Narrow Results

Rumor propagation and refutation form an important issue for spreading dynamics in online social networks (OSNs). In this paper, we introduce a novel two-stage rumor propagation and refutation model with time effect for OSNs. The dynamical mechanism of rumor propagation and refutation with time effect is investigated deeply. Then a two-stage model and the corresponding mean-field equations in both homogeneous and heterogeneous networks are obtained. Monte Carlo simulations are conducted to characterize the dynamics of rumor propagation and refutation in both Watts–Strogatz network and Barabási–Albert network. The results show that heterogeneous networks yield the most effective rumor and anti-rumor spreading. Besides, the sooner authority releases anti-rumor and the more attractive anti-rumor is, the less rumor influence is. What’s more, these findings suggest that individuals’ ability to control themselves and identify rumor accurately should be improved to reduce negative impact of rumor effectively. The results are helpful to understand better the mechanism of rumor propagation and refutation in OSNs.

Rumors can bring about a seriously negative impact on all respects of society in this information era. More targeted control strategies can be acquired through the research of rumor propagation. When receiving rumors, individuals may keep imperturbable according to their rationality or bygone experience, and then choose not to propagate rumors provisionally. Oppositely, others may ask people around them about the realness of rumors due to bewilderment, which may further lead to the propagation of rumors. Therefore, an Ignorant–Conservative–Disseminator–Restorer–Ignorant (ICDRI) rumor dissemination model is proposed, which comprehensively considers users’ various probable actions under rumor and anti-rumor information. Furthermore, new links are added among nodes in accordance with the individual discrepancy theory and the influencing factors of rumor spreading including negation factor, authority factor, exhaustion factor, etc. According to the calculated basic regeneration number, simulation analysis and model comparison, the steady state and superiority of the ICDRI model is proved. Finally, strategies to control the spread of rumors are obtained through the sensitivity analysis of parameters. The simulation results demonstrate that the ICDRI model can more realistically reflect the dissemination of rumors, and the official rumor refutation or circular can efficaciously curb the spreading of rumors.

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.

The development of social networks provides a broad platform for the dissemination of information and also leads to the proliferation of fake news and false information, which we collectively refer to as rumors. The spread of rumors causes unnecessary panic and loss to individuals and society. To reduce the negative impacts of rumors, an appropriate rumor control strategy is necessary. To come up with some reasonable strategies, we need to have a clearer understanding of the spread of rumors. In this paper, we analyze crowd attitudes during the spreading of rumors by setting the misinformation prevalent progress on the social network as a dynamic system. Considering that most people do not have a clear supportive or opposing attitude when exposed to rumor information, we introduce a new group, stiflers who remain neutral, based on the infectious disease model scheme. By deriving the mean-field equation describing the rumor propagation process, we judge the stability of the constructed model. Finally, we use the model to fit the real-world data related to COVID-19, and based on this, we discuss the properties of the model and propose related strategies.

With the development of social networks, misinformation including rumors is spreading through multiple channels, which brings many negative effects to society. The government and several Nongovernmental Organizations (NGOs) use relevant rumor rebuttal tactics to control the spread of rumors to prevent these detrimental impacts. In this paper, we consider the responses of different individuals to rumors and classify individuals into three categories: active, normal and inactive, with different activity rates for the three categories. In order to study the interaction between rumor repudiation mechanisms and rumor propagation, we propose a rumor propagation model that considers global and local rumor repudiation mechanisms as well as activity rates in multiplex networks. The upper layer represents the rumor refutation information propagation and the lower layer expresses the rumor propagation. And mean-field equations describing the dynamics of this model in multiplex networks are derived. We found that the threshold of rumor propagation is significantly affected by individual activity rates. Another interesting finding is that the global rumor refutation mechanism suppresses rumor propagation more than the local disinformation mechanism.

The rapid development of the Internet, especially the emergence of the social networks, leads rumor propagation into a new media era. Rumor propagation in social networks has brought new challenges to network security and social stability. This paper, based on partial differential equations (PDEs), proposes a new SIS rumor propagation model by considering the effect of the communication between the different rumor infected users on rumor propagation. The stabilities of a nonrumor equilibrium point and a rumor-spreading equilibrium point are discussed by linearization technique and the upper and lower solutions method, and the existence of a traveling wave solution is established by the cross-iteration scheme accompanied by the technique of upper and lower solutions and Schauder’s fixed point theorem. Furthermore, we add the time delay to rumor propagation and deduce the conditions of Hopf bifurcation and stability switches for the rumor-spreading equilibrium point by taking the time delay as the bifurcation parameter. Finally, numerical simulations are performed to illustrate the theoretical results.

In this paper, we improve an Ignorant-Lurker-Spreader-Removal (ILSR) rumor propagation model as in [Yang et al., 2019] in social networks with consideration to Logistic growth and two discrete delays. First, we prove the existence of equilibrium points by calculating the basic reproduction number according to the next generation matrix. Regarding the two discrete delays as bifurcating parameters, the local asymptotical stability and Hopf bifurcation of the positive equilibrium point are discussed for six different scenarios by analyzing the characteristic equations of linearized systems. Applying the normal form theory and the center manifold theorem, some important conclusions about the stability and direction of bifurcating periodic solution are given when the two time delays are equal. Subsequently we study the global stability of the equilibrium points by constructing Lyapunov functions when the two delays disappear. Finally, we verify the conclusions through numerical simulations and perform sensitivity analysis on the basic reproduction numbers.

The harm caused by rumors is immeasurable. Studying the dynamic characteristics of rumors can help control their spread. In this paper, we propose a nonsmooth rumor model with a nonlinear propagation rate. First, we utilize the positive invariant regions to prove the boundedness of solutions. Second, we analyze the conditions for the existence of equilibrium points in both the left and right systems. Additionally, we confirm the occurrence of saddle-node bifurcation in the left system. Next, by considering the influence of spatial diffusion, we establish the conditions for Turing instability. Then we discuss the conditions for spatial homogeneous and inhomogeneous Hopf bifurcations in the left and right systems, respectively. We differentiate between supercritical and subcritical bifurcations using the Lyapunov coefficient. Furthermore, we examine the conditions for the existence of discontinuous Hopf bifurcation at the demarcation point. Finally, in the numerical simulation section, we validate our theorems on Turing patterns. We also investigate the impact of parameter changes on rumor propagation and conclude that an increase in the psychological inhibitory factor significantly reduces the rate of rumor propagation, providing an effective strategy for curbing rumors. To that end, we fit actual data to our system and the results are excellent, confirming the validity of the system.

In view of different types of online rumors, when the governance institutions (government departments) intervene to achieve the least cost and the best effect is a core issue of rumor governance. Based on the perspective of the government, under the premise of limited human, material and financial resources, and considering the different impacts of government intervention opportunities on the spread of different types of rumors, this paper establishes an uncertain multi-objective network rumor transmission intervention timing model, so as to achieve the optimal allocation of government intervention opportunities for different types of online rumors, minimize the total cost and maximize the inhibition effect of rumor spreading. Then, the equivalent form of the model is given, and the model is solved. In addition, numerical experiments are conducted on three types of rumors during the COVID-19 pandemic. The experimental results show that when the types of online rumors and the focus of government departments on cost and governance effect are different, the optimal time for intervention will change. Finally, combined with the experimental results, corresponding countermeasures and suggestions are put forward for the supervision of online rumors by government departments.

The study of rumor propagation dynamics is of great significance to reduce false news and ensure the authenticity of news information. In this paper, a SI reaction-diffusion rumor propagation model with nonlinear saturation incidence is studied. First, through stability analysis, we obtain the conditions for the existence and local stability of the positive equilibrium point. By selecting suitable variable as the control parameter, the critical value of Turing bifurcation and the existence theorem of Turing bifurcation are obtained. Then, using the above theorem and multi-scale standard analysis, the expression of amplitude equation around Turing bifurcation point is obtained. By analyzing the amplitude equation, different types of Turing pattern are divided such as uniform steady-state mode, hexagonal mode, stripe mode and mixed structure mode. Further, in the numerical simulation part, by observing different patterns corresponding to different values of control variable, the correctness of the theory is verified. Finally, the effects of different network structures on patterns are investigated. The results show that there are significant differences in the distribution of users on different network structures.