Rumor Propagation Model Research Articles

Spatial dynamics and optimization method for a rumor propagation model in both homogeneous and heterogeneous environment.

Considering the influence of environmental capacity and forgetting on rumor spreading, we improve the traditional SIR (susceptible–infected–removed) rumor propagation model and give two dynamic models of rumor propagation in heterogeneous environment and homogeneous environment, respectively. The main purpose of this paper is to make a dynamic analysis of rumor propagation models. In the spatial heterogeneous environment, we have analyzed the uniform persistence of the rumor propagation model and the asymptotic behavior of the positive equilibrium point when the diffusion rate of rumor–susceptible tends to zero. In the spatial homogeneous environment, we discuss the stability of rumor propagation model. Further, optimal control and the necessary optimality conditions are obtained by using the maximum principle. Finally, we study the Hopf bifurcation phenomenon through inducing time delay in the reaction–diffusion model. In addition, the existence of Hopf bifurcation is verified and the influence of diffusion coefficients is studied by numerical simulations.

The research on propagation modeling and governance strategies of online rumors based on behavior–attitude

PurposeThe purpose of this paper is to achieve effective governance of online rumors through the proposed rumor propagation model and immunization strategy.Design/methodology/approachThe paper leverages the agent-based modeling (ABM) method to model individuals from two aspects, behavior and attitude. Based on the analysis and research of online data, we propose a rumor propagation model, namely the Untouched view transmit removed-Susceptible hesitate agree disagree (Unite-Shad), and devise an immunization strategy, namely the Gravity Immunization Strategy (GIS). A graph-based framework, namely Pregel, is used to carry out the rumor propagation simulation experiments. Through the experiments, the rationality of the Unite-Shad and the effectiveness of the GIS are verified.FindingsThe study discovers that the inconsistency between human behaviors and attitudes in rumor propagation can be explained by the Unite-shad model. Besides, the GIS, which shows better performance in small-world networks than in scale-free networks, can effectively suppress rumor propagation in the early stage.Research limitations/implicationsThis paper provides an effective immunization strategy for rumor governance. Specifically, the Unite-Shad model reveals the mechanism of rumor propagation, and the GIS provides an effective governance method for selecting immune nodes.Originality/valueThe inconsistency of human behaviors and attitudes in real scenes is modeled in the Unite-Shad model. Combined with the model, the definition of diffusion domain is proposed and a novel immunization strategy, namely GIS, is designed, which is significant for the social governance of rumor propagation.

How does rumor spreading affect people inside and outside an institution

In this paper, we study the propagation characteristics of rumors in an institution and develop the rumor dissemination model inside the institution. Different from the traditional model, a person in the proposed model can make a judgement about the message and decide to propagate it or refute it, and most people inside the institution can refute the rumor spreaders and propagate the genuine messages to uninformed people when they have confirmed the message is a rumor. Then, we split all the people into two institutions (inside and outside). Since the rumors and genuine messages from the institution can have a non-negligible impact on people outside the institution, we put forward a new double-institution rumor propagation model, and the model considers the impact of messages on the inside and outside of the institution simultaneously. Based on the two proposed models, the basic reproduction numbers are obtained respectively, and the local and global stability of the rumor-free equilibrium points are discussed separately. We numerically simulate the propagation of rumors in small-world networks. The simulation is carried out to verify the validity of the proposed model, and our model is closer to the reality than traditional models.

Dynamics of a stochastic rumor propagation model incorporating media coverage and driven by Lévy noise* *Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning, and the Project for the Natural Science Foundation of Shanghai (Grant No. 21ZR1444100), and the Project for the National Natural Science Foundation of China (Grant Nos. 71774111, 61702331, 71871144).

With the development of information technology, rumors propagate faster and more widely than in the past. In this paper, a stochastic rumor propagation model incorporating media coverage and driven by Lévy noise is proposed. The global positivity of the solution process is proved, and further the basic reproductive number R 0 is obtained. When R 0 < 1, the dynamical process of system with Lévy jump tends to the rumor-free equilibrium point of the deterministic system, and the rumor tends to extinction; when R 0 > 1, the rumor will keep spreading and the system will oscillate randomly near the rumor equilibrium point of the deterministic system. The results show that the oscillation amplitude is related to the disturbance of the system. In addition, increasing media coverage can effectively reduce the final spread of rumors. Finally, the above results are verified by numerical simulation.

Nonlinear dynamic analysis and optimum control of reaction-diffusion rumor propagation models in both homogeneous and heterogeneous networks

The spread of rumors will make a big influence on people's life. This paper aims to study the dynamic behavior of rumor propagation. We consider the effects of transmission rates between different groups and establish 2ISR rumor propagation models with diffusions and time delay in both homogeneous and heterogeneous networks. In the homogeneous network model, we gain the basic reproduction number through the next generation matrix. The existence of two equilibrium points is discussed according to the basic reproduction number. Besides, based on the LaSalle's invariance principle, we obtain the global stability of two equilibrium points. In the heterogeneous network model, we further discuss the global stability of the rumor-free equilibrium point. Moreover, a set of useful rumor control strategies are put forward respectively in two systems. Finally, some necessary numerical simulations are displayed, which also suggest the effectiveness of theories.

Modeling the dynamics of multi-cluster information propagation in presence of time delay

Abstract The dynamical behaviors of a new multi-cluster S ( 1 ) S ( 2 ) I R (Susceptible 1 - Susceptible 2 - Infected - Recovery) reaction-diffusion rumor propagation model are investigated in this paper. According to the next generation matrix method, we work out the basic reproduction number. Then applying the theory of upper and lower solutions, we have explored the unique existence and boundedness of the nonnegative solution. By using the Lyapunov-LaSalle principle and the graph-theoretic approach, the global dynamics can be obtained for both the rumor-free equilibrium point and the rumor-prevailing equilibrium point. Finally, several numerical simulations are given to illustrate the theoretical results.

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.

Dynamic analysis of the rumor propagation model with consideration of the wise man and social reinforcement

Rumor is defined as an unconfirmed public opinion or gossip, which can be propagated through various channels, causing serious economic losses and disturbing the normal order of life. Therefore, studying the rumor propagation mechanism is helpful to implement effective rumor propagation control strategies. In this paper, the wise man is involved in the dynamic process of rumor propagation, and the modified rumor propagation model is established with consideration of social reinforcement and forgetting factors in heterogeneous network. The theories analysis of the model is carried out based on the mean field equation. The rumor propagation threshold is obtained, which is closely related to dual social reinforcement, wisdom conversion rate and forgetting factors. The final size of the rumor is related to positive social reinforcement and negative social reinforcement. Numerical simulations indicate that, the social positive reinforcement promotes rumor propagation and social negative reinforcement suppresses rumor propagation. And the addition of wise men reduces the number of spreaders, thus affecting the process of rumor propagation.

Modeling the dynamics of rumor diffusion over complex networks

Rumor propagation on complex networks is rapidly affecting people’s life. As we all know, the regulatory control of rumors by regulators has a specific impact on the spread of rumors. Limited regulatory resources may saturate the regulatory level. Therefore, in this paper, we have introduced a saturation treatment function to model this phenomenon and further establish an SIS rumor propagation model with consideration of some comprehensive influence on rumor diffusion. First of all, we prove the boundedness of solutions, and the basic reproduction number R0 is obtained by the method of the next generation matrix. Secondly, by constructing Lyapunov function and applying the linearization method of differential equations, the stability conditions of the equilibrium points are derived. Further, we determine the condition for the backward bifurcation of the rumor propagation model. Moreover, in order to control the spread of rumors, we propose targeted immunization control, acquaintance immunization control and optimal control strategies based on complex networks. Finally, the sensitivity analysis of the basic reproduction number is carried out, and the correctness of the theoretical results is verified by numerical simulations. Our results may provide us with useful insights into the dynamics of online rumor propagation. For example, the basic reproduction number R0 gives the threshold of rumor propagation, which provides control conditions for suppressing the spread of rumors. Stability analysis indicates the likelihood of local or global outbreaks for rumors. In addition, the comparison of the effect for control strategies gives a variety of options for the control method.

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.

Minimize the impact of rumors by optimizing the control of comments on the complex network

The rapid development of Internet and information technology has intensified the spread of rumors. Making full use of the comment mechanism on the Internet can effectively prevent the spread of rumors. This article focuses on strategies to reduce rumors by controlling comments. Firstly, based on the comment mechanism, a rumor propagation model with mixed rumor and truth is established. Secondly, we measure the cost of the rumor and, on this basis, model the comment based rumor-truth problem as the optimal control problem. Thirdly, we prove the existence of optimal control and derive the optimal system. Finally, the superiority of the optimal control strategy is verified by numerical simulation, and the rumor propagation is effectively slowed down under the premise of cost control, and the influence of some parameter changes on rumor cost-effectiveness control is studied.

Spatial dynamics and optimization method for a network propagation model in a shifting environment

<p style='text-indent:20px;'>In this paper, a reaction-diffusion <inline-formula><tex-math id="M1">\begin{document}$ ISCT $\end{document}</tex-math></inline-formula> rumor propagation model with general incidence rate is proposed in a spatially heterogeneous environment. We first summarize the well-posedness of global solutions. Then the basic reproduction number <inline-formula><tex-math id="M2">\begin{document}$ \mathcal{R}_0 $\end{document}</tex-math></inline-formula> is introduced for the model which contains the spatial homogeneity as a special case. The threshold-type dynamics are also established in terms of <inline-formula><tex-math id="M3">\begin{document}$ \mathcal{R}_0 $\end{document}</tex-math></inline-formula>, including the global asymptotic stability of the rumor-free steady state and the uniform persistence of all positive solutions. Furthermore, by applying a controller to this model, we investigate the optimal control problem. Employing the operator semigroup theory, we prove the existence, uniqueness and some estimates of the positive strong solution to the controlled system. Subsequently, the existence of the optimal control strategy is established with the aid of minimal sequence techniques and the first order necessary optimality conditions for the optimal control is deduced. Finally, some numerical simulations are performed to validate the main analysis. The results of our study can theoretically promote the regulation of rumor propagation on the Internet.

Mathematical analysis of information propagation model in complex networks

In virtue of identifying the influence of nodes, the spatial distance of rumor propagation is defined with the partition and clustering in the network. Considering the temporal and spatial propagation characteristics of rumors in online social networks, we establish a delayed rumor propagation model based on the graph theory and partial functional differential equations. Firstly, the unique existence and uniform boundedness of the nonnegative solution are explored. Secondly, we discuss the existence of positive equilibrium points sufficiently. Thirdly, stabilities of the rumor-free and rumor-spreading equilibrium points are investigated according to the linearization approach and Lyapunov function. Finally, we perform several numerical simulations to validate theoretical results and show the influence of time delay on rumor propagation. Experimental results further illustrate that taking forceful actions such as increasing the time delay in the rumor-spreading process can control rumor propagation due to the timely effectiveness of the information.

Global Stability and Bifurcation Analysis of a Rumor Propagation Model with Two Discrete Delays in Social Networks

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.

A theoretical approach to understanding rumor propagation dynamics in a spatially heterogeneous environment

<p style='text-indent:20px;'>Most of the previous work on rumor propagation either focus on ordinary differential equations with temporal dimension or partial differential equations (PDE) with only consideration of spatially independent parameters. Little attention has been given to rumor propagation models in a spatiotemporally heterogeneous environment. This paper is dedicated to investigating a SCIR reaction-diffusion rumor propagation model with a general nonlinear incidence rate in both heterogeneous and homogeneous environments. In spatially heterogeneous case, the well-posedness of global solutions is established first. The basic reproduction number <inline-formula><tex-math id="M1">\begin{document}$ R_0 $\end{document}</tex-math></inline-formula> is introduced, which can be used to reveal the threshold-type dynamics of rumor propagation: if <inline-formula><tex-math id="M2">\begin{document}$ R_0 &lt; 1 $\end{document}</tex-math></inline-formula>, the rumor-free steady state is globally asymptotically stable, while <inline-formula><tex-math id="M3">\begin{document}$ R_0 &gt; 1 $\end{document}</tex-math></inline-formula>, the rumor is uniformly persistent. In spatially homogeneous case, after introducing the time delay, the stability properties have been extensively studied. Finally, numerical simulations are presented to illustrate the validity of the theoretical analysis and the influence of spatial heterogeneity on rumor propagation is further demonstrated.

Optimal control of a delayed rumor propagation model with saturated control functions and $$L^1$$-type objectives

Rumor is an important form of social interaction, and its spreading has a significant impact on human lives. The optimal control theory is an important tool to better manage the spread of rumors. Most of the literature on rumor propagation models deals with quadratic cost functions relative to the control variable. In this paper, we have considered a time-delay rumor propagation model with saturated control functions and an objective function of $$L^1$$ -type linear with respect to the control variables. In the general case, the introduction of the delay in the dynamic systems represents the time lag between the action on the system and the response of the system to this action. The delay is incorporated in our model to make it more realistic and to describe the latency period. The existence of the optimal control pair is also proved. Pontryagin’s maximum principle with delay is used to characterize these optimal controls. The optimality system is derived and then solved numerically using an algorithm based on the forward and backward difference approximation.

Spatiotemporal dynamics analysis and optimal control method for an SI reaction-diffusion propagation model

In the new social media era, it is becoming increasingly important to explore the propagation rules for rumors in social networks. This article is concerned with investigating a diffusive susceptible-infected rumor propagation model with a nonlinear propagation function in a spatially heterogeneous environment. We establish the uniform persistence and analyze the asymptotic behavior of the rumor-spreading steady state for the spatially heterogeneous model when one of the diffusion coefficients tends to zero. Moreover, to better reflect the effect of a time delay on the process of rumor propagation, we establish a spatially homogeneous model with a time delay and prove the existence and local stability of the corresponding equilibrium point. Furthermore, the optimal control in the spatially homogeneous environment case is derived. Finally, several numerical simulations are performed to verify the theoretical results in both spatially heterogeneous and spatially homogeneous systems.

Dynamical behaviors and optimal control of rumor propagation model with saturation incidence on heterogeneous networks

This paper is devoted to investigating a novel susceptible-exposed-infected-recovered (SEIR) delayed rumor propagation model with saturation incidence on heterogeneous networks. Firstly, by analyzing the corresponding mean-field equations of this model, the basic reproduction number R0 and the rumor-spreading equilibrium are obtained. Secondly, by utilizing the delay differential equations theorem and constructing the appropriate Lyapunov function, the global stability of the rumor equilibriums are proved in detail. Thirdly, optimal control strategy is proposed and analyzed by utilizing the Pontryagin’s Minimum Principle, which is to reduce the relative density of the rumor-spreading individuals and relevant costs. Finally, some numerical examples are used to demonstrate the validity of the derived results.

Rumor propagation model with consideration of scientific knowledge level and social reinforcement in heterogeneous network

In the Internet age, rumors bring great panic, research on the mechanism of propagation will help mitigate the bad influence of rumors. In this paper, we propose a modified rumor propagation model with consideration of scientific knowledge level and social reinforcement, and derive the mean-field equations that describe the dynamics of rumor propagation process. We obtain the rumor propagation threshold, which is closely related to scientific knowledge level and social reinforcement. The threshold of rumor propagation is increased by the scientific knowledge level, and the critical threshold of scientific knowledge level is also affected by the rumor propagation probability The results show that rumor propagates more quickly and more widely in people without scientific knowledge, while rumor propagates more slowly and the final size of the rumor is smaller in people with scientific knowledge. Positive social reinforcement will reduce the propagation threshold of rumor propagation, increase the propagation rate, and finally increase the rumor scale. Negative social reinforcement has the opposite effect on rumor. These results are verified by numerical simulations on scale-free networks. Research results also provide a good reference for future studies on how to control rumor propagation.

C-SIW Rumor Propagation Model with Variable Propagation Rate and Perception Mechanism in Social Networks

The propagation of rumor has become a common phenomenon in social networks. Studying the dynamic propagation of rumor can help locate the key points to control rumor propagation. To further research the internal motivation of state transition, a corrector-ignorant-spreader-weakener (C-SIW) model is proposed in this paper. When the individual changes state to transmit rumor, the neighbor may have a significant impact on rumor propagation. Considering the point, this paper constructs a function to describe the propagation rate, which relates to the state of neighbors and the reputation of the spreader. In addition, perception from life also can cause individual state changes. Based on the above fact, the links from the spreader and the weakener to the corrector are added to describe the perception mechanism. Then, combining the derived average field equations, the steady state of the model is analyzed and verified in experimental simulation. Moreover, the experimental results on different networks show that the perception mechanism reduces the rumor influence. Besides, the variable propagation rate can position the fast-growing stage of rumor propagation more accurately and facilitate the control of rumor propagation.