Rumor Spreading Model Research Articles

Timeliness-aware rumor sources identification in community-structured dynamic online social networks

Identifying rumor sources in online social networks (OSNs) plays a crucial role in controlling the spread of rumors and mitigating their damage. However, the community structure of OSNs and timeliness of rumors increase the complexity of accurately characterizing rumor-spreading behavior, making it extremely challenging to identify the source of rumor in OSNs. Conventional studies on rumor source identification often overlook the community structure of OSNs and timeliness of rumors. This paper proposes a rumor sources identification framework that take these two aspects into consideration. First, we transfer the snapshots of a dynamic OSN into a community-structured dynamic OSN through 4 meticulously designed phases. Second, instead of considering a constant influence of rumors in traditional techniques, we introduce a time-varying dynamic propagation parameter to quantify the timeliness of rumor, and apply the propagation parameter to establish a microscopic rumor spreading model. This process addresses the issue of modeling the timeliness of rumor. Third, we adopt sensor-based observation techniques to collect the propagation information of rumor, and a hybrid sensor deployment strategy is designed to improve the efficiency of information collection. Fourth, we propose an algorithm for identifying single and multiple rumor sources in community-structured dynamic OSN, this algorithm initiates with the utilization of some criteria to analyze the gathered propagation information and estimate the suspicious communities that harbor the source of rumors. Subsequently, it applies maximum likelihood estimation method within each community to determine the ultimate source of the rumor. Experimental results on real-world and synthetic networks indicate that our method can accurately identify the real rumor sources. To the best of our knowledge, the proposed method is the first that can be used to identify rumor sources in community-structured dynamic OSNs.

A stochastic rumor spreading model with event-triggered discontinuous feedback control in multilingual online networks

A stochastic rumor spreading model with event-triggered discontinuous feedback control in multilingual online networks

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.

Dynamic analysis and application of a stochastic rumor spreading model with education and punishment age under generalized nonlinear incidence on homogeneous networks

Dynamic analysis and application of a stochastic rumor spreading model with education and punishment age under generalized nonlinear incidence on homogeneous networks

A rumor propagation model in multilingual environment with time and state dependent impulsive control

In this paper we are interested in the problem of modeling, analysis and control of rumor spreading on online social networks. As the diversity of languages and the difference of user nodes in the network, a heterogeneous rumor spreading model with two language spreaders is proposed, and the impulsive isolation control strategy is considered. Firstly, the model with periodic impulsive isolation control and time-delay recovery rate is discussed. Based on the stability theory of impulsive differential equations, some conditions regarding the impulsive period and control gains are given for the rumor asymptotically disappearance and persistent existence. Secondly, a new type of event-triggered impulsive isolation control method is developed to address the tradeoff between restraining rumor and minimizing the cost of control, and some conditions are given to make the rumor disappear asymptotically. Furthermore, an improved event-triggered mechanism is established based on the fixed-time stability theory, which provides the conditions for the rumor to disappear within a fixed-time. Finally, some numerical simulations and an actual example are given to verify the rationality of the model and the effectiveness of the control methods.

Turing instability analysis of a reaction–diffusion system for rumor propagation in continuous space and complex networks

Research on the propagation of online rumors necessitates careful consideration of rumor-spreading mechanisms. Media correction, self-correction, and the time delays associated with contact propagation are expressly introduced into the established reactive–diffusion rumor-spreading model in this paper. The conditions for a unique positive equilibrium point in the model are analyzed, laying the necessary groundwork for the occurrence of Turing instability in reaction–diffusion rumor propagation systems. A linearization approach is employed to derive the conditions for Turing instability in scenarios involving small delay to address the challenges posed by models with time delay. Furthermore, in order to anticipate the Turing pattern formation in advance, we employed a multiscale analysis approach to derive the amplitude equation within this model. The validity of the theoretical results is verified through numerical simulations, while the propagation dynamics of the model were analyzed within two complex network models, namely small-world networks and scale-free networks. Simulation results indicate that increasing time delay decelerates rumor propagation, while higher degrees of cross-diffusion, contact spreading, media correction, and self-correction expedite the spread of rumors. In small-world networks, the trust level in rumors has a narrower range, while in scale-free networks, the stability of rumors is faster. This indicates how to effectively adjust network structures for controlling or managing the spread of rumors.

Rumor model on social networks contemplating self-awareness and saturated transmission rate

<p>The propagation of rumors indisputably inflicts profound negative impacts on society and individuals. This article introduces a new unaware ignorants-aware ignorants-spreaders-recovereds $ (2ISR) $ rumor spreading model that combines individual vigilance self-awareness with nonlinear spreading rate. Initially, the positivity of the system solutions and the existence of its positive invariant set are rigorously proved, and the rumor propagation threshold is solved using the next-generation matrix method. Next, a comprehensive analysis is conducted on the existence of equilibrium points of the system and the occurrence of backward bifurcation. Afterward, the stability of the system is validated at both the rumor-free equilibrium and the rumor equilibrium, employing the Jacobian matrix approach as well as the Lyapunov stability theory. To enhance the efficacy of rumor propagation management, a targeted optimal control strategy is formulated, drawing upon the Pontryagin's Maximum principle as a guiding framework. Finally, through sensitivity analyses, numerical simulations, and tests of real cases, we verify the reliability of the theoretical results and further consolidate the solid foundation of the above theoretical arguments.</p>

Dynamic analysis and optimum control of a rumor spreading model with multivariate gatekeepers

Dynamic analysis and optimum control of a rumor spreading model with multivariate gatekeepers

Intelligent computing knacks for infected media and time delay impacts on dynamical behaviors and control measures of rumor-spreading model

<abstract> <p>Artificial neural networks (ANNs) have transformed machine learning and computational intelligence by providing unprecedented powers in modeling complicated data and addressing a wide range of challenges. In the field of ANNs, back propagation is a key approach for training neural networks. However, obtaining optimum network efficiency while tackling over fitting and controlling uncertainty is a difficult task. The present study employs the Bayesian Regularization Method with Neural Network Backpropagation (BRM-NNB) technique to investigate the rumors spreading delay model. With their rapid spread, rumors have the potential to cause fear and even financial loss. Thus, we must take decisive actions to stop the rumor from spreading. Nowadays, rumors can spread through instant messaging, emails, or publishing, thanks to the development of the internet. In this research, an XY-SIR rumors spreading delay model (XY-SIR-RS-DM) is investigated in relation to the novel spreading pattern. Media networks can be categorized into susceptible and infected media, while friendship networks can be categorized into three groups: spreaders (S, I, and R), who actively disseminate rumors, those who are ignorant and those who have no desire to do so. To estimate the solution of the suggested model, the Bayesian regularization method with neural network back propagation (BRM-NNB) is used. The data set is generated by applying the explicit Runge-Kutta method. The computing BRM-NNB strategy is implemented for three different performances, where the training, testing, and verification data are reported as 80%, 15%, and 5%, respectively, with 10 hidden neurons. To verify the validity of the developed artificial intelligence (AI) approach represented by the BRM-NNB, outcome comparisons are presented. The result is compatible with obtaining a minimal absolute error that is nearly equal to zero, thereby proving the efficacy of the proposed method.</p> </abstract>

Rumor spreading model with a focus on educational impact and optimal control

Rumor spreading model with a focus on educational impact and optimal control

Stability Analysis of a Delayed Rumor Propagation Model with Nonlinear Incidence Incorporating Impulsive Vaccination.

The presence of information asymmetry can hinder the public's ability to make well-informed decisions, resulting in unwarranted suspicion and the widespread dissemination of rumors. Therefore, it is crucial to provide individuals with consistent and dependable scientific education. Regular popular science education is considered a periodic impulsive intervention to mitigate the impact of information asymmetry and promote a more informed and discerning public. Drawing on these findings, this paper proposes a susceptible-hesitant-infected-refuting-recovered (SHIDR) rumor-spreading model to explain the spread of rumors. The model incorporates elements such as time delay, nonlinear incidence, and refuting individuals. Firstly, by applying the comparison theorem of an impulsive differential equation, we calculate two thresholds for rumor propagation. Additionally, we analyze the conditions of global attractiveness of the rumor-free periodic solution. Furthermore, we consider the condition for the rumor's permanence. Finally, numerical simulations are conducted to validate the accuracy of our findings. The results suggest that increasing the proportion of impulsive vaccination, reducing the impulsive period, or prolonging the delay time can effectively suppress rumors.

Optimal control of a rumor propagation model in online social network by considering influential nodes

Social networking platforms give people an opportunity to get in contact with each other irrespective of boundaries. Through these platforms, any individual can easily follow the ideas of other individuals like friends, relatives, politicians, actors, etc, and get in contact with them. In this paper, we examine rumor propagation with two types of infected people: highly influential people and ordinary people. Some ordinary people, blindly follow the messages shared by highly influential people. By using this concept we analyze the rumor-spreading model in networks (homogeneous and heterogeneous). We applied control strategies in homogeneous networks and observed that government policies to control rumor propagation can reduce its spread. Immunization in heterogeneous networks by giving proper information and education to people about facts can also reduce the spread and help people make the right decision when they come across a rumor.

Bifurcation control for a fractional-order delayed SEIR rumor spreading model with incommensurate orders

Bifurcation control for a fractional-order delayed SEIR rumor spreading model with incommensurate orders

Lyapunov functions for studying global asymptotic stability of two rumor spreading models

In a previous work (2018, Commun. Theor. Phys. 70, 795–802), a new compartment model for the spreading of rumors was introduced and analyzed. However, only the local asymptotic stability of this model was discussed. In the present work, we first provide a rigorous mathematical analysis for the global asymptotic stability (GAS) of the above-mentioned rumor spreading model. By constructing suitable Lyapunov candidate functions, we obtain the GAS of a rumor-free (boundary) equilibrium point and a unique rumor-spreading (positive) equilibrium point. After that, we utilize the approach based on the Lyapunov candidate functions to study the GAS of another rumor spreading model with control strategies, which was proposed in (2022, Physica A 606, 128157). As an important consequence, the GAS of the rumor spreading model with control strategies is determined fully without resorting to technical hypotheses used in the benchmark work. Lastly, the theoretical findings are supported by a set of illustrative numerical examples. The obtained results not only improve the ones constructed in the two above-mentioned benchmark papers but also can be extended to study the global dynamics of other rumor propagation models in the context of both integer-order and fractional-order derivatives.

Modeling and controlling delayed rumor propagation with general incidence in heterogeneous networks

To explore the rumor propagation dynamics in online social networks (OSNs) and propose the corresponding control strategies, a novel Ignorants-Spreaders-1-Spreaders-2-Removers (I2SR) rumor-spreading model with general incidence is first formulated in heterogeneous networks. This model covers the bilinear incidence and nonlinear incidence, and considers the time delay in the rumor-spreading process, which is universal and practical. We analytically derive the basic reproduction numbers, which determine the existence of rumor-spreading equilibria but also the global dynamics of the model. Moreover, the Lyapunov–LaSalle principle and the graph-theoretic approach prove the global asymptotic stability of the rumor-free/rumor-spreading equilibria in detail. Significantly, the effects of various strategies, including uniform control, targeted control, and acquaintance control, are implemented and compared. Finally, the developed theoretical results are tested via numerical simulations and a real case data of rumors, showing that the model can more accurately simulate rumor-spreading in OSNs.

Rumor spreading in a dual-relationship network with diverse propagation abilities

The increasing number of online ties created on social platforms has made our social relations and influences more complex and diverse. This paper proposes a multilayer-like network model for rumor spreading that incorporates both strong and weak relations. Two types of fixed topologies are used to describe strong relations, while the activity-driven model is employed for weak relations. The model also takes into consideration the differential propagation abilities of individuals. The rumor spreading thresholds are theoretically derived using mean-field theory and an approximation method, which are consistent with simulation results. Results indicate that differences in individuals’ strong relations significantly influence rumor spreading. Specifically, when the strong relation structure is a heterogeneous network, the density of rumor spreaders reaches equilibrium in a shorter time, and the final density of rumor spreaders is higher. However, when the strong relation structure is a homogeneous network and individuals’ activity rates are negatively correlated with their propagation abilities, rumor spreading is easier. Interestingly, the opposite result is obtained when the strong relation structure is a heterogeneous network. Additionally, individuals’ propagation abilities and weak relations can affect the final density of rumor spreaders, but the effects are not identical.

Model Penyebaran Rumor di Media Sosial

Rumors are information that spreads widely without any confirmation of truth and definite facts. One of the media that is used in rumors spreading is social media. The negative impact raised by rumors spreading through social media is the disruption of social stability, economic systems, and politics. The research purpose is to analyze the rumor spreading model on social media. This research is basic research (theoretical) using descriptive methods. The analytical results are obtained of a rumor-free equilibrium point and a rumor spread equilibrium point, each of which is asymptotic stable. The basic reproduction number obtained by the rumor will spread if the rate of movement of the population of individual who never hear the rumor or counter-rumor increases and became a individual who have been exposed to the rumor or counter-rumor.

A Dual Rumor Spreading Model with Consideration of Fans versus Ordinary People

The spread of rumors in online social networks (OSNs) has caused a serious threat to the normal social order. In order to describe the rumor-spreading dynamics in OSNs during emergencies, a novel model with consideration of fans versus ordinary people is proposed in this paper. In contrast to previous studies, we consider the case that two rumors exist simultaneously. It is assumed that one is an entertainment rumor that fans care about, and the other is a common rumor. First, we derive the mean-field equations that describe the dynamics of this dual rumor propagation model and obtain the threshold parameter. Secondly, after finding the necessary and sufficient conditions for the existence of equilibriums, we examine the equilibrium’s local and global stability. Finally, simulations are used to explain how various parameters affect the process of spreading rumors.

Dynamic analysis and optimal control of a novel fractional-order 2I2SR rumor spreading model

In this paper, a novel fractional-order 2I2SR rumor spreading model is investigated. Firstly, the boundedness and uniqueness of solutions are proved. Then the next-generation matrix method is used to calculate the threshold. Furthermore, the stability of rumor-free/spreading equilibrium is discussed based on fractional-order Routh–Hurwitz stability criterion, Lyapunov function method, and invariance principle. Next, the necessary conditions for fractional optimal control are obtained. Finally, some numerical simulations are given to verify the results.

Dynamical Analysis of Hyper-ILSR Rumor Propagation Model with Saturation Incidence Rate.

With the development of the Internet, it is more convenient for people to obtain information, which also facilitates the spread of rumors. It is imperative to study the mechanisms of rumor transmission to control the spread of rumors. The process of rumor propagation is often affected by the interaction of multiple nodes. To reflect higher-order interactions in rumor-spreading, hypergraph theories are introduced in a Hyper-ILSR (Hyper-Ignorant-Lurker-Spreader-Recover) rumor-spreading model with saturation incidence rate in this study. Firstly, the definition of hypergraph and hyperdegree is introduced to explain the construction of the model. Secondly, the existence of the threshold and equilibrium of the Hyper-ILSR model is revealed by discussing the model, which is used to judge the final state of rumor propagation. Next, the stability of equilibrium is studied by Lyapunov functions. Moreover, optimal control is put forward to suppress rumor propagation. Finally, the differences between the Hyper-ILSR model and the general ILSR model are shown in numerical simulations.