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Abstract Efficient utilization of limited resources is crucial in controlling disease outbreaks. Usually, in the process of disease control, medical resources are either controlled globally by the government or allocated locally among individuals. Here, to explore systematically which of the two strategies is more efficient in suppressing the outbreaks of disease, a hybrid strategy is proposed, in which, a tunable parameter is introduced to tune the preference of global and local resource allocation. By studying the interplay between the resource allocation and disease spreading based on a generalized susceptible–infected–susceptible (SIS) model, we show that the global resource allocation has more advantages in controlling disease than local allocation. Besides, the hybrid resource allocation has significant influence on the dynamics of disease spreading. There is first order phase transition of the final infected fraction of nodes on homogeneous networks, however, the transition type changes from hybrid transitions to first order transition at a critical value of the tunable parameter on heterogeneous networks. When considering the initial conditions, hysteresis loops appear on both homogeneous and heterogeneous networks. Using mean-field approximation and a generalized dynamical message passing (GDMP) approach, we calculate exactly the fraction of infected nodes at the steady state, as well as the epidemic thresholds and the phase diagram of the disease on the homogeneous networks and heterogeneous networks respectively. Highlights • We propose a hybrid resource allocation model in suppressing the disease spreading. • The more globally the resources are allocated, the more efficiently the disease can be suppressed. • The strategy of resource allocation can alter the phase transition on heterogeneous networks. • Hysteresis loops appear on both homogeneous and heterogeneous networks. [ABSTRACT FROM AUTHOR]

Abstract Researches about complex contagions on complex networks always neglect the reinforcement effect from different layers and neighbors simultaneously. In this paper we propose a non-Markovian model to describe complex contagions in which a susceptible node becoming adopted must take the social reinforcement from different layers and neighbors into consideration. Through extensive numerical simulations we find that the final adoption size will increase sharply with the information transmission probability at a large adoption threshold. In addition, for small values of adoption threshold, a few seeds could trigger a global contagion. However, there is a critical seed size below which the global contagion becomes impossible for large values of adoption threshold. Besides that, we develop an edge-based compartmental (EBC) theory to describe the proposed model, and it agrees well with numerical simulations. Highlights • Proposing a non-Markovian social contagion model on multiplex networks. • The final adoption size increases sharply with information transmission probability at a large adoption threshold. • There is a critical seed size below which the global contagion becomes impossible for large value of adoption threshold. • An edge-based compartmental theory is developed. [ABSTRACT FROM AUTHOR]

Abstract An individual's credibility is strongly affected by their social status. Assuming that a person's level of credibility correlates with their degree from a microscopic perspective, we propose a non-Markovian model to understand how the heterogeneity of credibility levels affects social contagions within a population. To describe the model, we develop a heterogeneous edge-based compartmental theory. Through extensive numerical simulations, we find that the growth pattern of the final adoption size versus the information transmission probability is discontinuous, and that in ER networks the final adoption size increases when hubs have high levels of credibility. When hubs in an ER network have low levels of credibility, the growth pattern is continuous. We also study social contagions on SF networks and find that the growth pattern versus information transmission probability is always continuous. On both ER and SF networks, the final adoption size versus the heterogeneity parameter exhibits a discontinuous pattern. The results of our theory agree well with those of numerical simulations. Highlights • Proposed a non-Markovian model to understand how the heterogeneity of credibility from a microscopic perspective. • The growth pattern of the final adoption size is continuous when hubs in an ER network have low levels of credibility. • The growth pattern versus information transmission probability is always continuous on SF networks. • On both ER and SF networks, the final adoption size versus the heterogeneity parameter exhibits a discontinuous pattern. [ABSTRACT FROM AUTHOR]

One of the most important problems in complex network is the identification of the influential nodes. For this purpose, the use of differences and similarities of structure to enrich the centrality method in complex networks is proposed. The centrality method called ECDS centrality used is the eigen-centrality which is based on the Jaccard similarities between the two random nodes. This can be described by an eigenvalues problem. Here, we use a tunable parameter α to adjust the influence of the differences and similarities. Comparing with the results of the Susceptible Infected Recovered (SIR) model for four real networks, the ECDS centrality could identify influential nodes more accurately than the tradition centralities such as the k -shell, degree and closeness centralities. Especially, in the Erdös network, the Kendall’s tau could be reached to 0.93 when the spreading rate is 0.12. In the US airline network, the Kendall’s tau could be reached to 0.95 when the spreading rate is 0.06. [ABSTRACT FROM AUTHOR]