Dynamical vaccination behavior with risk perception and vaccination rewards.

Vaccination is the most effective way to control the epidemic spreading. However, the probability of people getting vaccinated changes with the epidemic situation due to personal psychology. Facing various risks, some people are reluctant to vaccinate and even prefer herd immunity. To encourage people to get vaccinated, many countries set up reward mechanisms. In this paper, we propose a disease transmission model combining vaccination behaviors based on the SIR (Susceptible-Infected-Recovered) model and introduce three vaccination mechanisms. We analyze the impact of the infection rate and the recovery rate on the total cost and the epidemic prevalence. Numerical simulations fit with our intuitive feelings. Then, we study the impact of vaccination rewards on the total social cost. We find that when vaccination rewards offset vaccination costs, both the total cost and the epidemic prevalence reach the lowest levels. Finally, this paper suggests that encouraging people to get vaccinated at the beginning of an epidemic has the best effect.

Stepwise reconstruction of higher-order networks from dynamics.

Higher-order networks present great promise in network modeling, analysis, and control. However, reconstructing higher-order interactions remains an open problem. A significant challenge is the exponential growth in the number of potential interactions that need to be modeled as the maximum possible node number in an interaction increases, making the reconstruction exceedingly difficult. For higher-order networks, where higher-order interactions exhibit properties of lower-order dependency and weaker or fewer higher-order connections, we develop a reconstruction scheme integrating a stepwise strategy and an optimization technique to infer higher-order networks from time series. This approach significantly reduces the potential search space for higher-order interactions. Simulation experiments on a wide range of networks and dynamical systems demonstrate the effectiveness and robustness of our method.

Critical behaviors of nonlinear contagion models with recurrent mobility patterns.

Recently, there has been a lot of discussion about the nonlinearity property of contagion processes in epidemic spreading on social networks with various structures. In this paper, we propose a nonlinear contagion model in networked metapopulations to investigate the critical behavior of epidemics with recurrent mobility patterns. First, we build up a discrete-time Markovian chain model to formulate the spreading of susceptible-infected-susceptible-like diseases. Additionally, we develop a practicable framework to analyze the impact of mobility on the epidemic threshold and derive the theoretical condition for the transition of an epidemic from a local to a global scale. This transition is associated with multiple discontinuous phase changes. We validate our analytical results through extensive numerical simulations on both regular and heterogeneous networks. Our findings offer a useful tool to discuss the implementation of prevention strategies such as quarantine and lockdown.

Occurrence of super-diffusion in two-layer networks.

Super-diffusion is a phenomenon that can be observed in multilayer networks, which describes that the diffusion in a multilayer network is faster than that in the fastest individual layer. In most studies of super-diffusion on two-layer networks, many researchers have focused on the overlap of edges in the two layers and the mode of interlayer connectivity. We discover that the occurrence of super-diffusion in two-layer networks is not necessarily related to the overlap degree. In particular, in a two-layer network, sparse topological structures of individual layers are more beneficial to the occurrence of super-diffusion than dense topological structures. Additionally, similar diffusion abilities of both layers favor super-diffusion. The density of interlayer edges and interlayer connection patterns also influence the occurrence of super-diffusion. This paper offers suggestions to improve the diffusion ability in two-layer networks, which can facilitate the selection of practical information transmission paths between different systems and optimize the design of the internal framework of a company composed of multiple departments.

Constructing In2S3/CdS/N-rGO Hybrid Nanosheets via One-Pot Pyrolysis for Boosting and Stabilizing Visible Light-Driven Hydrogen Evolution.

The construction of hybrid junctions remains challenging for the rational design of visible light-driven photocatalysts. Herein, In2S3/CdS/N-rGO hybrid nanosheets were successfully prepared via a one-step pyrolysis method using deep eutectic solvents as precursors. Benefiting from the surfactant-free pyrolysis method, the obtained ultrathin hybrid nanosheets assemble into stable three-dimensional self-standing superstructures. The tremella-like structure of hybrid In2S3/N-rGO exhibits excellent photocatalytic hydrogen production performance. The hydrogen evolution rate is 10.9 mmol·g-1·h-1, which is greatly superior to CdS/N-rGO (3.7 mmol·g-1·h-1) and In2S3/N-rGO (2.6 mmol·g-1·h-1). This work provides more opportunities for the rational design and fabrication of hybrid ultrathin nanosheets for broad catalytic applications in sustainable energy and the environment.

Identifying partial topology of simplicial complexes.

This paper investigates partial topology identification of simplicial complexes based on adaptive synchronization. For the nodes of interest, the interactions that they participate in can be accurately reconstructed by designing adaptive controllers and parameter estimators. Particularly, not only pairwise interactions but a higher-order structure can be effectively recovered by our method. Moreover, a new linear independence condition with a rigorous definition is established for parameter estimators to converge asymptotically to the true values. Numerical simulations on a general two-dimensional simplicial complex as well as a real-world structure are provided to show the validity of the result and discuss the influence of different parameters on the identification process.

A model for analyzing competitive dynamics on triplex networks.

This paper studies the evolution process of competitive dynamics on triplex complex networks. We propose a new triplex network model in which the state of the node in each layer is affected by its neighbors as well as inter-layer competition. Through this model, we combine the opinion diffusion model, the Ising model, and the signed network and extend their application from single-layer to multi-layer networks. We derive the evolution process and dynamical equations of the model and carry out a series of numerical simulations to discuss the influence of several factors on the evolution process and the competitiveness of the network. First, we find that the increase of global transition threshold p or the proportion of initial active nodes will lead to more surviving layers and more active nodes in each layer. In addition, we summarize the similarities and differences of the evolution curves under different conditions. Second, we discuss the influence of initial active nodes and the average degree on the competitiveness of the network and find the correlations between them. Finally, we study the relationship between network topology and network competitiveness and conclude the conditions for the best competitiveness of the network. Based on the simulation results, we give specific suggestions on how to improve the competitiveness of the platform in reality.

Maximizing synchronizability of networks with community structure based on node similarity.

In reality, numerous networks have a community structure characterized by dense intra-community connections and sparse inter-community connections. In this article, strategies are proposed to enhance synchronizability of such networks by rewiring a certain number of inter-community links, where the research scope is complete synchronization on undirected and diffusively coupled dynamic networks. First, we explore the effect of adding links between unconnected nodes with different similarity levels on network synchronizability and find that preferentially adding links between nodes with lower similarity can improve network synchronizability more than that with higher similarity, where node similarity is measured by our improved Asymmetric Katz (AKatz) and Asymmetric Leicht-Holme-Newman (ALHNII) methods from the perspective of link prediction. Additional simulations demonstrate that the node similarity-based link-addition strategy is more effective in enhancing network synchronizability than the node centrality-based methods. Furthermore, we apply the node similarity-based link-addition or deletion strategy as the valid criteria to the rewiring process of inter-community links and then propose a Node Similarity-Based Rewiring Optimization (NSBRO) algorithm, where the optimization process is realized by a modified simulated annealing technique. Simulations show that our proposed method performs better in optimizing synchronization of such networks compared with other centrality-based heuristic methods. Finally, simulations on the Rössler system indicate that the network structure optimized by the NSBRO algorithm also leads to better synchronizability of coupled oscillators.

Topology identification of fractional-order complex dynamical networks based on auxiliary-system approach.

Many practical systems can be well described by various fractional-order equations. This paper focuses on identifying the topology of the response layer of a drive-response fractional-order complex dynamical network using the auxiliary-system approach. Specifically, the response layer and the auxiliary layer receive the same input signals from the drive layer. By a designed adaptive control law, the unknown topology of the response layer is successfully identified. Moreover, the proposed method is effective even if the drive layer is made up of isolated nodes. The correctness of the theoretical results is demonstrated by numerical simulations.

Synchronizability of double-layer dumbbell networks.

Synchronization of multiplex networks has been a topical issue in network science. Dumbbell networks are very typical structures in complex networks which are distinguished from both regular star networks and general community structures, whereas the synchronous dynamics of a double-layer dumbbell network relies on the interlink patterns between layers. In this paper, two kinds of double-layer dumbbell networks are defined according to different interlayer coupling patterns: one with the single-link coupling pattern between layers and the other with the two-link coupling pattern between layers. Furthermore, the largest and smallest nonzero eigenvalues of the Laplacian matrix are calculated analytically and numerically for the single-link coupling pattern and also obtained numerically for the two-link coupling pattern so as to characterize the synchronizability of double-layer dumbbell networks. It is shown that interlayer coupling patterns have a significant impact on the synchronizability of multiplex systems. Finally, a numerical example is provided to verify the effectiveness of theoretical analysis. Our findings can facilitate company managers to select optimal interlayer coupling patterns and to assign proper parameters in terms of improving the efficiency and reducing losses of the whole team.

Synchronizability of two-layer correlation networks.

This study investigates the synchronizability of a typical type of two-layer correlation networks formed by two regular networks interconnected with two interlayer linking patterns, namely, positive correlation (PC) and negative correlation (NC). To analyze the network's stability, we consider the analytical expressions of the smallest non-zero and largest eigenvalues of the (weighted) Laplacian matrix as well as the linking strength and the network size for two linking patterns. According to the master stability function, the linking patterns, the linking strength, and the network size associated with two typical synchronized regions exhibit a profound influence on the synchronizability of the two-layer networks. The NC linking pattern displays better synchronizability than the PC linking pattern with the same set of parameters. Furthermore, for the two classical synchronized regions, the networks have optimal intralayer and interlayer linking strengths that maximize the synchronizability while minimizing the required cost. Finally, numerical results verify the validity of the theoretical analyses. The findings based on the representative two-layer correlation networks provide the basis for maximizing the synchronizability of general multiplex correlation networks.

A new SAIR model on complex networks for analysing the 2019 novel coronavirus (COVID-19).

Nowadays, the novel coronavirus (COVID-19) is spreading around the world and has attracted extremely wide public attention. From the beginning of the outbreak to now, there have been many mathematical models proposed to describe the spread of the pandemic, and most of them are established with the assumption that people contact with each other in a homogeneous pattern. However, owing to the difference of individuals in reality, social contact is usually heterogeneous, and the models on homogeneous networks cannot accurately describe the outbreak. Thus, we propose a susceptible-asymptomatic-infected-removed (SAIR) model on social networks to describe the spread of COVID-19 and analyse the outbreak based on the epidemic data of Wuhan from January 24 to March 2. Then, according to the results of the simulations, we discover that the measures that can curb the spread of COVID-19 include increasing the recovery rate and the removed rate, cutting off connections between symptomatically infected individuals and their neighbours, and cutting off connections between hub nodes and their neighbours. The feasible measures proposed in the paper are in fair agreement with the measures that the government took to suppress the outbreak. Furthermore, effective measures should be carried out immediately, otherwise the pandemic would spread more rapidly and last longer. In addition, we use the epidemic data of Wuhan from January 24 to March 2 to analyse the outbreak in the city and explain why the number of the infected rose in the early stage of the outbreak though a total lockdown was implemented. Moreover, besides the above measures, a feasible way to curb the spread of COVID-19 is to reduce the density of social networks, such as restricting mobility and decreasing in-person social contacts. This work provides a series of effective measures, which can facilitate the selection of appropriate approaches for controlling the spread of the COVID-19 pandemic to mitigate its adverse impact on people's livelihood, societies and economies.

Cluster synchronization: From single-layer to multi-layer networks.

Cluster synchronization is a very common phenomenon occurring in single-layer complex networks, and it can also be observed in many multilayer networks in real life. In this paper, we study cluster synchronization of an isolated network and then focus on that of the network when it is influenced by an external network. We mainly explore how the influence layer impacts the cluster synchronization of the interest layer in a multilayer network. Considering that the clusters are changeable, we introduce a term called "cluster synchronizability" to measure the ability of a network to reach cluster synchronization. Since cluster synchronizability is intimately associated with the structure of the coupled external layer, we consider community networks and networks with different densities as the coupled layer. Besides the topology structure, the connection between two layers may also have an influence on the cluster synchronization of the interest layer. We study three different patterns of connection, including typical positive correlation, negative correlation, and random correlation and find that they all have a certain influence. However, the general theoretical analysis of cluster synchronization on multilayer networks is still a challenging topic. In this paper, we mainly use numerical simulations to discuss cluster synchronization.

Compressive sensing-based topology identification of multilayer networks.

Recovering network topologies is of great significance in the study of complex networks. In this paper, a method for identifying structures of multilayer networks is proposed via compressive sensing and Taylor expansion. By using this method, the topologies of multilayer networks with unknown node dynamical functions can be identified from a relatively small number of observations. Numerical experiments are provided to show the effectiveness and efficiency of the method on different types of multilayer networks, where the intralayer topology and the interlayer topology of a multilayer network can be identified simultaneously. In particular, the topology of one layer can be identified even when nodes of the other layer are unobservable.

Phase synchronization on spatially embedded duplex networks with total cost constraint.

Synchronization on multiplex networks has attracted increasing attention in the past few years. We investigate collective behaviors of Kuramoto oscillators on single layer and duplex spacial networks with total cost restriction, which was introduced by Li et al. [Phys. Rev. Lett. 104, 018701 (2010)] and termed as the Li network afterwards. We first explore how the topology of the network influences synchronizability of Kuramoto oscillators on single layer Li networks and find that the closer the Li network is to a regular lattice, the more difficult for it to evolve into synchronization. Then, we investigate synchronizability of duplex Li networks and find that the existence of inter-layer interaction can greatly enhance inter-layer and global synchronizability. When the inter-layer coupling strength is larger than a certain critical value, inter-layer synchronization will always occur. Furthermore, on single layer Li networks, nodes with larger degrees reach global synchronization more easily than those with smaller degrees, while on duplex Li networks, due to inter-layer interaction, this phenomenon becomes much less obvious. The results are important for us to gain insight into collective behaviors of many real-world complex systems which inherently possess multiplex architecture.

Maximizing synchronizability of duplex networks.

We study the synchronizability of duplex networks formed by two randomly generated network layers with different patterns of interlayer node connections. According to the master stability function, we use the smallest nonzero eigenvalue and the eigenratio between the largest and the second smallest eigenvalues of supra-Laplacian matrices to characterize synchronizability on various duplexes. We find that the interlayer linking weight and linking fraction have a profound impact on synchronizability of duplex networks. The increasingly large inter-layer coupling weight is found to cause either decreasing or constant synchronizability for different classes of network dynamics. In addition, negative node degree correlation across interlayer links outperforms positive degree correlation when most interlayer links are present. The reverse is true when a few interlayer links are present. The numerical results and understanding based on these representative duplex networks are illustrative and instructive for building insights into maximizing synchronizability of more realistic multiplex networks.

The 3-cycle weighted spectral distribution in evolving community-based networks.

One of the main organizing principles in real-world networks is that of network communities, where sets of nodes organize into densely linked clusters. Many of these community-based networks evolve over time, that is, we need some size-independent metrics to capture the connection relationships embedded in these clusters. One of these metrics is the average clustering coefficient, which represents the triangle relationships between all nodes of networks. However, the vast majority of network communities is composed of low-degree nodes. Thus, we should further investigate other size-independent metrics to subtly measure the triangle relationships between low-degree nodes. In this paper, we study the 3-cycle weighted spectral distribution (WSD) defined as the weighted sum of the normalized Laplacian spectral distribution with a scaling factor n, where n is the network size (i.e., the node number). Using some diachronic community-based network models and real-world networks, we demonstrate that the ratio of the 3-cycle WSD to the network size is asymptotically independent of the network size and strictly represents the triangle relationships between low-degree nodes. Additionally, we find that the ratio is a good indicator of the average clustering coefficient in evolving community-based systems.

Cooperative spreading processes in multiplex networks.

This study is concerned with the dynamic behaviors of epidemic spreading in multiplex networks. A model composed of two interacting complex networks is proposed to describe cooperative spreading processes, wherein the virus spreading in one layer can penetrate into the other to promote the spreading process. The global epidemic threshold of the model is smaller than the epidemic thresholds of the corresponding isolated networks. Thus, global epidemic onset arises in the interacting networks even though an epidemic onset does not arise in each isolated network. Simulations verify the analysis results and indicate that cooperative spreading processes in multiplex networks enhance the final infection fraction.

Correlation between weighted spectral distribution and average path length in evolving networks.

The weighted spectral distribution (WSD) is a metric defined on the normalized Laplacian spectrum. In this study, synchronic random graphs are first used to rigorously analyze the metric's scaling feature, which indicates that the metric grows sublinearly as the network size increases, and the metric's scaling feature is demonstrated to be common in networks with Gaussian, exponential, and power-law degree distributions. Furthermore, a deterministic model of diachronic graphs is developed to illustrate the correlation between the slope coefficient of the metric's asymptotic line and the average path length, and the similarities and differences between synchronic and diachronic random graphs are investigated to better understand the correlation. Finally, numerical analysis is presented based on simulated and real-world data of evolving networks, which shows that the ratio of the WSD to the network size is a good indicator of the average path length.

An Unmanned Aerial Vehicle-Mounted Cold Mist Spray of Permethrin and Tetramethylfluthrin Targeting Aedes albopictus in China.

Aedes albopictus is the primary vector of dengue fever and dengue hemorrhagic fever in China. Although there are previous studies on the application of adulticides to control this species, the application methods have either been back-pack or vehicle-mounted systems. However, many sites are too large to be effectively treated with back-pack sprayers, and the lack of roads restricts the use of vehicle-mounted sprayers. This paper provides the first study of using unmanned aerial vehicles to conduct cold mist sprays on Ae. albopictus habitats. A spray containing 4% permethrin and 1% tetramethylfluthrin was applied at an effective application rate of 9.0 mg/m(2). This method reduced Ae. albopictus populations by more than 90%. The results indicate this novel spray system is a powerful method to achieve a rapid decline of mosquito population in Ae. albopictus habitats in China.