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 ${\beta }_c$ with the local awareness ratio $\alpha$ approximating $0.5$, which induces two-stage effects on epidemic threshold and the final epidemic size. These findings indicate that the increase of $\alpha$ can accelerate the outbreak of epidemics. Furthermore, a simple 1D lattice model is investigated to illustrate the two-stage-like sharp transition at ${\alpha }_c\approx 0.5$. 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.

The problem of session-aware recommendation aims to predict users’ next click based on their current session and historical sessions. Existing session-aware recommendation methods have defects in capturing complex item transition relationships. Other than that, most of them fail to explicitly distinguish the effects of different historical sessions on the current session. To this end, we propose a novel method, named Personalized Graph Neural Networks with Attention Mechanism (A-PGNN) for brevity. A-PGNN mainly consists of two components: one is Personalized Graph Neural Network (PGNN), which is used to extract the personalized structural information in each user behavior graph, compared with the traditional Graph Neural Network (GNN) model, which considers the role of the user when the node embedding is updated. The other is Dot-Product Attention mechanism, which draws on the Transformer net to explicitly model the effect of historical sessions on the current session. Extensive experiments conducted on two real-world data sets show that A-PGNN evidently outperforms the state-of-the-art personalized session-aware recommendation methods.

There has been growing interest in exploring the interplay between epidemic spreading with human response, since it is natural for people to take various measures when they become aware of epidemics. As a proper way to describe the multiple connections among people in reality, multiplex network, a set of nodes interacting through multiple sets of edges, has attracted much attention. In this paper, to explore the coupled dynamical processes, a multiplex network with two layers is built. Specifically, the information spreading layer is a time varying network generated by the activity driven model, while the contagion layer is a static network. We extend the microscopic Markov chain approach to derive the epidemic threshold of the model. Compared with extensive Monte Carlo simulations, the method shows high accuracy for the prediction of the epidemic threshold. Besides, taking different spreading models of awareness into consideration, we explored the interplay between epidemic spreading with awareness spreading. The results show that the awareness spreading can not only enhance the epidemic threshold but also reduce the prevalence of epidemics. When the spreading of awareness is defined as susceptible-infected-susceptible model, there exists a critical value where the dynamical process on the awareness layer can control the onset of epidemics; while if it is a threshold model, the epidemic threshold emerges an abrupt transition with the local awareness ratio α approximating 0.5. Moreover, we also find that temporal changes in the topology hinder the spread of awareness which directly affect the epidemic threshold, especially when the awareness layer is threshold model. Given that the threshold model is a widely used model for social contagion, this is an important and meaningful result. Our results could also lead to interesting future research about the different time-scales of structural changes in multiplex networks.

The evolution of network structure and the spreading of epidemic are common coexistent dynamical processes. In most cases, network structure is treated as either static or time-varying, supposing the whole network is observed in the same time window. In this paper, we consider the epidemics spreading on a network which has both static and time-varying structures. Meanwhile, the time-varying part and the epidemic spreading are supposed to be of the same time scale. We introduce a static and activity-driven coupling (SADC) network model to characterize the coupling between the static (“strong”) structure and the dynamic (“weak”) structure. Epidemic thresholds of the SIS and SIR models are studied using the SADC model both analytically and numerically under various coupling strategies, where the strong structure is of homogeneous or heterogeneous degree distribution. Theoretical thresholds obtained from the SADC model can both recover and generalize the classical results in static and time-varying networks. It is demonstrated that a weak structure might make the epidemic threshold low in homogeneous networks but high in heterogeneous cases. Furthermore, we show that the weak structure has a substantive effect on the outbreak of the epidemics. This result might be useful in designing some efficient control strategies for epidemics spreading in networks.

Exploring the interplay between information spreading and epidemic spreading is a topic that has been receiving increasing attention. As an efficient means of depicting the spreading of information, which manifests as a cascade phenomenon, awareness cascading is utilized to investigate this coupled transmission. Because in reality, different individuals facing the same epidemic will exhibit distinct behaviors according to their own experiences and attributes, it is important for us to consider the heterogeneity of individuals. Consequently, we propose a heterogeneous spreading model. To describe the heterogeneity, two of the most important but radically different methods for this purpose, the degree and k-core measures, are studied in this paper through three models based on different assumptions. Adopting a Markov chain approach, we succeed in predicting the epidemic threshold trend. Furthermore, we find that when the k-core measure is used to classify individuals, the spreading process is robust to these models, meaning that regardless of the model used, the spreading process is nearly identical at the macroscopic level. In addition, the k-core measure leads to a much larger final epidemic size than the degree measure. These results are cross-checked through numerous simulations, not only of a synthetic network but also of a real multiplex network. The presented findings provide a better understanding of k-core individuals and reveal the importance of considering network structure when investigating various dynamic processes.