Coevolution spreading in complex networks

Neuronal activity induces symmetry breaking in neurodegenerative disease spreading

Dynamical systems on networks typically involve several dynamical processes evolving at different timescales. For instance, in Alzheimer's disease, the spread of toxic protein throughout the brain not only disrupts neuronal activity but is also influenced by neuronal activity itself, establishing a feedback loop between the fast neuronal activity and the slow protein spreading. Motivated by the case of Alzheimer's disease, we study the multiple-timescale dynamics of a heterodimer spreading process on an adaptive network of Kuramoto oscillators. Using a minimal two-node model, we establish that heterogeneous oscillatory activity facilitates toxic outbreaks and induces symmetry breaking in the spreading patterns. We then extend the model formulation to larger networks and perform numerical simulations of the slow-fast dynamics on common network motifs and on the brain connectome. The simulations corroborate the findings from the minimal model, underscoring the significance of multiple-timescale dynamics in the modeling of neurodegenerative diseases.

Scalable parallel and distributed simulation of an epidemic on a graph

We propose an algorithm to simulate Markovian SIS epidemics with homogeneous rates and pairwise interactions on a fixed undirected graph, assuming a distributed memory model of parallel programming and limited bandwidth. This setup can represent a broad class of simulation tasks with compartmental models. Existing solutions for such tasks are sequential by nature. We provide an innovative solution that makes trade-offs between statistical faithfulness and parallelism possible. We offer an implementation of the algorithm in the form of pseudocode in the Appendix. Also, we analyze its algorithmic complexity and its induced dynamical system. Finally, we design experiments to show its scalability and faithfulness. In our experiments, we discover that graph structures that admit good partitioning schemes, such as the ones with clear community structures, together with the correct application of a graph partitioning method, can lead to better scalability and faithfulness. We believe this algorithm offers a way of scaling out, allowing researchers to run simulation tasks at a scale that was not accessible before. Furthermore, we believe this algorithm lays a solid foundation for extensions to more advanced epidemic simulations and graph dynamics in other fields.

Characteristic analysis of epileptic brain network based on attention mechanism

Constructing an efficient and accurate epilepsy detection system is an urgent research task. In this paper, we developed an EEG-based multi-frequency multilayer brain network (MMBN) and an attentional mechanism based convolutional neural network (AM-CNN) model to study epilepsy detection. Specifically, based on the multi-frequency characteristics of the brain, we first use wavelet packet decomposition and reconstruction methods to divide the original EEG signals into eight frequency bands, and then construct MMBN through correlation analysis between brain regions, where each layer corresponds to a specific frequency band. The time, frequency and channel related information of EEG signals are mapped into the multilayer network topology. On this basis, a multi-branch AM-CNN model is designed, which completely matches the multilayer structure of the proposed brain network. The experimental results on public CHB-MIT datasets show that eight frequency bands divided in this work are all helpful for epilepsy detection, and the fusion of multi-frequency information can effectively decode the epileptic brain state, achieving accurate detection of epilepsy with an average accuracy of 99.75%, sensitivity of 99.43%, and specificity of 99.83%. All of these provide reliable technical solutions for EEG-based neurological disease detection, especially for epilepsy detection.

Interlayer Link Prediction in Multiplex Social Networks Based on Multiple Types of Consistency Between Embedding Vectors

Online users are typically active on multiple social media networks (SMNs), which constitute a multiplex social network. With improvements in cybersecurity awareness, users increasingly choose different usernames and provide different profiles on different SMNs. Thus, it is becoming increasingly challenging to determine whether given accounts on different SMNs belong to the same user; this can be expressed as an interlayer link prediction problem in a multiplex network. To address the challenge of predicting interlayer links, feature or structure information is leveraged. Existing methods that use network embedding techniques to address this problem focus on learning a mapping function to unify all nodes into a common latent representation space for prediction; positional relationships between unmatched nodes and their common matched neighbors (CMNs) are not utilized. Furthermore, the layers are often modeled as unweighted graphs, ignoring the strengths of the relationships between nodes. To address these limitations, we propose a framework based on multiple types of consistency between embedding vectors (MulCEVs). In MulCEV, the traditional embedding-based method is applied to obtain the degree of consistency between the vectors representing the unmatched nodes, and a proposed distance consistency index based on the positions of nodes in each latent space provides additional clues for prediction. By associating these two types of consistency, the effective information in the latent spaces is fully utilized. In addition, MulCEV models the layers as weighted graphs to obtain representation. In this way, the higher the strength of the relationship between nodes, the more similar their embedding vectors in the latent representation space will be. The results of our experiments on several real-world and synthetic datasets demonstrate that the proposed MulCEV framework markedly outperforms current embedding-based methods, especially when the number of training iterations is small.

Impact of random and targeted disruptions on information diffusion during outbreaks

Outbreaks are complex multi-scale processes that are impacted not only by cellular dynamics and the ability of pathogens to effectively reproduce and spread, but also by population-level dynamics and the effectiveness of mitigation measures. A timely exchange of information related to the spread of novel pathogens, stay-at-home orders, and other measures can be effective at containing an infectious disease, particularly during the early stages when testing infrastructure, vaccines, and other medical interventions may not be available at scale. Using a multiplex epidemic model that consists of an information layer (modeling information exchange between individuals) and a spatially embedded epidemic layer (representing a human contact network), we study how random and targeted disruptions in the information layer (e.g., errors and intentional attacks on communication infrastructure) impact the total proportion of infections, peak prevalence (i.e., the maximum proportion of infections), and the time to reach peak prevalence. We calibrate our model to the early outbreak stages of the SARS-CoV-2 pandemic in 2020. Mitigation campaigns can still be effective under random disruptions, such as failure of information channels between a few individuals. However, targeted disruptions or sabotage of hub nodes that exchange information with a large number of individuals can abruptly change outbreak characteristics, such as the time to reach the peak of infection. Our results emphasize the importance of the availability of a robust communication infrastructure during an outbreak that can withstand both random and targeted disruptions.

Impact of contact rate on epidemic spreading in complex networks

Abstract

Contact reduction is an effective strategy to mitigate the spreading of epidemic. However, the existing reaction-diffusion equations for infectious disease are unable to characterize this effect. Thus, we here propose an extended susceptible-infected-recovered model by incorporating contact rate into the standard SIR model, and concentrate on investigating its impact on epidemic transmission. We analytically derive the epidemic thresholds on homogeneous and heterogeneous networks, respectively. The effects of contact rate on spreading speed, scale and outbreak threshold are explored on ER and SF networks. Simulations results show that epidemic dissemination is significantly mitigated when contact rate is reduced. Importantly, epidemic spreads faster on heterogeneous networks while broader on homogeneous networks, and the outbreak thresholds of the former are smaller.

Graphical abstract

Research on the co-evolution of temporal networks structure and public opinion propagation

Under the new media environment, social platforms, as the carrier of information propagation, have shown a drastic change in their form and structure, endowing public opinion with unique propagation characteristics. In view of this, considering the dynamic changes of online social network (OSN) structure, this article intends to analyse the spreading mechanism of public opinion in temporal networks and improve the applicability of public opinion governance strategies. Combing the changes of OSN topology with the classical susceptible–infected–recovered (SIR) dynamics model, we constructed a co-evolution model of temporal networks structure and public opinion propagation, and the propagation threshold of public opinion was derived with the help of Markov process. Then, the propagation characteristics of public opinion in temporal networks and their co-evolution process under different factors were discussed through simulation experiments. The results show that the propagation of public opinion in temporal networks has faster speed and wider scope compared with that in static networks; netizens’ social activity has a phased impact on the evolution process of public opinion and with its significant heterogeneity, the propagation of public opinion is gradually suppressed; compared with [Formula: see text], the evolution process of public opinion in temporal networks is more sensitive to the state change of public opinion [Formula: see text]. Our research can further enrich the theoretical research system of network science and information science and also provide a certain decision-making reference for the regulators to reasonably govern the propagation of public opinion in social platforms.

Synergistic epidemic spreading in correlated networks

We investigate the effect of degree correlation on a susceptible-infected-susceptible (SIS) model with a nonlinear cooperative effect (synergy) in infectious transmissions. In a mean-field treatment of the synergistic SIS model on a bimodal network with tunable degree correlation, we identify a discontinuous transition that is independent of the degree correlation strength unless the synergy is absent or extremely weak. Regardless of synergy (absent or present), a positive and negative degree correlation in the model reduces and raises the epidemic threshold, respectively. For networks with a strongly positive degree correlation, the mean-field treatment predicts the emergence of two discontinuous jumps in the steady-state infected density. To test the mean-field treatment, we provide approximate master equations of the present model. We quantitatively confirm that the approximate master equations agree with not only all qualitative predictions of the mean-field treatment but also corresponding Monte Carlo simulations.

Two competing simplicial irreversible epidemics on simplicial complex

Higher-order interactions have significant implications for the dynamics of competing epidemic spreads. In this paper, a competing spread model for two simplicial irreversible epidemics (i.e., susceptible-infected-removed epidemics) on higher-order networks is proposed. The simplicial complexes are based on synthetic (including homogeneous and heterogeneous) and real-world networks. The spread process of two epidemics is theoretically analyzed by extending the microscopic Markov chain approach. When the two epidemics have the same 2-simplex infection rate and the 1-simplex infection rate of epidemic A ( _λ) is fixed at zero, an increase in the 1-simplex infection rate of epidemic B ( _λ) causes a transition from continuous growth to sharp growth in the spread of epidemic B with _λ. When _λ > 0, the growth of epidemic B is always continuous. With the increase of _λ, the outbreak threshold of epidemic B is delayed. When the difference in 1-simplex infection rates between the two epidemics reaches approximately three times, the stronger side obviously dominates. Otherwise, the coexistence of the two epidemics is always observed. When the 1-simplex infection rates are symmetrical, the increase in competition will accelerate the spread process and expand the spread area of both epidemics; when the 1-simplex infection rates are asymmetrical, the spread area of one epidemic increases with an increase in the 1-simplex infection rate from this epidemic while the other decreases. Finally, the influence of 2-simplex infection rates on the competing spread is discussed. An increase in 2-simplex infection rates leads to sharp growth in one of the epidemics.

The effect of information-driven resource allocation on the propagation of epidemic with incubation period

In the pandemic of COVID-19, there are exposed individuals who are infected but lack distinct clinical symptoms. In addition, the diffusion of related information drives aware individuals to spontaneously seek resources for protection. The special spreading characteristic and coevolution of different processes may induce unexpected spreading phenomena. Thus we construct a three-layered network framework to explore how information-driven resource allocation affects SEIS (susceptible-exposed-infected-susceptible) epidemic spreading. The analyses utilizing microscopic Markov chain approach reveal that the epidemic threshold depends on the topology structure of epidemic network and the processes of information diffusion and resource allocation. Conducting extensive Monte Carlo simulations, we find some crucial phenomena in the coevolution of information diffusion, resource allocation and epidemic spreading. Firstly, when E-state (exposed state, without symptoms) individuals are infectious, long incubation period results in more E-state individuals than I-state (infected state, with obvious symptoms) individuals. Besides, when E-state individuals have strong or weak infectious capacity, increasing incubation period has an opposite effect on epidemic propagation. Secondly, the short incubation period induces the first-order phase transition. But enhancing the efficacy of resources would convert the phase transition to a second-order type. Finally, comparing the coevolution in networks with different topologies, we find setting the epidemic layer as scale-free network can inhibit the spreading of the epidemic.

Emotional Contagion in Physical-Cyber Integrated Networks: The Phase Transition Perspective

Understanding the emotional contagion process in the crowd will help to take measures in advance to avoid the large-scale spread of negative emotions in emergencies and reduce the loss of lives and properties. Studying the phase transition phenomenon is fundamental to analyzing and evaluating the crowd emotional contagion. However, it is a challenging issue since most people participate in both the physical and cyber networks at the same time. In this article, we focus on the emotional contagion in physical-cyber integrated networks from the phase transition perspective. To achieve this, we first construct a physical-cyber integrated network model to describe the interactions between physical and cyber networks. Second, we build an emotional contagion model to capture the characteristics of emotional contagion in the physical and cyber integrated networks accurately. Finally, we study the phase transition phenomenon of emotional contagion and identify the critical threshold by mapping the emotional contagion to the joint site/bond percolation model. Numerical simulations and experiments further support and enrich our conclusions. The proposed method is expected to provide guidance for controlling emotional contagion in emergencies.

Heterogeneous mean-field theory for two-species symbiotic processes on networks

A simple model to study cooperation is the two-species symbiotic contact process (2SCP), in which two different species spread on a graph and interact by a reduced death rate if both occupy the same vertex, representing a symbiotic interaction. The 2SCP is known to exhibit a complex behavior with a rich phase diagram, including continuous and discontinuous transitions between the active phase and extinction. In this work, we advance the understanding of the phase transition of the 2SCP on uncorrelated networks by developing a heterogeneous mean-field (HMF) theory, in which the heterogeneity of contacts is explicitly reckoned. The HMF theory for networks with power-law degree distribution shows that the region of bistability (active and inactive phases) in the phase diagram shrinks as the heterogeneity level is increased by reducing the degree exponent. Finite-size analysis reveals a complex behavior where a pseudodiscontinuous transition at a finite size can be converted into a continuous one in the thermodynamic limit, depending on degree exponent and symbiotic coupling. The theoretical results are supported by extensive numerical simulations.

The effect of information literacy heterogeneity on epidemic spreading in information and epidemic coupled multiplex networks

With the COVID-19 pandemic, better understanding of the co-evolution of information and epidemic diffusion networks is important for pandemic-related policies. Using the microscopic Markov chain method, this study proposed an aware-susceptible-infected model (ASI) to explore the effect of information literacy on the spreading process in such multiplex networks. We first introduced a parameter that adjusts the self-protection related execution ability of aware individuals in order to emphasis the importance of protective behaviors compared to awareness in decreasing the infection probability. The model also captures individuals' heterogeneity in their information literacy. Simulation experiments found that the high information-literate individuals are more sensitive to information adoption. In addition, epidemic information can help to suppress the epidemic diffusion only when individuals' abilities of transforming awareness into actual protective behaviors attain a threshold. In communities dominated by highly literate individuals, a larger information literacy gap can improve awareness acquisition and thus help to suppress the epidemic among the whole group. By contrast, in communities dominated by low information-literate individuals, a smaller information literacy gap can better prevent the epidemic diffusion. This study contributes to the literature by revealing the importance of individuals' heterogeneity of information literacy on epidemic spreading in different communities and has implications for how to inform people when a new epidemic disease emerges.

Analysis of the competition among viral strains using a temporal interaction-driven contagion model

The temporal dynamics of social interactions were shown to influence the spread of disease. Here, we model the conditions of progression and competition for several viral strains, exploring various levels of cross-immunity over temporal networks. We use our interaction-driven contagion model and characterize, using it, several viral variants. Our results, obtained on temporal random networks and on real-world interaction data, demonstrate that temporal dynamics are crucial to determining the competition results. We consider two and three competing pathogens and show the conditions under which a slower pathogen will remain active and create a second wave infecting most of the population. We then show that when the duration of the encounters is considered, the spreading dynamics change significantly. Our results indicate that when considering airborne diseases, it might be crucial to consider the duration of temporal meetings to model the spread of pathogens in a population.

Double transition in kinetic exchange opinion models with activation dynamics

In this work, we study a model of opinion dynamics considering activation/deactivation of agents. In other words, individuals are not static and can become inactive and drop out from the discussion. A probability [Formula: see text] governs the deactivation dynamics, whereas social interactions are ruled by kinetic exchanges, considering competitive positive/negative interactions. Inactive agents can become active due to interactions with active agents. Our analytical and numerical results show the existence of two distinct non-equilibrium phase transitions, with the occurrence of three phases, namely ordered (ferromagnetic-like), disordered (paramagnetic-like) and absorbing phases. The absorbing phase represents a collective state where all agents are inactive, i.e. they do not participate in the dynamics, inducing a frozen state. We determine the critical value [Formula: see text] above which the system is in the absorbing phase independently of the other parameters. We also verify a distinct critical behaviour for the transitions among different phases. This article is part of the theme issue 'Kinetic exchange models of societies and economies'.

Epidemics on multilayer simplicial complexes

Simplicial complexes describe the simple fact that in social networks a link can connect more than two individuals. As we show here, this has far-reaching consequences for epidemic spreading, in particular in the context of a multilayer network model, where one layer is a virtual social network and the other one is a physical contact network. The social network layer is responsible for the transmission of information via pairwise or higher order 2-simplex interactions among individuals, while the physical layer is responsible for the epidemic spreading. We use the microscopic Markov chain approach to derive the probability transition equations and to determine epidemic outbreak thresholds. We further support these results with Monte Carlo simulations, which are in good agreement, thus confirming the analytical tractability of the proposed model. We find that information transmission rates are frequently low when actual disease transmission rates in the physical network are low or medium, and we show that this can be mitigated effectively by introducing 2-simplex interactions in the social network. The relative ease of introducing higher-order interactions in virtual social networks means that this could be exploited to inhibit epidemic outbreaks.

Epidemic Dynamics of a Fractional-Order SIR Weighted Network Model and Its Targeted Immunity Control

With outbreaks of epidemics, an enormous loss of life and property has been caused. Based on the influence of disease transmission and information propagation on the transmission characteristics of infectious diseases, in this paper, a fractional-order SIR epidemic model is put forward on a two-layer weighted network. The local stability of the disease-free equilibrium is investigated. Moreover, a conclusion is obtained that there is no endemic equilibrium. Since the elderly and the children have fewer social tiers, a targeted immunity control that is based on age structure is proposed. Finally, an example is presented to demonstrate the effectiveness of the theoretical results. These studies contribute to a more comprehensive understanding of the epidemic transmission mechanism and play a positive guiding role in the prevention and control of some epidemics.

Logistic growth on networks: Exact solutions for the susceptible-infected model

The susceptible-infected (SI) model is the most basic of all compartmental models used to describe the spreading of information through a population. Despite its apparent simplicity, the analytic solution of this model on networks is still lacking. We address this problem here using a novel formulation inspired by the mathematical treatment of many-body quantum systems. This allows us to organize the time-dependent expectation values for the state of individual nodes in terms of contributions from subgraphs of the network. We compute these contributions systematically and find a set of symmetry relations among subgraphs of differing topologies. We use our novel approach to compute the spreading of information on three different sample networks. The exact solution, which matches with Monte Carlo simulations, visibly departs from the mean-field results.

Characterization of Group Behavior of Corruption in Construction Projects Based on Contagion Mechanism

With the rapid development of construction projects, more and more engineering corruption problems have emerged. Therefore, this paper proposes a SEIR (susceptible-exposed-infected-recovered) based corruption model to better understand the propagation process of corruption cases in construction projects. In this model, the data samples are collected from the 2018 Engineering Corruption Case Judgment Document, the propagation parameters are obtained through actual case analysis with the help of complex networks, the change process and key influencing factors of actual nodes in engineering corruption cases are simulated by Python. The study results indicate that the personnel conforms to the “4–9 transmission law,” in which the early stage is a period of high incidence of corruption cases. The network of corruption cases is somewhat vulnerable, and its spread is about minus 8 times the change in crackdown rate and 10 times the change in infection rate. The variation range of the susceptible population S and the removed person R in the propagation simulation curve can predict the relationship between corruption infection rate and crackdown rate, which can provide theoretical guidance for preventing the occurrence of corruption.

Effects of void nodes on epidemic spreads in networks

We present the pair approximation models for susceptible–infected–recovered (SIR) epidemic dynamics in a sparse network based on a regular network. Two processes are considered, namely, a Markovian process with a constant recovery rate and a non-Markovian process with a fixed recovery time. We derive the implicit analytical expression for the final epidemic size and explicitly show the epidemic threshold in both Markovian and non-Markovian processes. As the connection rate decreases from the original network connection, the epidemic threshold in which epidemic phase transits from disease-free to endemic increases, and the final epidemic size decreases. Additionally, for comparison with sparse and heterogeneous networks, the pair approximation models were applied to a heterogeneous network with a degree distribution. The obtained phase diagram reveals that, upon increasing the degree of the original random regular networks and decreasing the effective connections by introducing void nodes accordingly, the final epidemic size of the sparse network is close to that of the random network with average degree of 4. Thus, introducing the void nodes in the network leads to more heterogeneous network and reduces the final epidemic size.

Large deviations of a susceptible-infected-recovered model around the epidemic threshold

We numerically study the dynamics of the SIR disease model on small-world networks by using a large-deviation approach. This allows us to obtain the probability density function of the total fraction of infected nodes and of the maximum fraction of simultaneously infected nodes down to very small probability densities like 10^{-2500}. We analyze the structure of the disease dynamics and observed three regimes in all probability density functions, which correspond to quick mild, quick extremely severe, and sustained severe dynamical evolutions, respectively. Furthermore, the mathematical rate functions of the densities are investigated. The results indicate that the so-called large-deviation property holds for the SIR model. Finally, we measured correlations with other quantities like the duration of an outbreak or the peak position of the fraction of infections, also in the rare regions which are not accessible by standard simulation techniques.

Estimating the state of epidemics spreading with graph neural networks

When an epidemic spreads into a population, it is often impractical or impossible to continuously monitor all subjects involved. As an alternative, we propose using algorithmic solutions that can infer the state of the whole population from a limited number of measures. We analyze the capability of deep neural networks to solve this challenging task. We base our proposed architecture on Graph Convolutional Neural Networks. As such, it can reason on the effect of the underlying social network structure, which is recognized as the main component in spreading an epidemic. The proposed architecture can reconstruct the entire state with accuracy above 70%, as proven by two scenarios modeled on the CoVid-19 pandemic. The first is a generic homogeneous population, and the second is a toy model of the Boston metropolitan area. Note that no retraining of the architecture is necessary when changing the model.

Antivax movement and epidemic spreading in the era of social networks: Nonmonotonic effects, bistability, and network segregation

In this work, we address a multicoupled dynamics on complex networks with tunable structural segregation. Specifically, we work on a networked epidemic spreading under a vaccination campaign with agents in favor and against the vaccine. Our results show that such coupled dynamics exhibits a myriad of phenomena such as nonequilibrium transitions accompanied by bistability. Besides we observe the emergence of an intermediate optimal segregation level where the community structure enhances negative opinions over vaccination but counterintuitively hinders-rather than favoring-the global disease spreading. Thus our results hint vaccination campaigns should avoid policies that end up segregating excessively antivaccine groups so that they effectively work as echo chambers in which individuals look to confirmation without jeopardizing the safety of the whole population.

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.

The combination of targeted vaccination and ring vaccination

Complex networks have become an important tool for investigating epidemic dynamics. A widely concerned research field for epidemics is to develop and study mitigation strategies or control measures. In this paper, we devote our attention to ring vaccination and targeted vaccination and consider the combination of them. Based on the different roles ring vaccination plays in the mixed strategy, the whole parameter space can be roughly divided into two regimes. In one regime, the mixed strategy performs poorly compared with targeted vaccination alone, while in the other regime, the addition of ring vaccination can improve the performance of targeted vaccination. This result gives us the more general and overall comparison between targeted and ring vaccination. In addition, we construct a susceptible-infected-recovered epidemic model coupled with the immunization dynamics on random networks. The comparison between stochastic simulations and numerical simulations confirms the validity of the model we propose.

A toy model for the epidemic-driven collapse in a system with limited economic resource

ABSTRACT

Based on a toy model for a trivial socioeconomic system, we demonstrate that the activation-type mechanism of the epidemic-resource coupling can lead to the collapsing effect opposite to thermal explosion. We exploit a SIS-like (susceptible-infected-susceptible) model coupled with the dynamics of average economic resource for a group of active economic agents. The recovery rate of infected individuals is supposed to obey the Arrhenius-like law, resulting in a mutual negative feedback between the number of active agents and resource acquisition. The economic resource is associated with the average amount of money or income per agent and formally corresponds to the effective market temperature of agents, with their income distribution obeying the Boltzmann-Gibbs statistics. A characteristic level of resource consumption is associated with activation energy. We show that the phase portrait of the system features a collapse phase, in addition to the well-known disease-free and endemic phases. The epidemic intensified by the increasing resource deficit can ultimately drive the system to a collapse at nonzero activation energy because of limited resource. We briefly discuss several collapse mitigation strategies involving either financial instruments like subsidies or social regulations like quarantine.

Analyzing the Coevolution of Mobile Application Diffusion and Social Network: A Multi-Agent Model

The successful diffusion of mobile applications in user groups can establish a good image for enterprises, gain a good reputation, fight for market share, and create commercial profits. Thus, it is of great significance for the successful diffusion of mobile applications to study mobile application diffusion and social network coevolution. Firstly, combined with a social network’s dynamic change characteristics in real life, a mobile application users’ social network evolution mechanism was designed. Then, a multi-agent model of the coevolution of a social network and mobile application innovation diffusion was constructed. Finally, the impact of mobile applications’ value perception revenue, use cost, marketing promotion investment, and the number of seed users on the coevolution of social network and mobile application diffusion were analyzed. The results show that factors such as the network structure, the perceived value income, the cost of use, the marketing promotion investment, and the number of seed users have an important impact on mobile application diffusion.

Modelling community structure and temporal spreading on complex networks

We present methods for analysing hierarchical and overlapping community structure and spreading phenomena on complex networks. Different models can be developed for describing static connectivity or dynamical processes on a network topology. In this study, classical network connectivity and influence spreading models are used as examples for network models. Analysis of results is based on a probability matrix describing interactions between all pairs of nodes in the network. One popular research area has been detecting communities and their structure in complex networks. The community detection method of this study is based on optimising a quality function calculated from the probability matrix. The same method is proposed for detecting underlying groups of nodes that are building blocks of different sub-communities in the network structure. We present different quantitative measures for comparing and ranking solutions of the community detection algorithm. These measures describe properties of sub-communities: strength of a community, probability of formation and robustness of composition. The main contribution of this study is proposing a common methodology for analysing network structure and dynamics on complex networks. We illustrate the community detection methods with two small network topologies. In the case of network spreading models, time development of spreading in the network can be studied. Two different temporal spreading distributions demonstrate the methods with three real-world social networks of different sizes. The Poisson distribution describes a random response time and the e-mail forwarding distribution describes a process of receiving and forwarding messages.

Social interaction layers in complex networks for the dynamical epidemic modeling of COVID-19 in Brazil

We are currently living in a state of uncertainty due to the pandemic caused by the SARS-CoV-2 virus. There are several factors involved in the epidemic spreading, such as the individual characteristics of each city/country. The true shape of the epidemic dynamics is a large, complex system, considerably hard to predict. In this context, Complex networks are a great candidate for analyzing these systems due to their ability to tackle structural and dynamic properties. Therefore, this study presents a new approach to model the COVID-19 epidemic using a multi-layer complex network, where nodes represent people, edges are social contacts, and layers represent different social activities. The model improves the traditional SIR, and it is applied to study the Brazilian epidemic considering data up to 05/26/2020, and analyzing possible future actions and their consequences. The network is characterized using statistics of infection, death, and hospitalization time. To simulate isolation, social distancing, or precautionary measures, we remove layers and reduce social contact's intensity. Results show that even taking various optimistic assumptions, the current isolation levels in Brazil still may lead to a critical scenario for the healthcare system and a considerable death toll (average of 149,000). If all activities return to normal, the epidemic growth may suffer a steep increase, and the demand for ICU beds may surpass three times the country's capacity. This situation would surely lead to a catastrophic scenario, as our estimation reaches an average of 212,000 deaths, even considering that all cases are effectively treated. The increase of isolation (up to a lockdown) shows to be the best option to keep the situation under the healthcare system capacity, aside from ensuring a faster decrease of new case occurrences (months of difference), and a significantly smaller death toll (average of 87,000).

Epidemic spreading on modular networks: The fear to declare a pandemic

In the past few decades, the frequency of pandemics has been increased due to the growth of urbanization and mobility among countries. Since a disease spreading in one country could become a pandemic with a potential worldwide humanitarian and economic impact, it is important to develop models to estimate the probability of a worldwide pandemic. In this paper, we propose a model of disease spreading in a structural modular complex network (having communities) and study how the number of bridge nodes n that connect communities affects disease spread. We find that our model can be described at a global scale as an infectious transmission process between communities with global infectious and recovery time distributions that depend on the internal structure of each community and n. We find that near the critical point as n increases, the disease reaches most of the communities, but each community has only a small fraction of recovered nodes. In addition, we obtain that in the limit n→∞, the probability of a pandemic increases abruptly at the critical point. This scenario could make the decision on whether to launch a pandemic alert or not more difficult. Finally, we show that link percolation theory can be used at a global scale to estimate the probability of a pandemic since the global transmissibility between communities has a weak dependence on the global recovery time.

Modeling the competitive diffusions of rumor and knowledge and the impacts on epidemic spreading

The interaction between epidemic spreading and information diffusion is an interdisciplinary research problem. During an epidemic, people tend to take self-protective measures to reduce the infection risk. However, with the diffusion of rumor, people may be difficult to make an appropriate choice. How to reduce the negative impact of rumor and to control epidemic has become a critical issue in the social network. Elaborate mathematical model is instructive to understand such complex dynamics. In this paper, we develop a two-layer network to model the interaction between the spread of epidemic and the competitive diffusions of information. The results show that knowledge diffusion can eradicate both rumor and epidemic, where the penetration intensity of knowledge into rumor plays a vital role. Specifically, the penetration intensity of knowledge significantly increases the thresholds for rumor and epidemic to break out, even when the self-protective measure is not perfectly effective. But eradicating rumor shouldn't be equated with eradicating epidemic. The epidemic can be eradicated with rumor still diffusing, and the epidemic may keep spreading with rumor being eradicated. Moreover, the communication-layer network structure greatly affects the spread of epidemic in the contact-layer network. When people have more connections in the communication-layer network, the knowledge is more likely to diffuse widely, and the rumor and epidemic can be eradicated more efficiently. When the communication-layer network is sparse, a larger penetration intensity of knowledge into rumor is required to promote the diffusion of knowledge.

Effective control of SARS-CoV-2 transmission in Wanzhou, China

The effectiveness of control measures to contain coronavirus disease 2019 (COVID-19) in Wanzhou, China was assessed. Epidemiological data were analyzed for 183 confirmed COVID-19 cases and their close contacts from five generations of transmission of severe acute respiratory syndrome coronavirus 2 throughout the entire COVID-19 outbreak in Wanzhou. Approximately 67.2% and 32.8% of cases were symptomatic and asymptomatic, respectively. Asymptomatic and presymptomatic transmission accounted for 75.9% of the total recorded transmission. The reproductive number was 1.64 (95% confidence interval: 1.16-2.40) for G1-to-G2 transmission, decreasing to 0.31-0.39 in later generations, concomitant with implementation of rigorous control measures. Substantially higher infection risk was associated with contact within 5 d after the infectors had been infected, frequent contact and ≥8 h of contact duration. The spread of COVID-19 was effectively controlled in Wanzhou by breaking the transmission chain through social distancing, extensive contact tracing, mass testing and strict quarantine of close contacts.

Network temporality can promote and suppress information spreading

Temporality is an essential characteristic of many real-world networks and dramatically affects the spreading dynamics on networks. In this paper, we propose an information spreading model on temporal networks with heterogeneous populations. Individuals are divided into activists and bigots to describe the willingness to accept the information. Through a developed discrete Markov chain approach and extensive numerical simulations, we discuss the phase diagram of the model and the effects of network temporality. From the phase diagram, we find that the outbreak phase transition is continuous when bigots are relatively rare, and a hysteresis loop emerges when there are a sufficient number of bigots. The network temporality does not qualitatively alter the phase diagram. However, we find that the network temporality affects the spreading outbreak size by either promoting or suppressing, which relies on the heterogeneities of population and of degree distribution. Specifically, in networks with homogeneous and weak heterogeneous degree distribution, the network temporality suppresses (promotes) the information spreading for small (large) values of information transmission probability. In networks with strong heterogeneous degree distribution, the network temporality always promotes the information spreading when activists dominate the population, or there are relatively fewer activists. Finally, we also find the optimal network evolution scale, under which the network information spreading is maximized.

Security Evaluation under Different Exchange Strategies Based on Heterogeneous CPS Model in Interdependent Sensor Networks

In the real Internet of Everything scenario, many large-scale information systems can be converted into interdependent sensor networks, such as smart grids, smart medical systems, and industrial Internet systems. These complex systems usually have multiple interdependent sensor networks. Small faults or failure behaviors between networks may cause serious cascading failure effects of the entire system. Therefore, in this paper, we will focus on the security of interdependent sensor networks. Firstly, by calculating the size of the largest functional component in the entire network, the impact of random attacks on the security of interdependent sensor networks is analyzed. Secondly, it compares and analyzes the impact of cascading failures between interdependent sensor networks under different switching edge strategies. Finally, the simulation results verify the effect of the security of the system under different strategies, and give a better exchange strategy to enhance the security of the system. In addition, the research work in this article can help design how to further optimize the topology of interdependent sensor networks by reducing the impact of cascading failures.

Spontaneous divergence of disease status in an economic epidemiological game

We introduce a game inspired by the challenges of disease management in livestock farming and the transmission of endemic disease through a trade network. Success in this game comes from balancing the cost of buying new stock with the risk that it will be carrying some disease. When players follow a simple memory-based strategy we observe a spontaneous separation into two groups corresponding to players with relatively high, or low, levels of infection. By modelling the dynamics of both the disease and the formation and breaking of trade relationships, we derive the conditions for which this separation occurs as a function of the transmission rate and the threshold level of acceptable disease for each player. When interactions in the game are restricted to players that neighbour each other in a small-world network, players tend to have similar levels of infection as their neighbours. We conclude that success in economic-epidemiological systems can originate from misfortune and geographical circumstances as well as by innate differences in personal attitudes towards risk.

A generalized linear threshold model for an improved description of the spreading dynamics

Many spreading processes in our real-life can be considered as a complex contagion, and the linear threshold (LT) model is often applied as a very representative model for this mechanism. Despite its intensive usage, the LT model suffers several limitations in describing the time evolution of the spreading. First, the discrete-time step that captures the speed of the spreading is vaguely defined. Second, the synchronous updating rule makes the nodes infected in batches, which cannot take individual differences into account. Finally, the LT model is incompatible with existing models for the simple contagion. Here, we consider a generalized linear threshold (GLT) model for the continuous-time stochastic complex contagion process that can be efficiently implemented by the Gillespie algorithm. The time in this model has a clear mathematical definition, and the updating order is rigidly defined. We find that the traditional LT model systematically underestimates the spreading speed and the randomness in the spreading sequence order. We also show that the GLT model works seamlessly with the susceptible-infected or susceptible-infected-recovered model. One can easily combine them to model a hybrid spreading process in which simple contagion accumulates the critical mass for the complex contagion that leads to the global cascades. Overall, the GLT model we proposed can be a useful tool to study complex contagion, especially when studying the time evolution of the spreading.

A two-layer model for coevolving opinion dynamics and collective decision-making in complex social systems

Motivated by the literature on opinion dynamics and evolutionary game theory, we propose a novel mathematical framework to model the intertwined coevolution of opinions and decision-making in a complex social system. In the proposed framework, the members of a social community update their opinions and revise their actions as they learn of others' opinions shared on a communication channel and observe others' actions through an influence channel; these interactions determine a two-layer network structure. We offer an application of the proposed framework by tailoring it to study the adoption of a novel social norm, demonstrating that the model is able to capture the emergence of several real-world collective phenomena such as paradigm shifts and unpopular norms. Through the establishment of analytical conditions and Monte Carlo numerical simulations, we shed light on the role of the coupling between opinion dynamics and decision-making, and of the network structure, in shaping the emergence of complex collective behavior in social systems.

Competition between vaccination and disease spreading

We study the interaction between epidemic spreading and a vaccination process. We assume that, similar to the disease spreading, the vaccination process also occurs through direct contact, i.e., it follows the standard susceptible-infected-susceptible (SIS) dynamics. The two competing processes are asymmetrically coupled as vaccinated nodes can directly become infected at a reduced rate with respect to susceptible ones. We study analytically the model in the framework of mean-field theory finding a rich phase diagram. When vaccination provides little protection toward infection, two continuous transitions separate a disease-free immunized state from vaccinated-free epidemic state, with an intermediate mixed state where susceptible, infected, and vaccinated individuals coexist. As vaccine efficiency increases, a tricritical point leads to a bistable regime, and discontinuous phase transitions emerge. Numerical simulations for homogeneous random networks agree very well with analytical predictions.

Spreading of two interacting diseases in multiplex networks

We consider the interacting processes between two diseases on multiplex networks, where each node can be infected by two interacting diseases with general interacting schemes. A discrete-time individual-based probability model is rigorously derived. By the bifurcation analysis of the equilibrium, we analyze the outbreak condition of one disease. The theoretical predictions are in good agreement with discrete-time stochastic simulations on scale-free networks. Furthermore, we discuss the influence of network overlap and dynamical parameters on the epidemic dynamical behaviors. The simulation results show that the network overlap has almost no effect on both epidemic threshold and prevalence. We also find that the epidemic threshold of one disease does not depend on all system parameters. Our method offers an analytical framework for the spreading dynamics of multiple processes in multiplex networks.

Exploring the Clustering Property and Network Structure of a Large-Scale Basin’s Precipitation Network: A Complex Network Approach

Understanding of the spatial connections in rainfall is a challenging and essential groundwork for reliable modeling of catchment processes. Recent developments in network theory offer new avenues to understand of the spatial variability of rainfall. The Yellow River Basin (YRB) in China is spatially extensive, with pronounced environmental gradients driven primarily by precipitation and air temperature on broad scales. Therefore, it is an ideal region to examine the availability of network theory. The concepts of clustering coefficient, degree distribution and small-world network are employed to investigate the spatial connections and architecture of precipitation networks in the YRB. The results show that (1) the choice of methods has little effect on the precipitation networks, but correlation thresholds significantly affected vertex degree and clustering coefficient values of precipitation networks; (2) the spatial distribution of the clustering coefficient appears to be high–low–high from southeast to northwest and the vertex degree is the opposite; (3) the precipitation network has small-world properties in the appropriate threshold range. The findings of this paper could help researchers to understand the spatial rainfall connections of the YRB and, therefore, become a foundation for developing a hydrological model in further studies.

Analysis of E-mail Account Probing Attack Based on Graph Mining

E-mail has become the main carrier of spreading malicious software and been widely used for phishing, even high-level persistent threats. The e-mail accounts with high social reputation are primary targets to be attacked and utilized by attackers, suffering a lot of probing attacks for a long time. In this paper, in order to understand the probing pattern of the e-mail account attacks, we analyse the log of email account probing captured in the campus network based on graph mining. By analysing characteristics of the dataset in different dimensions, we find a kind of e-mail account probing attack and give it a new definition. Based on the analysis results, its probing pattern is figured out. From the point of probing groups and individuals, we find definitely opposite characteristics of the attack. Owing to the probing pattern and its characteristics, attacks can escape from the detection of security devices, which has a harmful effect on e-mail users and administrators. The analysis results of this paper provide support for the detection and defence of such distributed attacks.

Evolutionary Game Simulation of Knowledge Transfer in Industry-University-Research Cooperative Innovation Network under Different Network Scales

This paper takes the industry-university-research cooperation innovation network constructed by the weighted evolutionary BBV model as the research object, which is based on bipartite graph and evolutionary game theory, and constructing the game model of knowledge transfer in the industry-university-research cooperation innovation network, by using the simulation analysis method and analyzing the evolution law of knowledge transfer in the industry-university-research cooperation innovation network under different network scales, three scenarios, the knowledge transfer coefficient and the knowledge reorganization coefficient. The results show that the increase of network scale reduces the speed of knowledge transfer in the network, and the greater the average cooperation intensity of the nodes, the higher the evolution depth of knowledge transfer. Compared with university-research institutes, the evolution depth of knowledge transfer in enterprises is higher, and with the increase of network scale, the gap between the evolution depth of knowledge transfer between them is gradually increasing. Only when reward, punishment and synergistic innovation benefits are higher than the cost of knowledge transfer that can promote the benign evolution of industry-university-research cooperation innovation networks. Only when the knowledge transfer coefficient and the knowledge reorganization coefficient exceed a certain threshold will knowledge transfer behavior emerge in the network. With the increase of the knowledge transfer coefficient and the knowledge reorganization coefficient, the knowledge transfer evolutionary depth of the average cooperation intensity of all kinds of nodes is gradually deepening.

Prediction of COVID-19 spread by sliding mSEIR observer

The outbreak of COVID-19 has brought unprecedented challenges not only in China but also in the whole world. Thousands of people have lost their lives, and the social operating system has been affected seriously. Thus, it is urgent to study the determinants of the virus and the health conditions in specific populations and to reveal the strategies and measures in preventing the epidemic spread. In this study, we first adopt the long short-term memory algorithm to predict the infected population in China. However, it gives no interpretation of the dynamics of the spread process. Also the long-term prediction error is too large to be accepted. Thus, we introduce the susceptible-exposed-infected-removed (SEIR) model and further the metapopulation SEIR (mSEIR) model to capture the spread process of COVID-19. By using a sliding window algorithm, we suggest that the parameter estimation and the prediction of the SEIR populations are well performed. In addition, we conduct extensive numerical experiments to show the trend of the infected population for several provinces. The results may provide some insight into the research of epidemics and the understanding of the spread of the current COVID-19.

Co-evolution spreading of multiple information and epidemics on two-layered networks under the influence of mass media

During epidemic outbreaks, there are various types of information about epidemic prevention disseminated simultaneously among the population. Meanwhile, the mass media also scrambles to report the information related to the epidemic. Inspired by these phenomena, we devise a model to discuss the dynamical characteristics of the co-evolution spreading of multiple information and epidemic under the influence of mass media. We construct the co-evolution model under the framework of two-layered networks and gain the dynamical equations and epidemic critical point with the help of the micro-Markov chain approach. The expression of epidemic critical point show that the positive and negative information have a direct impact on the epidemic critical point. Moreover, the mass media can indirectly affect the epidemic size and epidemic critical point through their interference with the dissemination of epidemic-relevant information. Though extensive numerical experiments, we examine the accuracy of the dynamical equations and expression of the epidemic critical point, showing that the dynamical characteristics of co-evolution spreading can be well described by the dynamic equations and the epidemic critical point is able to be accurately calculated by the derived expression. The experimental results demonstrate that accelerating positive information dissemination and enhancing the propaganda intensity of mass media can efficaciously restrain the epidemic spreading. Interestingly, the way to accelerate the dissemination of negative information can also alleviate the epidemic to a certain extent when the positive information hardly spreads. Current results can provide some useful clues for epidemic prevention and control on the basis of epidemic-relevant information dissemination.

Dynamical correlations and pairwise theory for the symbiotic contact process on networks

The two-species symbiotic contact process (2SCP) is a stochastic process in which each vertex of a graph may be vacant or host at most one individual of each species. Vertices with both species have a reduced death rate, representing a symbiotic interaction, while the dynamics evolves according to the standard (single species) contact process rules otherwise. We investigate the role of dynamical correlations on the 2SCP on homogeneous and heterogeneous networks using pairwise mean-field theory. This approach is compared with the ordinary one-site theory and stochastic simulations. We show that our approach significantly outperforms the one-site theory. In particular, the stationary state of the 2SCP model on random regular networks is very accurately reproduced by the pairwise mean-field, even for relatively small values of vertex degree, where expressive deviations of the standard mean-field are observed. The pairwise approach is also able to capture the transition points accurately for heterogeneous networks and provides rich phase diagrams with transitions not predicted by the one-site method. Our theoretical results are corroborated by extensive numerical simulations.