Awareness of disease outbreaks can trigger changes in human behavior and has a significant impact on the spread of epidemics. Previous studies usually considered the coupled awareness-epidemic dynamics to be two competing processes that interact in the information and epidemic layers. However, these studies mostly assumed that all aware individuals have the same reduced infectivity and that different neighbors have the same influence on one's perception, ignoring the heterogeneity of individuals. In this paper, we propose a coupled awareness-epidemic spreading model in multiplex networks incorporating three types of heterogeneity: (1) the heterogeneity of individual responses to disease outbreaks, (2) the influence heterogeneity in the epidemic layer, and (3) the influence heterogeneity in the information layer. The theoretical analysis shows that the influence heterogeneity in the information layer has two-stage effects on the epidemic threshold. Moreover, we find that the epidemic threshold in the higher stage depends on the heterogeneity of individual responses and the influence heterogeneity in the epidemic layer, while the epidemic threshold in the lower stage is independent of awareness spreading and individual behaviors. The results give us a better understanding of how individual heterogeneity affects epidemic spreading and provide some practical implications for the control of epidemics.

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We investigate the impact of people's perceptions regarding the risk of an epidemic by analyzing the differences between local and global risk perceptions on affecting the epidemic threshold. Three issues are introduced to explain such differences: the indirect risk source, the heterogeneous global risk, and heterogeneity in individuals' intrinsic susceptibilities. When the direct risk source is completely undetected, the local risk perception tends to have no effect on the epidemic threshold, and the effect of the local risk is nearly equivalent to that of the global risk perception, thereby also suggesting a reason why global risk perception cannot affect the epidemic threshold. However, there is a surprising effect of the global risk perception: When its heterogeneity is sufficiently high, an increased epidemic threshold value sometimes may lead to a greater infected ratio.

h i g h l i g h t s• We study the impact of asymptomatic infection on the epidemic spread dynamics in multiplex networks.• We assume infected can be isolation and non isolation, then compare the research results of these two cases.• We take the individual heterogeneity into consideration and study whether it affect research results. a b s t r a c tMultiplex network theory is widely introduced to deepen the understanding of the dynamical interplay between self-protective behavior and epidemic spreading. Most of the existing studies assumed that all infected individuals can transmit diseaserelated information or can be perceived by their neighbors. However, owing to lack of distinct symptoms for patients in the initial stage of infection, the disease information cannot be transmitted in the population, which may lead to the wrong perception of infection risk and inappropriate behavior response. In this work, we divide infected individuals into Exposed-state (without obvious clinical symptoms) individuals and Infected-state (with evident clinical symptoms) individuals, both of whom can spread disease, but only Infected-state individuals can diffuse disease information. Then, in this work we establish UAU-SEIS (Unaware-Aware-Unaware-Susceptible-Exposed-Infected-Susceptible) model in multiplex networks and analyze the effect of asymptomatic infection and the isolation of Infected-state individuals on the density of infection and the epidemic threshold. Furthermore, we extend the UAU-SEIS model by taking the individual heterogeneity into consideration. Combined Markov chain approach and Monte-Carlo Simulations, we find that asymptomatic infection has an effect on the density of infected individuals and the epidemic threshold, and the extent of the effect is influenced by whether Infected-state individuals are isolated or treated. In addition, results show that the individual heterogeneity can lower the density of infected individuals, but cannot enhance the epidemic threshold.

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PurposeOne challenge for tourism recommendation systems (TRSs) is the long-tail phenomenon of ratings or popularity among tourist products. This paper aims to improve the diversity and efficiency of TRSs utilizing the power-law distribution of long-tail data.Design/methodology/approachUsing Sina Weibo check-in data for example, this paper demonstrates that the long-tail phenomenon exists in user travel behaviors and fits the long-tail travel data with power-law distribution. To solve data sparsity in the long-tail part and increase recommendation diversity of TRSs, the paper proposes a collaborative filtering (CF) recommendation algorithm combining with power-law distribution. Furthermore, by combining power-law distribution with locality sensitive hashing (LSH), the paper optimizes user similarity calculation to improve the calculation efficiency of TRSs.FindingsThe comparison experiments show that the proposed algorithm greatly improves the recommendation diversity and calculation efficiency while maintaining high precision and recall of recommendation, providing basis for further dynamic recommendation.Originality/valueTRSs provide a better solution to the problem of information overload in the tourism field. However, based on the historical travel data over the whole population, most current TRSs tend to recommend hot and similar spots to users, lacking in diversity and failing to provide personalized recommendations. Meanwhile, the large high-dimensional sparse data in online social networks (OSNs) brings huge computational cost when calculating user similarity with traditional CF algorithms. In this paper, by integrating the power-law distribution of travel data and tourism recommendation technology, the authors’ work solves the problem existing in traditional TRSs that recommendation results are overly narrow and lack in serendipity, and provides users with a wider range of choices and hence improves user experience in TRSs. Meanwhile, utilizing locality sensitive hash functions, the authors’ work hashes users from high-dimensional vectors to one-dimensional integers and maps similar users into the same buckets, which realizes fast nearest neighbors search in high-dimensional space and solves the extreme sparsity problem of high dimensional travel data. Furthermore, applying the hashing results to user similarity calculation, the paper greatly reduces computational complexity and improves calculation efficiency of TRSs, which reduces the system load and enables TRSs to provide effective and timely recommendations for users.

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