The impact of authorities’ media and rumor dissemination on the evolution of emergency

Rumor dissemination will induce emergencies. Authorities’ information is an essential factor for avoiding rumor dissemination when emergencies occur. The credibility of authorities’ media and audience rating of authorities’ information greatly influence the evolution of emergencies which are induced by rumor dissemination. To explore the interplay mechanism among authorities’ media, rumor dissemination and the evolution of emergency, we propose a new interplay model and perform stability analysis by the Routh stability criterion. We find a stability condition under which the deterioration of emergency can be effectively prevented. Recommendations for policy makers and consulting advice for related commissions are explored in the case study of the iodized sail shortage panic in China. Results show that applying media with high audience rating but low credibility will cause widespread panic and inspire a slew of ancillary rumors. Authorities should choose proper media to release the truth to public according to the seriousness of the situation and the rumor spreading rate. Pertinent countermeasures and appropriate tactics are also brought out for decision makers to alleviate intense feelings of panic.     

An interplay model for rumour spreading and emergency development

Rumours influence how people make decisions in an emergency-affected environment. Conversely, the development of situation is affected by public action as well. We present a model for describing the interplay between rumour spreading and emergency development. Then, we describe a formulation of this model and derive, from differential equations for some possibility of the positive role of rumours in the control of situation and social loss. Our results show that rumour spreading at certain rate has positive effects on situation stability and especially has delaying effects on the rapid proliferation of an emergency. Finally, we outline a strategy for authorities that can contribute to rumour management in an emergency event.     

SEIR Model of Rumor Spreading in Online Social Network with Varying Total Population Size

Based on the infectious disease model with disease latency, this paper proposes a new model for the rumor spreading process in online social network. In this paper what we establish an SEIR rumor spreading model to describe the online social network with varying total number of users and user deactivation rate. We calculate the exact equilibrium points and reproduction number for this model. Furthermore, we perform the rumor spreading process in the online social network with increasing population size based on the original real world Facebook network. The simulation results indicate that the SEIR model of rumor spreading in online social network with changing total number of users can accurately reveal the inherent characteristics of rumor spreading process in online social network.     

A Class of Rumor Spreading Models with Population Dynamics

Based on the characteristics of rumor spreading in online social networks, this paper proposes a new rumor spreading model. This is an improved SIS rumor spreading model in online social networks that combines the transmission dynamics and population dynamics with consideration of the impact of both of the changing number of online social network users and different levels of user activity. We numerically simulate the rumor spreading process. The results of numerical simulation show that the improved SIS model can successfully characterize the rumor spreading behavior in online social networks. We also give the effective strategies of curbing the rumor spreading in online social networks.     

基于移动社交网络的谣言传播动力学研究

本文在CSR传播模型的基础上提出基于移动社交网络的CSR的谣言传播模型. 改进了CSR模型的传播规则和传播动力学方程, 使得更符合移动SNS上用户的使用习惯. 在CSR模型中的接受概率数学模型基础上, 考虑个人接受阈值对接受概率的影响, 更符合人类接受谣言的心理学特点. 本文对该传播模型进行了理论分析. 并在仿真实验中, 利用多agent仿真平台对新模型和CSR模型以及SIR模型 在匀质网络和异质网络中的传播效果进行了对比研究, 从实验的结果来看, 新的谣言传播模型在匀质网络中传播范围更广, 传播速度更快. 新模型具有初值敏感性的特点. 关键词： 复杂网络 移动社交网络 谣言传播     

Near-optimal control of a stochastic rumor spreading model with Holling II functional response function and imprecise parameters

In recent years, rumor spreading has caused widespread public panic and affected the whole social harmony and stability. Consequently, how to control the rumor spreading effectively and reduce its negative influence urgently needs people to pay much attention. In this paper, we mainly study the near-optimal control of a stochastic rumor spreading model with Holling II functional response function and imprecise parameters. Firstly, the science knowledge propagation and the refutation mechanism as the control strategies are introduced into a stochastic rumor spreading model. Then, some sufficient and necessary conditions for the near-optimal control of the stochastic rumor spreading model are discussed respectively. Finally, through some numerical simulations, the validity and availability of theoretical analysis is verified. Meanwhile, it shows the significance and effectiveness of the proposed control strategies on controlling rumor spreading, and demonstrates the influence of stochastic disturbance and imprecise parameters on the process of rumor spreading.     

Emergence of Influential Spreaders in Modified Rumor Models

The burst in the use of online social networks over the last decade has provided evidence that current rumor spreading models miss some fundamental ingredients in order to reproduce how information is disseminated. In particular, recent literature has revealed that these models fail to reproduce the fact that some nodes in a network have an influential role when it comes to spread a piece of information. In this work, we introduce two mechanisms with the aim of filling the gap between theoretical and experimental results. The first model introduces the assumption that spreaders are not always active whereas the second model considers the possibility that an ignorant is not interested in spreading the rumor. In both cases, results from numerical simulations show a higher adhesion to real data than classical rumor spreading models. Our results shed some light on the mechanisms underlying the spreading of information and ideas in large social systems and pave the way for more realistic diffusion models.     

复杂网络上的意见动力学对谣言传播的影响

通过在SIR(susceptible-infected-recovered)模型中引入抑制者对谣言的辟谣机制研究了在线社交网络上的意见动力学对谣言传播的影响.在这一模型中,节点可以与自身的邻居组成1个群,传播者可以通过该群传播信息,抑制者也可以在此群中对信息发表意见进行辟谣.辟谣机制在降低未知者对于谣言的接受概率的同时也可以促使传播者向抑制者转变.本文采用ER(Erd?s-Rényi)随机网络、无标度网络以及真实的社交网络研究了抑制者的沉默概率对于谣言传播范围的影响.首先发现,谣言传播的过程以传播者的峰值为界可以分为两个阶段,即谣言自由传播的前期以及抑制者和传播者互相制衡的后期;其次,谣言的传播会随着抑制者的沉默概率的增大而突然暴发.在谣言暴发阈值之下,沉默概率的增大不会导致谣言传播范围显著增大,这是由于未知者在感知到谣言并转变为传播者后又迅速转变为抑制者;而当沉默概率达到谣言暴发阈值时,抑制者将不能控制传播者对谣言的传播从而导致抑制者的降低和谣言的暴发;最后,无标度上的谣言自由传播的前期阶段比随机网络持续的时间更短,从而使无标度上的谣言更难以暴发.本文的模型综合考虑了意见动力学和谣言传播的相互作用,更加真实地模拟了真实世界社交网络中的谣言传播过程.为谣言传播的控制和干预提供了一些有用的思路和见解.     

SIHR rumor spreading model in social networks

There are significant differences between rumor spreading and epidemic spreading in social networks, especially with consideration of the mutual effect of forgetting and remembering mechanisms. In this paper, a new rumor spreading model, Susceptible-Infected-Hibernator-Removed (SIHR) model, is developed. The model extends the classical Susceptible-Infected-Removed (SIR) rumor spreading model by adding a direct link from ignorants to stiflers and a new kind of people-Hibernators. We derive mean-field equations that describe the dynamics of the SIHR model in social networks. Then a steady-state analysis is conducted to investigate the final size of the rumor spreading under various spreading rate, stifling rate, forgetting rate, and average degree of the network. We discuss the spreading threshold and find the relationship between the final size of the rumor and two probabilities. Also Runge-Kutta method is used for numerical simulation which shows that the direct link from the ignorants to the stiflers advances the rumor terminal time and reduces the maximum rumor influence. Moreover, the forgetting and remembering mechanisms of hibernators postpone the rumor terminal time and reduce the maximum rumor influence.     

A rumor spreading model with variable forgetting rate

A rumor spreading model with the consideration of forgetting rate changing over time is examined in small-world networks. The mean-field equations are derived to describe the dynamics of rumor spreading in small-world networks. Further, numerical solutions are conducted on LiveJournal, an online social blogging platform, to better understand the performance of the model. Results show that the forgetting rate has a significant impact on the final size of rumor spreading: the larger the initial forgetting rate or the faster the forgetting speed, the smaller the final size of the rumor spreading. Numerical solutions also show that the final size of rumor spreading is much larger under a variable forgetting rate compared to that under a constant forgetting rate.     

考虑谣言清除过程的网络谣言传播与抑制

网络谣言传播是网络传播动力学的重要课题之一. 网络谣言传播常常同时混杂谣言感染和谣言清除两个过程, 对这一现象的分析可以帮助我们更好地认识社会网络中的信息传播. 本文在susceptible-infective-refractory谣言传播模型的基础上增加谣言清除者, 定义了谣言感染和谣言清除的规则, 提出SIERsEs谣言传播模型, 建立了模型的平均场方程, 从理论上分析了谣言传播的稳态, 并求解出谣言传播的感染阈值和清除阈值. 仿真计算分析了感染和清除过程同时作用时, 感染率、清除率和网络平均度对谣言传播的影响. 研究发现, 网络平均度过小或过大, 谣言传播稳定后的影响力都将处于低水平. 分析了目标免疫和熟人免疫等传统免疫策略的不足, 针对网络环境下谣言抑制的特点, 提出主动免疫和被动免疫两种网络谣言免疫策略, 并研究了传播者遗忘率、清除者遗忘率和开始免疫时间参数对这两种谣言免疫策略有效性的影响. 需要重视的是: 研究发现一些直观看来有效的谣言抑制措施反而可能提高谣言的影响力. 研究结果有助于深化对于网络传播动力学的理解, 同时为发展有效的网络谣言抑制策略提供新的思路.     

Reliability and Efficiency of Generalized Rumor Spreading Model on Complex Social Networks

We introduce the generalized rumor spreading model and investigate some properties of this model on different complex social networks. Despite pervious rumor models that both the spreader-spreader (SS) and the spreader-stifler (SR) interactions have the same rate α, we define α⁽¹⁾ and α⁽²⁾ for SS and SR interactions, respectively. The effect of variation of α⁽¹⁾ and α⁽²⁾ on the final density of stiflers is investigated. Furthermore, the influence of the topological structure of the network in rumor spreading is studied by analyzing the behavior of several global parameters such as reliability and efficiency. Our results show that while networks with homogeneous connectivity patterns reach a higher reliability, scale-free topologies need a less time to reach a steady state with respect the rumor.     

基于辟谣机制的时滞谣言传播模型的动力学分析

在社交网络谣言传播模型中,考虑到辟谣机制和时滞效应对网络谣言传播的影响,建立基于辟谣机制和时滞效应的SIR谣言传播模型.利用再生矩阵谱半径方法得到R0;根据二次函数图像特征给出谣言盛行平衡点存在的条件;通过特征值理论和Routh-Hurwitz判据确定无谣言平衡点和谣言盛行平衡点的局部稳定性以及发生Hopf分支的条件;数值仿真结果表明政府和媒体发布的辟谣信息会加快谣言收敛的速度和降低谣言传播者的最大密度.     

A model for the spread of rumors in Barrat–Barthelemy–Vespignani (BBV) networks

Rumor propagation is a typical form of social communication and plays a significant role in social life. In this paper, we studied the process of rumor propagation by accounting for the mechanism of forgetting in Barrat–Barthelemy–Vespignani (BBV) networks. First, we derived mean-field equations for rumor propagation based on the strength of the nodes in the propagation network. We then analyzed the stability of the model to determine whether a propagation threshold existed in the BBV networks. We also conducted numerical simulations of the BBV networks and found that rumors propagate more slowly in BBV networks than in unweighted networks. The numerical simulation results also demonstrated that as the forgetting rate increases, the rumor’s influence decreases in both BBV networks and unweighted networks. Finally, the simulation results confirmed that a threshold exists for rumor propagation in BBV networks, but that it was independent of the value of the stifling rate.     

Dynamical behavior and optimal impulse control analysis of a stochastic rumor spreading model

The Internet era has brought great convenience to our life and communication. Meanwhile, it also makes a bunch of rumors propagate faster and causes even more harm to human life. Therefore, it is necessary to perform effective control mechanisms to minimize the negative social impact from rumors. Thereout, firstly, we formulate a rumor spreading model considering psychological factors and thinking time, then, we add white noise (i.e., stochastic interference) and two pulse control strategies which denote education mechanism and refutation mechanism into the model. Secondly, we obtain the global positive solutions and demonstrate the global exponential stability of the unique positive periodic rumor-free solution. Thirdly, we discuss the extinction and persistence of rumor. Moreover, we use Pontriagin's minimum principle to explore the optimal impulse control. Finally, several numerical simulations are carried out to verify the effectiveness and availability of the theoretical analysis. We conclude that the pulse control strategies have a great influence on controlling rumor spreading, and different control strategies should be adopted under different transmission scenarios.     

Dynamics and near-optimal control in a stochastic rumor propagation model incorporating media coverage and Lévy noise

The appearance of rumors intensifies people's panic and affects social stability. How to control the spread of rumors has become an important issue which is worth studying. In order to more accurately reflect the actual situation in the real world, a stochastic model incorporating media coverage and Lévy noise is proposed to describe the dynamic process of rumor propagation. By introducing two control strategies of popular science education and media coverage in an emergency event, an near-optimal control problem that minimizes the influence and control cost of rumor propagation is proposed. Sufficient conditions for near-optimal control of the model are established by using a Hamiltonian function. Then the necessary conditions for near-optimal control are obtained by using the Pontryagin maximum principle. Finally, the effect of popular science education, media coverage and Lévy noise on rumor propagation process control is verified by numerical simulation.     

Rumor spreading model considering forgetting and remembering mechanisms in inhomogeneous networks

The SIHR rumor spreading model with consideration of the forgetting and remembering mechanisms was studied in homogeneous networks. We further investigate the properties of the SIHR model in inhomogeneous networks. The SIHR model is refined and mean-field equations are derived to describe the dynamics of the rumor spreading model in inhomogeneous networks. Steady-state analysis is carried out, which shows no spreading threshold existing. Numerical simulations are conducted in a BA scale-free network. The simulation results show that the network topology exerts significant influences on the rumor spreading: In comparison with the ER network, the rumor spreads faster and the final size of the rumor is smaller in BA scale-free network; the forgetting and remembering mechanisms greatly impact the final size of the rumor. Finally, through the numerical simulation, we examine the effects that the spreading rate and the stifling rate have on the the influence of the rumor. In addition, the no threshold result is verified.     

Rumor Spreading Model with Trust Mechanism in Complex Social Networks

In this paper, to study rumor spreading, we propose a novel susceptible-infected-removed (SIR) model by introducing the trust mechanism. We derive mean-field equations that describe the dynamics of the SIR model on homogeneous networks and inhomogeneous networks. Then a steady-state analysis is conducted to investigate the critical threshold and the final size of the rumor spreading. We show that the introduction of trust mechanism reduces the final rumor size and the velocity of rumor spreading, but increases the critical thresholds on both networks. Moreover, the trust mechanism not only greatly reduces the maximum rumor influence, but also postpones the rumor terminal time, which provides us with more time to take measures to control the rumor spreading. The theoretical results are confirmed by sufficient numerical simulations.     

基于复杂网络理论的微博用户关系网络演化模型研究

微博给人们提供便利的同时也产生了较大的负面影响.为获取微博谣言的传播规律,进而采取有效措施防控其传播,本文基于复杂网络理论研究微博用户关系网络的内部特征,提出一种微博用户关系网络演化模型,借助于平均场理论,分析该演化模型的拓扑统计特性,以及谣言在该演化模型上的传播动力学行为.理论分析和仿真实验表明,由该模型演化生成的微博用户关系网络具有无标度特性.度分布指数不仅与反向连接概率有关,而且还取决于节点的吸引度分布.研究还发现,与指数分布和均匀分布相比,当节点吸引度满足幂律分布时,稳态时的谣言传播程度较大.此外,随着反向连接概率或节点初始连边数量的增加,谣言爆发的概率以及网络中最终接受谣言的节点数量都会明显增大.