Rumor Propagation Research Articles

Dynamics and event-triggered control of rumor propagation model with saturated incidence and time delay on heterogeneous networks

Considering the impact of user’s cognitive ability in rumor propagation, this paper proposes a new susceptible infection recovery (2SIR) rumor propagation model with saturation incidence and time delay on heterogeneous networks. First, the existence of the equilibria is discussed by using mean field theory and basic reproduction number. Second, the dynamic behaviors of the rumor-free and persistent equilibria are analyzed via the local linearization method, Lyapunov stability theory and irreducible matrix properties. Furthermore, an event-triggered impulsive control strategy is proposed to control the rumor spreaders and some corresponding control conditions are given. Finally, some numerical simulation results and a practical example are presented to verify the correctness of the theoretical results and reflect the impact of cognitive ability and time delay on rumor propagation.

Analysis of Rumor Propagation Model Based on Coupling Interaction Between Official Government and Media Websites

The COVID-19 pandemic has not only brought a virus to the public, but also spawned a large number of rumors. The Internet has made it very convenient for media websites to record and spread rumors, while the official government, as the subject of rumor control, can release rumor-refutation information to reduce the harm of rumors. Therefore, this study took into account information-carrying variables, such as media websites and official governments, and expanded the classic ISR rumor propagation model into a five-dimensional, two-level rumor propagation model that interacts between the main body layer and the information layer. Based on the constructed model, the mean field equation was obtained. Through mathematical analysis, the equilibrium point and the basic reproduction number of rumors were calculated. At the same time, stability analysis was conducted using the Routh Hurwitz stability criterion. Finally, a numerical simulation verified that when the basic regeneration number was less than 1, rumors disappeared in the system; when the basic regeneration number was greater than 1, rumors continued to exist in the system and rumors erupted. The executive power of the official government to dispel rumors, that is, the effectiveness of the government, played a decisive role in suppressing the spread of rumors.

Long time behavior of a rumor model with Ornstein-Uhlenbeck process

In order to study the propagation of rumors under the influence of media, this paper analyzes a random rumor propagation system with Ornstein-Uhlenbeck process. By constructing the Lyapunov function, we get that the established model has a stationary distribution, which means that rumors will persist under the side effects of the media. In addition, we solve the corresponding matrix and get the exact expression of the probability density near the positive equilibrium. At the end of this paper, numerical simulations verify our results.

Dynamics and Control of a Novel Discrete Internet Rumor Propagation Model in a Multilingual Environment

In the Internet age, the development of intelligent software has broken the limits of multilingual communication. Recognizing that the data collected on rumor propagation are inherently discrete, this study introduces a novel SIR discrete Internet rumor propagation model with the general nonlinear propagation function in a multilingual environment. Then, the propagation threshold R0 is obtained by the next-generation matrix method. Besides, the criteria determining the spread or demise of rumors are obtained by the stability theory of difference equations. Furthermore, combined with optimal control theory, prevention and refutation mechanisms are proposed to curb rumors. Finally, the validity and applicability of the model are demonstrated by numerical simulations and a real bilingual rumor case study.

How Fast do Rumours Spread?

We study a rumour propagation model along the lines of Lebensztayn and Rodriguez (Stat Probab Lett 78(14):2130–2136, 2008) as a long-range percolation model on Z\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {Z}$$\\end{document}. We begin by showing a sharp phase transition-type behaviour in the sense of exponential decay of the survival time of the rumour cluster in the sub-critical phase. In the super-critical phase, under the assumption that radius of influence r.v. has 2+ϵ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2+\\epsilon $$\\end{document} moment finite (for some ϵ>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\epsilon >0$$\\end{document}), we show that the rightmost vertex in the rumour cluster has a deterministic speed in the sense that after appropriate scaling, the location of the rightmost vertex converges a.s. to a deterministic positive constant. Under the assumption that radius of influence r.v. has 4+ϵ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$4+\\epsilon $$\\end{document} moment finite, we obtain a central limit theorem for appropriately scaled and centered rightmost vertex. Later, we introduce a rumour propagation model with reactivation. For this section, we work with a family of exponentially decaying i.i.d. radius of influence r.v.’s, and we obtain the speed result for the scaled rightmost position of the rumour cluster. Each of these results is novel, in the sense that such properties have never been established before in the context of the rumour propagation model on Z\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {Z}$$\\end{document}, to the best of our knowledge.

Stochastic dynamic effects of rumor propagation on heterogeneous social networks incorporating age-related education and immunity

Stochastic dynamic effects of rumor propagation on heterogeneous social networks incorporating age-related education and immunity

Rumor Detection With Hierarchical Representation on Bipartite Ad Hoc Event Trees.

The rapid growth of social media has caused tremendous effects on information propagation, raising extreme challenges in detecting rumors. Existing rumor detection methods typically exploit the reposting propagation of a rumor candidate for detection by regarding all reposts to a rumor candidate as a temporal sequence and learning semantics representations of the repost sequence. However, extracting informative support from the topological structure of propagation and the influence of reposting authors for debunking rumors is crucial, which generally has not been well addressed by existing methods. In this article, we organize a claim post in circulation as an ad hoc event tree, extract event elements, and convert it into bipartite ad hoc event trees in terms of both posts and authors, i.e., author tree and post tree. Accordingly, we propose a novel rumor detection model with hierarchical representation on the bipartite ad hoc event trees called BAET. Specifically, we introduce word embedding and feature encoder for the author and post tree, respectively, and design a root-aware attention module to perform node representation. Then we adopt the tree-like RNN model to capture the structural correlations and propose a tree-aware attention module to learn tree representation for the author tree and post tree, respectively. Extensive experimental results on two public Twitter datasets demonstrate the effectiveness of BAET in exploring and exploiting the rumor propagation structure and the superior detection performance of BAET over state-of-the-art baseline methods.

Dynamic Quarantine Model for Rumor Propagation Control in Online Social Networks

Dynamic Quarantine Model for Rumor Propagation Control in Online Social Networks

The eco-evolutionary dynamics of two strategic species: From the predator-prey to the innocent-spreader rumor model

Species frequently engage in both competitive and cooperative interactions, delicately balancing these dynamics to optimize their chances of survival and reproduction. While competition drives individuals to compete for limited resources, cooperation can emerge as a strategic response, mitigating risk and enhancing collective payoff. To bridge theoretical game approaches such as payoff, cooperation, and defections in ecological systems, we propose a two-species predator–prey model inspired by the principles and variations of the prisoner’s dilemma game. We comprehensively address and analytically verify all stable strategic states, exploring the role of payoff parameters both individually and collectively. Additionally, we investigate the effect of free space. Beyond ecological contexts, we present a model of rumor propagation within a social system to establish connections with the prisoner’s dilemma game. In both systems, our primary focus is to discuss strategies and enhance the cooperative factor within the system, given its crucial importance across diverse environments.

Pattern formation in reaction-diffusion information propagation model on multiplex simplicial complexes

Turing patterns for explaining spatial distribution in nature mostly focus on continuous media and existing networks, but only few attempts exist to study them on systems with high-order interactions. Considering that high-order interactions have a particularly significant impact on rumor propagation, this study establishes a generalized reaction-diffusion rumor propagation model based on a multiplex network, where simplicial complexes are employed to describe high-order structures. It aims to provide the spatial distribution patterns of the population participating in rumor propagation and identify the structural factors that affect such patterns. We theoretically provide the necessary conditions for Turing instability in single-layer and multiplex networks by considering high-order interactions. In the numerical simulation, we demonstrate that the Turing pattern could be controlled by adjusting the diffusion coefficient, high-order structure intensity, and average degree of the network. The results indicate that: (i) in a single-layer network, the Turing pattern only exists when high-order interactions appear, and the difference in diffusion rate plays a decisive role, (ii) in a multiplex network, the Turing pattern can still be observed under the same diffusion rates, which are affected by the difference in higher-order intensity between the two layers, and (iii) in existing networks, the average degree of the network has an important impact on Turing pattern. These findings contribute toward comprehending the impact of network structure on pattern formation, particularly the high-order interactions on the Turing pattern.

Research on rumor propagation and rumor refutation strategies in complex network environment

Research on rumor propagation and rumor refutation strategies in complex network environment

IRLTS rumor propagation model considering the influence of lurking psychology and the truth of rumors

IRLTS rumor propagation model considering the influence of lurking psychology and the truth of rumors

Graph Contrastive Learning With Feature Augmentation for Rumor Detection

While online social media brings convenience to people’s communication, it has also caused the widespread spread of rumors and brought great harm. Recent deep-learning approaches attempt to identify rumors by engaging in interactive user feedback. However, the performance of these models suffers from insufficient and noisy labeled data. In this article, we propose a novel rumor detection model called graph contrastive learning with feature augmentation (FAGCL), which injects noise into the feature space and learns contrastively by constructing asymmetric structures. FAGCL takes user preference and news embedding as the initial features of the rumor propagation tree and then adopts a graph attention network to update node representations. To obtain the graph-level representation for rumor classification, FAGCL fuses multiple pooling techniques. Moreover, FAGCL adopts graph contrastive learning as an auxiliary task to constrain the representation consistency. Contrastive learning on noisy data mines the supervision information of the rumor propagation tree itself, making the model more robust and effective. Results on two real-world datasets demonstrate that our proposed FAGCL model achieves significant improvements over the baseline models.

Research on the dynamic spread of information in social networks based on relationship strength theory and feedback mechanism

Introduction: Studying the main factors and related paths of rumor propagation contributes to the precise governance of rumor information in social networks. Most existing network representation learning methods do not fit with real-world information propagation networks well, and the network cannot effectively model the temporal characteristics and dynamic evolution features of rumor information propagation.Methods: Our study proposes a new dynamic network representation model for information propagation. Additionally, the study introduces a feedback mechanism where the latest node representations are fed back to neighboring nodes.Results: The method solves the problem of delayed network representation and improves network representation performance.Discussion: We conducted experimental simulations, and the results indicate that a higher level of trust contributes to stable group relationships and converging opinions, reducing the likelihood of opinion dispersion. Furthermore, novelty of topics, and interactivity between users, and opinion leaders exhibit distinct characteristics in guiding public opinion. The viewpoint evolution of the newly constructed dynamic network representation model aligns more closely with viewpoint evolution in real-world social networks.

Dynamic analysis of a novel SI network rumour propagation model with self-regulatory mechanism

Dynamic analysis of a novel SI network rumour propagation model with self-regulatory mechanism

Unifying multimodal interactions for rumor diffusion prediction with global hypergraph modeling

A central issue in rumor surveillance and management is decoding the complex dynamics of rumor propagation, with an emphasis on predicting diffusion cascades. Recent studies focus on node embedding or the sequence of dissemination in a rumor cascade based on user social interaction, while neglecting interactions between users and rumors, as well as between various rumors. Online rumor diffusion is a complex system that encompasses two fundamental components: rumors and users. A comprehensive understanding of this system’s dynamics requires a global perspective. Consequently, it is necessary to develop models that capture the inherent multimodal interactions in rumor propagation. To tackle this challenge, we propose an HG2RLink framework of rumor diffusion prediction, which unifies multimodal interactions by global encoding. Specifically, our methodology begins with the establishment of a hypergraph structure. We then refine these interactions by leveraging a hypergraph neural network that aggregates users’ preferences for rumors. Two high-order graphs are generated to capture latent spatial interactions of rumors. By employing a learning approach for multimodal interactions, each rumor diffusion sequence is modeled with a long-range vision field of users in a deep neural network. Moreover, to validate the effectiveness of our method, we introduce a new dataset available for further exploration of new methods. Finally, experimental results show that HG2RLink outperforms other methods with improvements ranging from 0.8% to 7.6% for the Hits@k metric and from 0.4% to 2.6% for the MAP@k metric across four diverse datasets.

Dynamic analysis of a rumor propagation model based on a familiarity mechanism and refuters

The spread of rumors not only causes massive economic losses, but also seriously threatens social harmony and stability of human livelihoods. As a result, preventing rumors from spreading is critical. Individuals' familiarity with rumors and refuters has a significant impact on their spread. We develop a rumor propagation model that introduces familiar mechanisms and refuters, as well as demonstrating the existence of an equilibrium point and its local and global asymptotic stability in the model. We also calculate the model's basic regeneration number. Subsequently, we select two appropriate control variables: the contact rate between the ignorant, who are familiar with the rumor, and the disseminators; and the probability that the disseminators will become refuters. We discover that the control effect is optimal when the first variable is minimum and the second variable is maximum. Numerical simulation verifies the accuracy of the obtained results, and sensitivity analysis of the parameters is investigated. According to the research, an increase in the proportion of disseminators who become refuters will slow the spread of rumors, while an increase in the population of ignorant people who are familiar with rumors contacting the disseminators will accelerate the spread of rumors.

The dynamic analysis of the rumor spreading and behavior diffusion model with higher-order interactions

Rumor spreading occurs not only between two individuals but also among multiple individuals or influenced by groups. However, pairwise interactions in complex networks are insufficient to describe this process. In this study, we propose a rumor spreading model with higher-order interactions, in which the rumor propagation process is represented by simplicial complexes. By selecting the propagation coefficient and time delay as the threshold, the model shows richer dynamic behaviors, such as the bi-stability, discontinuous transition, forward bifurcation, backward bifurcation, Hopf bifurcation, and periodic oscillation. Besides, for exploring the collective behavior induced by rumors, the rumor synchronization model is first established by applying the adaptive feedback mechanism, which erects a theoretical bridge between rumor spreading and behavior diffusion. Moreover, an improved optimal control strategy considering system gains is performed to curb rumor diffusion. Numerical simulations suggest that rumor spreading models with higher-order interactions are more consistent with actual data than network-based ones. Our results may shed some light on comprehending higher-order interactions in rumor spreading and the coupling between rumor and behavior, and provide a promising approach to control rumors and irrational behaviors.

A rumor propagation model based on nuclear fission

The propagation of online rumors is rapid, and its propagation mechanism has always been a research difficulty. In this paper, the network rumors are compared to the nuclear fission process, and a network rumors propagation model is constructed. First, the initial online rumors are compared to neutrons, uranium nuclei are compared to individual rumor receivers, and fission barriers are compared to individual active propagation thresholds. Second, the process of nuclear fission is analyzed and the degree of energy accumulation is used to compare the social impact of online rumors. Finally, the online rumor propagation model based on nuclear fission is constructed. Through experimental simulation, it has been shown that compared to classic infectious disease models, this model can better describe the propagation process of rumors in social networks. Through research and analysis, suggestions for suppressing rumors have been proposed, providing new ideas and references for future researchers.

Parameter identification method of information propagation models based on different network structures

In this paper, we create the rumor propagation model with diffusion behavior by considering the state of the rumor in both the time dimension and the space dimension comprehensively. Meanwhile, we demonstrate the reaction–diffusion model using Turing patterns after determining the prerequisites for their occurrence. In order to achieve the purpose of predicting and controlling rumors in time, we choose to utilize the parameter identification technique based on the Barzilai–Borwein (BB) algorithm and the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm. In the numerical simulation section, we first investigate how the rumor avoidance rate and cross-diffusion coefficients affect the propagation of rumors. Then, based on a continuous spatio-temporal system and complex network system, respectively, we perform parameter identification for the propagation model. We thoroughly examine how the type of algorithm, the quantity of unknown parameters, and the network structure affect the identification outcomes in terms of the cost function, error curve, and program function time. When the model constructed in this paper is used for parameter identification on different network structures, the error gap between the final value and the target value is not significant. However, the cost function and time consumption for parameter identification on complex networks are much smaller than on the continuous medium.