Social contagions on time-varying community networks

Social Contagion and General Diffusion Models of Adolescent Religious Transitions: A Tutorial, and EMOSA Applications

Epidemic Models of the Onset of Social Activities (EMOSA) describe behaviors that spread through social networks. Two social influence methods are represented, social contagion (one-to-one spread) and general diffusion (spread through cultural channels). Past models explain problem behaviors-smoking, drinking, sexuality, and delinquency. We provide review, and a tutorial (including examples). Following, we present new EMOSA models explaining changes in adolescent and young adult religious participation. We fit the model to 10 years of data from the 1997 U.S. National Longitudinal Survey of Youth. Innovations include a three-stage bi-directional model, Bayesian Markov Chain Monte Carlo (MCMC) estimation, graphical innovations, and empirical validation. General diffusion dominated rapid reduction in church attendance during adolescence; both diffusion and social contagion explained church attendance stability in early adulthood.

A SIRD epidemic model with community structure

The study of epidemics spreading with community structure has become a hot topic. The classic SIR epidemic model does not distinguish between dead and recovered individuals. It is inappropriate to classify dead individuals as recovered individuals because the real-world epidemic spread processes show different recovery rates and death rates in different communities. In the present work, a SIRD epidemic model with different recovery rates is proposed. We pay more attention to the changes in the number of dead individuals. The basic reproductive number is obtained. The stationary solutions of a disease-free state and an endemic state are given. We show that quarantining communities can decrease the basic reproductive number, and the total number of dead individuals decreases in a disease-free steady state with an increase in the number of quarantined communities. The most effective quarantining strategy is to preferentially quarantine some communities/cities with a greater population size and a fraction of initially infected individuals. Furthermore, we show that the population flows from a low recovery rate and high population density community/city/country to some high recovery rate and low population density communities/cities/countries, which helps to reduce the total number of dead individuals and prevent the prevalence of epidemics. The numerical simulations on the real-world network and the synthetic network further support our conclusions.

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.

Epidemic spreading in heterogeneous networks with recurrent mobility patterns

Much recent research has shown that network structure and human mobility have great influences on epidemic spreading. In this paper, we propose a discrete-time Markov chain method to model susceptible-infected-susceptible epidemic dynamics in heterogeneous networks. There are two types of locations, residences and common places, for which different infection mechanisms are adopted. We also give theoretical results about the impacts of important factors, such as mobility probability and isolation, on epidemic threshold. Numerical simulations are conducted, and experimental results support our analysis. In addition, we find that the dominations of different types of residences might reverse when mobility probability varies for some networks. In summary, the findings are helpful for policy making to prevent the spreading of epidemics.

Leader-follower consensus on activity-driven networks

Social groups such as schools of fish or flocks of birds display collective dynamics that can be modulated by group leaders, which facilitate decision-making toward a consensus state beneficial to the entire group. For instance, leaders could alert the group about attacking predators or the presence of food sources. Motivated by biological insight on social groups, we examine a stochastic leader-follower consensus problem where information sharing among agents is affected by perceptual constraints and each individual has a different tendency to form social connections. Leveraging tools from stochastic stability and eigenvalue perturbation theories, we study the consensus protocol in a mean-square sense, offering necessary-and-sufficient conditions for asymptotic stability and closed-form estimates of the convergence rate. Surprisingly, the prediction of our minimalistic model share similarities with observed traits of animal and human groups. Our analysis anticipates the counterintuitive result that heterogeneity can be beneficial to group decision-making by improving the convergence rate of the consensus protocol. This observation finds support in theoretical and empirical studies on social insects such as spider or honeybee colonies, as well as human teams, where inter-individual variability enhances the group performance.

Containing misinformation spreading in temporal social networks

Many researchers from a variety of fields, including computer science, network science, and mathematics, have focused on how to contain the outbreaks of Internet misinformation that threaten social systems and undermine societal health. Most research on this topic treats the connections among individuals as static, but these connections change in time, and thus social networks are also temporal networks. Currently, there is no theoretical approach to the problem of containing misinformation outbreaks in temporal networks. We thus propose a misinformation spreading model for temporal networks and describe it using a new theoretical approach. We propose a heuristic-containing (HC) strategy based on optimizing the final outbreak size that outperforms simplified strategies such as those that are random-containing and targeted-containing. We verify the effectiveness of our HC strategy on both artificial and real-world networks by performing extensive numerical simulations and theoretical analyses. We find that the HC strategy dramatically increases the outbreak threshold and decreases the final outbreak threshold.

Epidemic spreading on multilayer homogeneous evolving networks

Multilayer networks are widely used to characterize the dynamic behavior of complex systems. The study of epidemic spreading dynamics on multilayer networks has become a hot topic in network science. Although many models have been proposed to explore epidemic spreading across different networks, there is still a lack of models to study the spreading of diseases in the process of evolution on multilayer homogeneous networks. In the present work, we propose an epidemic spreading dynamic model of homogeneous evolving networks that can be used to analyze and simulate the spreading of epidemics on such networks. We determine the global epidemic threshold. We make the interesting discovery that increasing the epidemic threshold of a single network layer is conducive to mitigating the spreading of an epidemic. We find that the initial average degree of a network and the evolutionary parameters determine the changes in the epidemic threshold and the spreading process. An approach for calculating the falling and rising threshold zones is presented. Our work provides a good strategy to control epidemic spreading. Generally, controlling or changing the threshold in a single network layer is easier than trying to directly change the threshold in all network layers. Numerical simulations of small-world and random networks further support and enrich our conclusions.

Coevolution spreading in complex networks

The propagations of diseases, behaviors and information in real systems are rarely independent of each other, but they are coevolving with strong interactions. To uncover the dynamical mechanisms, the evolving spatiotemporal patterns and critical phenomena of networked coevolution spreading are extremely important, which provide theoretical foundations for us to control epidemic spreading, predict collective behaviors in social systems, and so on. The coevolution spreading dynamics in complex networks has thus attracted much attention in many disciplines. In this review, we introduce recent progress in the study of coevolution spreading dynamics, emphasizing the contributions from the perspectives of statistical mechanics and network science. The theoretical methods, critical phenomena, phase transitions, interacting mechanisms, and effects of network topology for four representative types of coevolution spreading mechanisms, including the coevolution of biological contagions, social contagions, epidemic-awareness, and epidemic-resources, are presented in detail, and the challenges in this field as well as open issues for future studies are also discussed.

Epidemic spreading with awareness diffusion on activity-driven networks

Acknowledging the significance of awareness diffusion and behavioral response in contagion outbreaks has been regarded as an indispensable prerequisite for a complete understanding of epidemic spreading. Recent studies from the research community have accumulated overwhelming evidence for the incessantly evolving structure of the underlying networks. Thus there is an impelling need to capture the interplay between the epidemic spreading and awareness diffusion on time-varying networks. In this paper, we consider a behavioral model in which susceptible individuals become alert and adopt a preventive behavior under the local risk perception characterized by a decision-making threshold. The impact of awareness diffusion on the epidemic threshold is investigated under the framework of activity-driven network. Results show that the local epidemic situation in risk perception and the duration of preventive effect are crucial for raising the epidemic threshold. The analytical results are corroborated by Monte Carlo simulations.

Modeling and analysis of epidemic spreading on community networks with heterogeneity

A large number of real world networks exhibit community structure, and different communities may often possess heterogeneity. In this paper, considering the heterogeneity among communities, we construct a new community network model in which the communities show significant differences in average degree. Based on this heterogeneous community network, we propose a novel mathematical epidemic model for each community and study the epidemic dynamics in this network model. We find that the location of the initial infection node only affects the spreading velocity and barely influences the epidemic prevalence. And the epidemic threshold of entire network decreases with the increase of heterogeneity among communities. Moreover, the epidemic prevalence increases with the increase of heterogeneity around the epidemic threshold, while the converse situation holds when the infection rate is much greater than the epidemic threshold.

Synergistic interactions promote behavior spreading and alter phase transitions on multiplex networks

Synergistic interactions are ubiquitous in the real world. Recent studies have revealed that, for a single-layer network, synergy can enhance spreading and even induce an explosive contagion. There is at the present a growing interest in behavior spreading dynamics on multiplex networks. What is the role of synergistic interactions in behavior spreading in such networked systems? To address this question, we articulate a synergistic behavior spreading model on a double layer network, where the key manifestation of the synergistic interactions is that the adoption of one behavior by a node in one layer enhances its probability of adopting the behavior in the other layer. A general result is that synergistic interactions can greatly enhance the spreading of the behaviors in both layers. A remarkable phenomenon is that the interactions can alter the nature of the phase transition associated with behavior adoption or spreading dynamics. In particular, depending on the transmission rate of one behavior in a network layer, synergistic interactions can lead to a discontinuous (first-order) or a continuous (second-order) transition in the adoption scope of the other behavior with respect to its transmission rate. A surprising two-stage spreading process can arise: due to synergy, nodes having adopted one behavior in one layer adopt the other behavior in the other layer and then prompt the remaining nodes in this layer to quickly adopt the behavior. Analytically, we develop an edge-based compartmental theory and perform a bifurcation analysis to fully understand, in the weak synergistic interaction regime where the dynamical correlation between the network layers is negligible, the role of the interactions in promoting the social behavioral spreading dynamics in the whole system.

Dynamics of social contagions with local trend imitation

Research on social contagion dynamics has not yet included a theoretical analysis of the ubiquitous local trend imitation (LTI) characteristic. We propose a social contagion model with a tent-like adoption probability to investigate the effect of this LTI characteristic on behavior spreading. We also propose a generalized edge-based compartmental theory to describe the proposed model. Through extensive numerical simulations and theoretical analyses, we find a crossover in the phase transition: when the LTI capacity is strong, the growth of the final adoption size exhibits a second-order phase transition. When the LTI capacity is weak, we see a first-order phase transition. For a given behavioral information transmission probability, there is an optimal LTI capacity that maximizes the final adoption size. Finally we find that the above phenomena are not qualitatively affected by the heterogeneous degree distribution. Our suggested theoretical predictions agree with the simulation results.

Epidemic spreading in modular time-varying networks

We investigate the effects of modular and temporal connectivity patterns on epidemic spreading. To this end, we introduce and analytically characterise a model of time-varying networks with tunable modularity. Within this framework, we study the epidemic size of Susceptible-Infected-Recovered, SIR, models and the epidemic threshold of Susceptible-Infected-Susceptible, SIS, models. Interestingly, we find that while the presence of tightly connected clusters inhibits SIR processes, it speeds up SIS phenomena. In this case, we observe that modular structures induce a reduction of the threshold with respect to time-varying networks without communities. We confirm the theoretical results by means of extensive numerical simulations both on synthetic graphs as well as on a real modular and temporal network.

Epidemic spreading on activity-driven networks with attractiveness

We study SIS epidemic spreading processes unfolding on a recent generalization of the activity-driven modeling framework. In this model of time-varying networks, each node is described by two variables: activity and attractiveness. The first describes the propensity to form connections, while the second defines the propensity to attract them. We derive analytically the epidemic threshold considering the time scale driving the evolution of contacts and the contagion as comparable. The solutions are general and hold for any joint distribution of activity and attractiveness. The theoretical picture is confirmed via large-scale numerical simulations performed considering heterogeneous distributions and different correlations between the two variables. We find that heterogeneous distributions of attractiveness alter the contagion process. In particular, in the case of uncorrelated and positive correlations between the two variables, heterogeneous attractiveness facilitates the spreading. On the contrary, negative correlations between activity and attractiveness hamper the spreading. The results presented contribute to the understanding of the dynamical properties of time-varying networks and their effects on contagion phenomena unfolding on their fabric.