Rumor Spreading Model Research Articles

Dynamical study and event-triggered impulsive control of rumor propagation model on heterogeneous social network incorporating delay

• Considering the multilingual environment, a new I2SR rumor spreading model with propagation delay is established, and the stability of this propagation model is analyzed. We find that the time delay does not change the final state of rumor propagation, but it affects the moment and peak of rumor outbreak. • For the time delay dependent rumor propagation model, it is the first time to employ the event-triggered impulsive control (ETIC) to restrain the propagation of rumor. This control method can effectively reduce the cost of limited public resources. • Using a rumor example of SinaWeibo in 2017, we find that our proposed model can well fit the real rumor spreading process, and the event-triggered impulsive control can effectively suppress the spread of this rumor. Considering the multilingual environment of rumors propagation, we propose a novel I2SR rumor propagation model with time delay on heterogeneous networks. Firstly, the basic reproduction number, depending on the network structure, is given to ensure the existence of the equilibrium points. Meanwhile, the dynamic behaviors of the rumor free equilibrium point (RFEP) are analyzed via the local linearization method and comparison principle. We also prove that the rumor equilibrium point (REP) is globally asymptotically stable (G-stable) by employing the Lyapunov stability theory and irreducible matrix properties and demonstrate the effect of time delay on the outbreak point and stability. Secondly, in order to reduce the cost of limited public resources, a new event-triggered impulsive control (ETIC) is applied to restrain the propagation of rumor. The event-triggering function is carefully designed and some criteria are obtained to guarantee that the rumor disappeared. Finally, we recognize the most sensitive parameter to the model and numerically simulate the model with some useful parameter sets to justify the theoretical results. Furthermore, using a rumor example of Sina Weibo in 2017, we find that our model can well fit the real rumor spreading process, and the ETIC can effectively inhibit the rumor propagation.

Dynamical behaviors and control measures of rumor-spreading model in consideration of the infected media and time delay

With the development and the progress of science and technology, the spread of rumors presents new characteristics. The spreaders publish false and malicious rumors on public social networks media, and individuals visit these networks and share them with their friends through the friendship network, which provides a convenient hotbed for the indiscriminate spread of rumors. In this paper, an improved rumor spreading model is established to explore the new characteristics of rumor spreading process on the basis of considering the delay of interactive system. By studying the dynamic behavior of the delay spreading model, we calculate the threshold of rumor spreading extinction, and prove the local and global asymptotic behavior of the boundary equilibrium point and endemic equilibrium point of the model. On this basis, we further consider the control strategies such as deleting rumor posts, popular science education, immunotherapy, etc., and propose an optimal control problem to minimize the spread scale and control cost of rumors. The optimal condition of the optimal control problem is calculated by mathematical analysis, and the correctness of the theoretical results is verified by numerical simulations. Finally, we compare the influence of time delays, optimal control and the media network on rumor spreading.

On ISRC Rumor Spreading Model for Scale-Free Networks with Self-Purification Mechanism

At present, the feasibility of using self-purification mechanism to inhibit rumor spreading has been confirmed by studies from different perspectives. This paper improves the classical rumor spreading models with self-purification mechanism, analyzes the correlation between spreading threshold in the model and its self-purification level theoretically, and conducts numerical simulations to study the impact of the changes of model parameters on key indicators in the process of rumor spreading. The simulation results show that changes of model parameters, including self-purification level and forgetting rate, exert significant influences on rumor spreading exactly.

CSRT rumor spreading model based on complex network

Rumors mislead judgments of people, affect economic development, and the stability of social order. The research on the rule of spreading rumors is significant and meaningful. This paper improves the traditional Barabási–Albert scale-free network and proposes a network topology model that conforms to the characteristics of sharing social networks based on the complex network theory and the actual characteristics of sharing social networks. In addition, the credulous spider rational taciturn rumor propagation model is proposed by improving the credulous spider rational model, which solves the overspread problem of the traditional rumor propagation model. This paper further studies the influence of anxiety on the spread of rumors, and finds that the anxiety of audience is increasing with the spread degree of rumors.

Spreading Dynamics of a 2SIH2R, Rumor Spreading Model in the Homogeneous Network

With the rapid development of social network in recent years, the threshold of information dissemination has become lower. Most of the time, rumors, as a special kind of information, are harmful to society. And once the rumor appears, the truth will follow. Considering that the rumor and truth compete with each other like light and darkness in reality, in this paper, we study a rumor spreading model in the homogeneous network called 2SIH2R, in which there are both spreader1 (people who spread the rumor) and spreader2 (people who spread the truth). In this model, we introduced discernible mechanism and confrontation mechanism to quantify the level of people′s cognitive abilities and the competition between the rumor and truth. By mean‐field equations, steady‐state analysis, and numerical simulations in a generated network which is closed and homogeneous, some significant results can be given: the higher the discernible rate of the rumor, the smaller the influence of the rumor; the stronger the confrontation degree of the rumor, the smaller the influence of the rumor; the larger the average degree of the network, the greater the influence of the rumor but the shorter the duration. The model and simulation results provide a quantitative reference for revealing and controlling the spread of the rumor.

Modeling Repeated Rumor Spreading in Coupled Social Networks

Social networks are becoming increasingly collaborative and interdependent for achieving a broader market and profits. However, the coupled social networks which caused by the collaboration and interdependence bring more significant security risks. Rumors will spread more effectively and more rampant in coupled social networks than in separate social networks. Rumors spread in a single social network have attracted considerable attention. In coupled networks, whereas, the research remains to be explored. In coupled networks, in view of the fact that the public will face more rumors, this paper proposes a SIHR rumor spreading model with the “hesitation” psychological state for studying the dynamic course of rumors. The mean-field equation is given for describing and analyzing the diffusion course. The various propagation performances of SIHR model are explained by theoretical and experimental analysis. At last, targeted security scheme is discussed.

Developing Cost-Effective Rumor-Refuting Strategy Through Game-Theoretic Approach

A rumor about an entity can spread rapidly through online social networks (OSNs), which may lead to serious consequences. This article focuses on developing a cost-effective rumor-refuting strategy in the situation where the rumormonger is strategic. Based on a novel individual-based rumor spreading model, we estimate the expected net benefit of the rumormonger as well as the expected total loss of the rumor victim. On this basis, we reduce the original problem to a differential game-theoretic model. Next, we derive a system for solving the model. By solving the system, we get a dynamic strategy pair. Through extensive comparative experiments, we find that this strategy pair is effective in terms of the solution concept of Nash equilibrium. Hence, we conclude that the rumor-refuting strategy contained in this strategy pair is cost-effective. Finally, we examine the effect of the structure of the OSN on the cost effectiveness of the rumor-supporting and rumor-refuting strategies contained in the proposed strategy pair. To our knowledge, this is the first time the rumor-refuting problem is addressed under the assumption that the rumormonger is strategic.

Dynamical analysis of a stochastic rumor-spreading model with Holling II functional response function and time delay

With the rapid development of information society, rumor plays an increasingly crucial part in social communication, and its spreading has a significant impact on human life. In this paper, a stochastic rumor-spreading model with Holling II functional response function considering the existence of time delay and the disturbance of white noise is proposed. Firstly, the existence of a unique global positive solution of the model is studied. Then the asymptotic behavior of the global solution around the rumor-free and rumor-local equilibrium nodes of the deterministic system is discussed. Finally, through some numerical results, the validity and availability of theoretical analysis is verified powerfully, and it shows that some factors such as the transmission rate, the intensity of white noise, and the time delay have significant relationship with the dynamical behavior of rumor spreading.

The stationary distribution of a stochastic rumor spreading model

In this paper, we develop a rumor spreading model by introducing white noise into the model. We establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the stochastic model by constructing a suitable stochastic Lyapunov function, which provides us a good description of persistence. Finally, we provide some numerical simulations to illustrate the analytical results.

Dynamics of the rumor-spreading model with hesitation mechanism in heterogenous networks and bilingual environment

In this paper, a novel rumor-spreading model is proposed under bilingual environment and heterogenous networks, which considers that exposures may be converted to spreaders or stiflers at a set rate. Firstly, the nonnegativity and boundedness of the solution for rumor-spreading model are proved by reductio ad absurdum. Secondly, both the basic reproduction number and the stability of the rumor-free equilibrium are systematically discussed. Whereafter, the global stability of rumor-prevailing equilibrium is explored by utilizing Lyapunov method and LaSalle’s invariance principle. Finally, the sensitivity analysis and the numerical simulation are respectively presented to analyze the impact of model parameters and illustrate the validity of theoretical results.

Defending against Online Social Network Rumors through Optimal Control Approach

Rumors have been widely spread in online social networks and they become a major concern in modern society. This paper is devoted to the design of a cost-effective rumor-containing scheme in online social networks through an optimal control approach. First, a new individual-based rumor spreading model is proposed, and the model considers the influence of the external environment on rumor spreading for the first time. Second, the cost-effectiveness is recommended to balance the loss caused by rumors against the cost of a rumor-containing scheme. On this basis, we reduce the original problem to an optimal control model. Next, we prove that this model is solvable, and we present the optimality system for the model. Finally, we show that the resulting rumor-containing scheme is cost-effective through extensive computer experiments.

The stochastic evolution of a rumor spreading model with two distinct spread inhibiting and attitude adjusting mechanisms in a homogeneous social network

In this paper, we propose and analyze from a stability viewpoint a deterministic, ODE-based class of rumor spreading models with two distinct inhibiting and adjusting mechanisms, together with its corresponding stochastic counterpart. For the deterministic model, a threshold parameter R0 defined ad hoc, called the basic influence number, is used to ascertain whether the rumors are prevailing or not. If R0<1, the rumor-free equilibrium is found to be locally asymptotically stable, while if R0>1 it is shown that there is at least one additional rumor-prevailing equilibrium, which is necessarily locally asymptotically stable. For the stochastic model, we first show that there exists a unique global solution. Subsequently, we investigate the asymptotic behavior of the stochastic system around the equilibria of the deterministic system by constructing suitable Lyapunov functionals. Furthermore, numerical simulations are given to illustrate, support and enhance our theoretical analysis.

Rumor spreading in complex networks under stochastic node activity

The research on rumor spreading has a long history, and its wanton flooding has brought huge impact on people’s life. In the process of its spreading, the individual’s activity plays an important role. However, in the complex and changeable environment, randomness cannot be ignored, not to mention its influence on individual activity Based on the ISR model of individual activity, this paper explores the stochastic version of the rumor model including fluctuations in the activity. Then, the influence of Stratonovich stochastic noise on the asymptotic behavior of non-linear rumor spreading model is studied. Through the mathematical analysis, we get the critical values to measure whether the deterministic and stochastics models spread or not, as well as the threshold conditions for rumor to spread wantonly. At the same time, the effects of Stratonovich stochastic noise on the asymptotic behavior of rumor-free equilibrium point E0 and endemic equilibrium point E∗ are obtained respectively, and the condition that the rumor-free equilibrium is globally asymptotically stable in the presence of noise is given. Finally, the theoretical results are verified by numerical simulation.

Rumor spreading model considering the influence of public opinion environment

Rumor spreading has a profound influence on daily lives. There are several factors influencing rumor spreading. In this paper, we assume that there are two kinds of individuals in the crowd: those who do not know the rumors and those who learn about the rumors. And in the latter category, there are two attitudes toward rumors: those who are convinced of rumors and those who hold an objective attitude. Those convinced and objective individuals form a public opinion environmental factor conducive to the spread of rumors. Based on the public opinion environmental influence whose intensity decays with time, a model with two attitudes toward rumors is established. With numerical simulations, we illustrated the conversion state of three categories because of public opinion environmental factors, analyzing the sensitivity of the model. The results showed that it is beneficial to control the rumor propagation when controlling the influence of those who are convinced of rumors and those who hold an objective attitude rather than constraining one of them individually. And it was commonsensical that increasing the attenuation intensity of the two attitude rumors was also an effective way conducive to the control.

Dynamical analysis of rumor spreading model in multi-lingual environment and heterogeneous complex networks

A novel rumor propagation model with education mechanism is firstly proposed in multi-lingual environment and heterogeneous networks. Firstly, the threshold behaviour and dynamics of model are examined through analyzing the acquired differential equations. Next, based on Routh-Hurwitz judgment, Lyapunov method and LaSalle’s invariance principle, the existence and stability of rumor-free/spreading equilibrium points (RFEP/RSEP) are carried out. Furthermore, we found that the educational mechanism has significance influence on rumor spreading through sensitivity analysis. Therefore, the optimal control is presented to optimize the educational mechanism. Additionally, numerical simulations is given to show the correctness of theoretical results. Finally, combine with practice, a model application is presented to verify the effectiveness of the established model and the proposed optimal control.

Dynamical Analysis and Control Strategies of Rumor Spreading Models in Both Homogeneous and Heterogeneous Networks

In recent years, rumor propagation in social networks attracts more researchers’ attention. In this paper, we have established I2S2R rumor spreading models in both homogeneous networks and heterogeneous networks considering the effect of time delay. In the homogeneous network model, we obtain the basic reproduction number by means of the next-generation matrix. Besides, the local stability and the global stability of the equilibrium points are discussed by linearization approach of nonlinear systems and Lyapunov function. In the heterogeneous network model, we calculate the basic reproduction number through algebraic method. In addition, Lyapunov functional method and Lasalle invariance principle are applied to study the stability of equilibrium points in the complex network model. Further, we put forward some useful strategies to control the spreading of rumor based on the complex network theory. Finally, we take advantage of numerical simulations to verify the theory above and come up with necessary conclusions.

A Discrete Mathematical Modeling and Optimal Control of the Rumor Propagation in Online Social Network

In this paper, a new rumor spreading model in social networks has been investigated. We propose a new version primarily based on the cholera model in order to take into account the expert pages specialized in the dissemination of rumors from an existing IRCSS model. In the second part, we recommend an optimal control strategy to fight against the spread of the rumor, and the study aims at characterizing the three optimal controls which minimize the number of spreader users, fake pages, and corresponding costs; theoretically, we have proved the existence of optimal controls, and we have given a characterization of controls in terms of states and adjoint functions based on a discrete version of Pontryagin’s maximum principle. To illustrate the theoretical results obtained, we propose numerical simulations for several scenarios applying the forward-backward sweep method (FBSM) to solve our optimality system in an iterative process.

SIR-IM: SIR rumor spreading model with influence mechanism in social networks

Rumor, with the fast speed of transmission, may bring us panic, even economic loss. Thus, it is significant for us to take effective steps to control the rumor spreading. Unfortunately, most of the existing works ignore that the spreading probability is not a constant, but depends on the number of spreaders currently. That is to say, the more spreaders, the larger spreading probability. In order to overcome this shortcoming, in this paper, we propose a novel susceptible–infected–removed (SIR) rumor spreading model with the influence mechanism, called SIR-IM, which first incorporates the number of current spreaders into the spreading probability. Then, it employs time function to describe the rate of people from spreader to stifler as time goes on. Moreover, we not only derive mean-field equations to describe the dynamics of our SIR model, but also give theoretical analysis. Numerical simulations are conducted on social networks, which show that the influence mechanism can accelerate the rumor spreading.

Rumor spreading model considering rumor credibility, correlation and crowd classification based on personality

The study of rumor spreading or rumor controlling is important and necessary because rumors can cause serious negative effects on society. The process of rumor spreading is influenced by many factors. In this paper, we suggest that people with different personalities will behave differently after hearing rumors. Thus, we divide the population into two types: radical people and steady people. Furthermore, we suggest that the credibility of rumors and the correlation between rumors and people’s lives are important factors that will influence the spread of rumors. Based on these considerations, we propose the SEIsIrR model. We establish differential equations to describe the dynamics of the rumor spreading process in homogeneous and heterogeneous networks. Using the Jacobian matrix and next generation matrix, we obtain the spreading threshold of the SEIsIrR model and discuss the relationship of the spreading threshold between homogeneous networks and heterogeneous networks. We employ a real rumor dataset obtained from Twitter to verify the SEIsIrR model and perform numerical simulations in Watts-Strogatz (WS) networks and Barabasi-Albert (BA) networks to verify the obtained spreading thresholds and discuss the impacts of these factors on the rumor spreading process and the differences in the rumor spreading processes between WS networks and BA networks. The simulation results show that these factors influence the speed and range of rumor spreading.

Stability analysis of a SAIR rumor spreading model with control strategies in online social networks

Nowadays rumors spread by virtual identities of people in online social networks. In order to study the influence of forcing silence on spreaders, we propose a rumor propagation model with a silence-forcing function in online social networks. The theoretical analysis of the rumor propagation model reveals the existence of the equilibrium points, the backward bifurcation and the local stability. Meanwhile, by choosing the key parameter and time delay as the bifurcation parameters, we have given some conditions of Hopf bifurcation that are easy to judge. Furthermore, the optimal control is discussed to reduce the frequency of rumor propagation. Finally, numerical simulations are presented to prove the correctness of the theoretical results.