Narrow Results

The rapid spread of rumors on social media is mainly caused by individual retweets. This paper applies uncertain time series analysis to analyze a rumor retweeting behavior on Weibo. First, the rumor forwarding is modeled using uncertain time series, including order selection, parameter estimation, residual analysis, uncertain hypothesis test and forecast and the validity of using uncertain time series analysis is further supported by analyzing the characteristics of the residual plot. The experimental results show that the uncertain time series analysis can better predict the next stage of rumor forwarding. The results of the study have important practical significance for rumor management and the management of social media information dissemination.

A rumor spreading model for the web forums based on the heterogeneity of the web forum user behaviors and SEIR model is proposed in this paper. First, according to the meanfield equations of the model on inhomogeneous networks, the critical threshold of the spreading of rumor is deduced; Then the simulation and numerical analysis of the model itself and the influences of trust mechanism to the model are given, which verify the validity of the model and the introduction of trust mechanism can effectively reduce the rumor influence, the velocity of rumor spreading and the rumor size; Finally, combined with the previous conclusions and the high-influence limited trust relationships between the web forum users, a high-influence immunization algorithm is given. The experimental results show that the algorithm able to reach better effect than traditional immunization algorithm.

In this paper, a new rumor spreading model which quantifies a specific rumor spreading feature is proposed. The specific feature focused on is the important role the event ambiguity plays in the rumor spreading process. To study the impact of this event ambiguity on the spread of rumors, the probability p(t) that an individual becomes a rumor spreader from an initially unaware person at time t is built. p(t) reflects the extent of event ambiguity, and a parameter c of p(t) is used to measure the speed at which the event moves from ambiguity to confirmation. At the same time, a principle is given to decide on the correct value for parameter c A rumor spreading model is then developed with this function added as a parameter to the traditional model. Then, several rumor spreading model simulations are conducted with different values for c on both regular networks and ER random networks. The simulation results indicate that a rumor spreads faster and more broadly when c is smaller. This shows that if events are ambiguous over a longer time, rumor spreading appears to be more effective, and is influenced more significantly by parameter c in a random network than in a regular network. We then determine parameters of this model through data fitting of the missing Malaysian plane, and apply this model to an analysis of the missing Malaysian plane. The simulation results demonstrate that the most critical time for authorities to control rumor spreading is in the early stages of a critical event.

In this paper, we study the effect of difference in network nodes’ identification capabilities on rumor propagation. A novel susceptible-infected-removed (SIR) model is proposed, based on the mean-field theory, to investigate the dynamical behaviors of such model on homogeneous networks and inhomogeneous networks, respectively. Theoretical analysis and simulation results demonstrate that when we consider the influence of difference in nodes’ identification capabilities, the critical thresholds obviously increase, but the final rumor sizes are apparently reduced. We also find that the difference in nodes’ identification capabilities prolongs the time of rumor propagation reaching a steady state, and decreases the number of nodes that finally accept rumors. Additionally, under the influence of difference of nodes’ identification capabilities, compared with the homogeneous networks, the rumor transmission rate on the inhomogeneous networks is relatively large.

This paper proposes a rumor spreading model that considers three main factors: the event importance, event ambiguity, and the publics critical sense, each of which are defined by decision makers using linguistic descriptions and then transformed into triangular fuzzy numbers. To calculate the resultant force of these three factors, the transmission capacity and a new parameter category with fuzzy variables are determined. A rumor spreading model is then proposed which has fuzzy parameters rather than the fixed parameters in traditional models. As the proposed model considers the comprehensive factors affecting rumors from three aspects rather than examining special factors from a particular aspect. The proposed rumor spreading model is tested using different parameters for several different conditions on BA networks and three special cases are simulated. The simulation results for all three cases suggested that events of low importance, those that are only clarifying facts, and those that are strongly critical do not result in rumors. Therefore, the model assessment results were proven to be in agreement with reality. Parameters for the model were then determined and applied to an analysis of the 7.23 Yong–Wen line major transportation accident (YWMTA). When the simulated data were compared with the real data from this accident, the results demonstrated that the interval for the rumor spreading key point in the model was accurate, and that the key point for the YWMTA rumor spread fell into the range estimated by the model.

We explore the impact of positive news on rumor spreading in this paper. It is a fact that most of the rumors related to hot events or emergencies can be propagated rapidly on the hotbed of online social networks. In Chinese words, it is better to divert rather than block. Therefore, we propose the spreading model $IS{S}_{P}R$ in which positive news is a good factor to guide rumor spreading. Based on transition probability method, we have got the spreading parameters of the $IS{S}_{P}R$ model by running the rumor spreading process in online social networks with scale-free characteristics. The results give a good proof that improving the activity of the positive news spreader $S_P$ derived from the $IS{S}_{P}R$ model can guide and restrain the spreading speed of rumor smoothly.

The spread of rumors on complex networks has attracted wide attention in the field of management. In this paper, the generalized rumor spreading model is modified to take into account the vital of the spreader and the tie strength for the pairwise contacts between nodes in complex networks at degree-dependent spreading rate. Concretely, we introduce the infectivity exponent $\alpha$, and the degree influenced real exponent $\beta$ into the analytical rumor spreading model. Rumor infectivity, $\phi (k)=k^{\alpha }$, where $0<\alpha \le 1$, defines that each spreader node may contact $k^{\alpha }$ neighbors within one time step. The tie strength between two nodes with degrees $k$ and $l$ are measured by ${\omega }_{kl}=b{(kl)}^{\beta }$, $\beta$ is the degree influenced real exponent which depends on the type of complex networks and $b$ is a positive quantity. We use a tuning parameter $\theta$ to combine both the effect of the vital nodes and the strength of connectivity between nodes. We use analytical and numerical solutions to examine the threshold behavior and dynamics of the model on several models of social network. It was found that the infectivity exponent $\alpha$, the degree influenced real exponent $\beta$ and tuning parameter $\theta$ affect the rumor threshold, one can adjust the parameters to control the rumor threshold which is absent for the standard rumor spreading model.

Studying more realistic propagation mechanisms of rumors is crucial to controlling their spreading. Considering the reality of people’s forgetting and losing interest in the process of rumor spreading, the oblivion-recall mechanism and the loss-interest mechanism are both introduced in this paper to construct a novel susceptible-infected-removed (SIR) model. In our SIR model, the forgetting is regarded as an independent state type of the population, and we use the forgetting factor $\alpha$ and the recall factor $\beta$ to characterize the oblivion-recall mechanism. The mean-field equations are established respectively to describe the transmission dynamics of rumors in homogeneous networks and inhomogeneous networks. By performing stable state analysis, the relationship between these two parameters $\alpha$, $\beta$ and the propagation critical thresholds ${\lambda }_c$ is investigated. It shows that ${\lambda }_c$ is directly proportional to $\alpha$, which indicates that the loss-interest mechanism makes ${\lambda }_c$ exist, and the oblivion-recall mechanism increases the value of ${\lambda }_c$. Thus, the oblivion-recall mechanism reduces the outbreak probability of rumor spreading. It also reveals that when considering the impact of oblivion-recall mechanism, both the final rumor size and the propagation velocity of rumors decrease. Moreover, in the case of considering the existence of oblivion-recall mechanism, it is still found that the network topology is an important factor affecting the spread of rumors. We wish that our study can offer a new angle of view on the issue of the spread of rumors.

The spread of rumors has caused serious social and economic problems, especially during emergencies. Reducing the harm caused by rumors requires understanding the dynamical mechanism by which they propagate. To include the influence of time-dependent psychological factors, this paper proposes an improved rumor spreading model and derives mean-field equations describing the dynamics of rumor spreading. The psychological factors considered are the attenuation of individual interest, the cumulative effect of memory, and changes in sensory intensity with time. We also obtain the threshold condition of rumor spreading. Numerical simulations are used to verify our theoretical results. It is proved that the extremum of the cumulative effect of memory and the rumor attraction rate are positively correlated with the peak number of rumor spreaders, and negatively with the time required to reach the final rumor size. Time grows geometrically, while sensory intensity grows arithmetically. The initial approval rate of the memory accumulation effect and the stifling mechanism have little effect on the final rumor size. Finally, it is found that increasing the attenuation of interest coefficient reduces the time needed for the rumor to reach its final size.

To avoid social and economic losses, governments need to control rumor propagation by releasing official rumor-refuting information (ORI) to dispel the rumors. Therefore, understanding the complex competition mechanism between ORI and rumors is key to successfully refuting rumors. This paper presents an in-depth analysis of the function of ORI in suppressing and quashing rumors. First, the influencing factors were determined from which a competition model was constructed and the quenched mean-field method employed to determine the rumor outbreak threshold. It was found that public cognition could affect the rumor threshold and lead to rumor depletion, which was confirmed in a model simulation. The simulation results also indicated that government credibility and the release time of ORI played a critical role in controlling rumors. Specifically, it was found that when government credibility was high, the ORI release was able to quash the rumor spread. And it is shown that the government should release the ORI as soon as possible, and ensure the continuous dissemination of ORI to dispel rumors effectively.

Rumor, as a form of information, can be widely spread in a short time. A host of researchers focus on the spread of rumor, aiming to explore the rules of rumor spreading and put forward effective measures to help control the spread of rumor. In real life, when the individual is not interested in the rumor spread or feels that the rumor is not related to him, it is easy to trigger the individual’s vigilance awareness. On the contrary, if the rumor is more closely related to the individual’s life, the individual will usually be less alert and have great motivation to share it with friends. Based on the typical Susceptible–Infected–Recovered (SIR) model, a new vigilant state is added to describe the above phenomenon and a Susceptible–Vigilant–Infectious–Recovered (SVIR) rumor model is proposed. In addition, considering the fact that the infectious with high emotion may cause emotional resonance among individuals, this model adds a connection edge from the recovered to the infectious triggered by emotional infection. Based on the obtained dynamic equations, the steady state of the model is analyzed by utilizing basic reproduction number method and verified on the generated homogeneous network as well as Facebook network. Simulation results reveal that the improvement of individual vigilance awareness can reduce the influence of rumor. Although high emotional infectious can promote the spread of rumor, appealing them to clarify the fact for curbing rumor spreading is a forceful measure.

Rumors, as a typical social phenomenon in real life, have a negative impact on the harmony of the society. When people hear rumors, they may not resonate with rumors because they do not trust them during the process of rumors transmission. Thus, they will not spread rumors. The essential difference between chord mechanism and spreader mechanism is that spreaders will spread regardless of whether they think it is true or false. The chord needs to believe that the rumor is true in order to keep spreading it, otherwise they become immune to spreading it. Therefore, this paper proposes a new Spreader-Chord-Ignorant-Restorer (SCIR) model, which considers that the trust may affect the level of empathy. Since the level of trust affects the spread of rumors and the extent to which the immune person trusts the rumor is different, the connecting edges from the restorer to the chord and the restorer to the ignorant were added to the model. First, the basic reproductive number $R_{(0)}$ is derived by the next generation matrix method and thus equilibriums are obtained. Then, the global stability of the rumor-free equilibrium $E_{(0)}$ and the persistence of rumor propagation are proved in detail during the theoretical analysis.

As an important area of social networks, rumor spread has attracted the attention of many scholars. It aims to explore the rumor propagation, and to propose effective measures to curb the further spread of rumors. Different from some existing works, this paper believes that susceptible persons affected by rumor-refuting information will first enter the critical state, while ones who related to rumors will directly turn into the spread state. Therefore, this paper proposes a Susceptible-Infectious-Critical-Recovered (SICR) rumor model. In addition, considering that infectious persons with high levels of refuting rumors may cause emotional resonance among individuals, this model adds a connecting edge from the recovered to the infectious who are triggered by the information of refuting the rumors. First, the basic regeneration number $R(0)$ is obtained by using the next generation matrix method. Then, the global stability of the rumor-free equilibrium $E(0)$ and the persistence of rumor propagation are proved in detail in theoretical analysis. The simulation results show that the existence of a critical state can reduce the influence of rumors. Rumor refutation mechanism, as soon as possible to curb the spread of rumors, is an effective measure.

Rumor, as an important form of information dissemination, has always been a research hotspot in the field of complex networks. How to better understand the rules of rumor propagation and establish a practical dissemination model is a significant challenge. To further study the state transfer in information transmission, this paper established the Ignorant-Spreader-Stifler-Transition (ISRT) model, introduced different influence mechanisms and calculate the influence rate accurately by function. Specifically, (1) Based on SIR model, this paper introduces the transition state, considering that transition may awaken spontaneously to spread rumors due to individual cognition. In this paper, the ratio of the current communicator and the degree of doubt of the transition are introduced into the spontaneous arousal function. (2) This paper redefines the propagation probability function and the forgetting probability function, and introduces the time function to describe the rate from the propagator to the restorer. (3) Due to the presence of highly emotional leader propagators in the network who would awaken the immune to spread rumors again, the model added a link from the recovering person to the infected person. Finally, the nonpropagation equilibrium point $E_0$ and propagation equilibrium point $E_1$ are obtained by establishing the mean field equation. The experimental results show that different influencing mechanisms can more accurately locate the stage change of rumor transmission, which provides theoretical support for more effective control of information transmission.

The implications and contagion effect of emotion cannot be ignored in rumor spreading. This paper sheds light on how decision makers’ (DMs) emotion type and intensity affect rumor spreading. Based on the rank-dependent expected utility (RDEU) and evolutionary game theory (EGT), we construct an evolutionary game model between rumormongers (RMs) and managers (Ms) by considering emotions. We use MATLAB to simulate and reveal the influencing mechanism of DMs’ emotion type and intensity on rumor spreading. The results indicate that the DMs’ strategy choice is not only affected by their own emotion preference and intensity, but also by the other players in rumor spreading. Moreover, pessimism has a more significant influence than optimism on the stability of the evolutionary game, Ms’ emotion is more sensitive to the game results than RMs’ emotion and the emotion intensity is proportional to the evolution speed. More significantly, some earthshaking emotional thresholds are found, which can be used to predict RMs’ behavior, help Ms gain critical time to deal with rumors, and avoid the Tacitus Trap crisis. Furthermore, the evolution results fall into five categories: risk, opportunity, ideal, security and hostility. The results of this work can benefit Ms’ public governance.

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.

Rumor spreading is a good sample of spreading in which human beings are the main players in the spreading process. Therefore, in order to have a more realistic model of rumor spreading on online social networks, the influence of psycho-sociological factors particularly those which affect users’ reactions toward rumor/anti-rumor should be considered. To this aim, we present a new model that considers the influence of dissenting opinions on those users who have already believed in rumor/anti-rumor but have not spread the rumor/anti-rumor yet. We hypothesize that influence is a motive for the believers to spread their beliefs in rumor/anti-rumor. We derive the stochastic equations of the new model and evaluate it by using two real datasets of rumor spreading on Twitter. The evaluation results support the new hypothesis and show that the novel model which is relied on the new hypothesis is able to better represent rumor spreading.

Rumors greatly impact consumers' attitudes and purchasing intention. Rumor spreading can disrupt supply chain demand, particularly in today's Internet age. We propose a mathematical model for the quantitative analysis of demand disruption caused by rumor spreading based on the susceptible-infective-isolated-immune (SI2I) rumor spreading model, which extends the susceptible-infective-recovered (SIR) rumor spreading model by dividing stiflers into isolators and immunes. Both groups represent individuals who do not propagate a rumor, but the former believes the rumor while the latter does not. From the firms' perspective, only ignorants and immunes will still purchase their products and services after a rumor has spread. Hence, the influence of rumors on demand can be quantitatively reflected by the proportion of ignorants and immunes in the population. This study offers a new method for company managers to predict the variation trend of demand and estimate demand loss when a firm is attacked by rumors.