more realistic description of our society, multiplex networks have been receiving a growing interest, as well as the dynamical processes that occur on top of them. Here, inspired by one specific model of random walks that seems to be ubiquitous across many scientific fields, the Lévy flight, we study a new navigation strategy on top of multiplex networks. Capitalizing on spectral graph and stochastic matrix theories, we derive analytical expressions for the mean first passage time and the average time to reach a node on these networks. Moreover, we also explore the efficiency of Lévy random walks, which we found to be very different as compared to the single layer scenario, accounting for the structure and dynamics inherent to the multiplex network. Finally, by comparing with some other important random walk processes defined on multiplex networks, we find that in some region of the parameters, a Lévy random walk is the most efficient strategy. Our results give us a deeper understanding of Lévy random walks and show the importance of considering the topological structure of multiplex networks when trying to find efficient navigation strategies.