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.     

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.     

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     

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.     

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.     

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.     

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.     

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.     

The spreading of opposite opinions on online social networks with authoritative nodes

The study of opinion dynamics, such as spreading and controlling of rumors, has become an important issue on social networks. Numerous models have been devised to describe this process, including epidemic models and spin models, which mainly focus on how opinions spread and interact with each other, respectively. In this paper, we propose a model that combines the spreading stage and the interaction stage for opinions to illustrate the process of dispelling a rumor. Moreover, we set up authoritative nodes, which disseminate positive opinion to counterbalance the negative opinion prevailing on online social networking sites. With analysis of the relationship among positive opinion proportion, opinion strength and the density of authoritative nodes in networks with different topologies, we demonstrate that the positive opinion proportion grows with the density of authoritative nodes until the positive opinion prevails in the entire network. In particular, the relationship is linear in homogeneous topologies. Besides, it is also noteworthy that initial locations of the negative opinion source and authoritative nodes do not influence positive opinion proportion in homogeneous networks but have a significant impact on heterogeneous networks. The results are verified by numerical simulations and are helpful to understand the mechanism of two different opinions interacting with each other on online social networking sites.     

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.     

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.     

Disease spreading in structured scale-free networks

We study the spreading of a disease on top of structured scale-free networks recently introduced. By means of numerical simulations we analyze the SIS and the SIR models. Our results show that when the connectivity fluctuations of the network are unbounded whether the epidemic threshold exists strongly depends on the initial density of infected individuals and the type of epidemiological model considered. Analytical arguments are provided in order to account for the observed behavior. We conclude that the peculiar topological features of this network and the absence of small-world properties determine the dynamics of epidemic spreading. Received 16 October 2002 Published online 4 February 2003 RID="a" ID="a"e-mail: yamir@ictp.trieste.it     

Hybrid phase transitions of spreading dynamics in multiplex networks

In this paper, we study the spreading dynamics of social behaviors and focus on heterogenous responses of individuals depending on whether they realize the spreading or not. We model the system with a two-layer multiplex network, in which one layer describes the spreading of social behaviors and the other layer describes the diffusion of the awareness about the spreading. We use the susceptible-infected-susceptible (SIS) model to describe the dynamics of an individual if it is unaware of the spreading of the behavior. While when an individual is aware of the spreading of the social behavior its dynamics will follow the threshold model, in which an individual will adopt a behavior only when the fraction of its neighbors who have adopted the behavior is above a certain threshold. We find that such heterogenous reactions can induce intriguing dynamical properties. The dynamics of the whole network may exhibit hybrid phase transitions with the coexistence of continuous phase transition and bi-stable states. Detailed study of how the diffusion of the awareness influences the spreading dynamics of social behavior is provided. The results are supported by theoretical analysis.     

Correlation and trust mechanism-based rumor propagation model in complex social networks

In real life, the rumor propagation is influenced by many factors. The complexity and uncertainty of human psychology make the diffusion model more challenging to depict. In order to establish a comprehensive propagation model, in this paper, we take some psychological factors into consideration to mirror rumor propagation. Firstly, we use the Ridenour model to combine the trust mechanism with the correlation mechanism and propose a modified rumor propagation model. Secondly, the mean-field equations which describe the dynamics of the modified SIR model on homogenous and heterogeneous networks are derived. Thirdly, a steady-state analysis is conducted for the spreading threshold and the final rumor size. Fourthly, we investigate rumor immunization strategies and obtain immunization thresholds. Next, simulations on different networks are carried out to verify the theoretical results and the effectiveness of the immunization strategies. The results indicate that the utilization of trust and correlation mechanisms leads to a larger final rumor size and a smaller terminal time. Moreover, different immunization strategies have disparate effectiveness in rumor propagation.     

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.     

Theory of rumour spreading in complex social networks

We introduce a general stochastic model for the spread of rumours, and derive mean-field equations that describe the dynamics of the model on complex social networks (in particular, those mediated by the Internet). We use analytical and numerical solutions of these equations to examine the threshold behaviour and dynamics of the model on several models of such networks: random graphs, uncorrelated scale-free networks and scale-free networks with assortative degree correlations. We show that in both homogeneous networks and random graphs the model exhibits a critical threshold in the rumour spreading rate below which a rumour cannot propagate in the system. In the case of scale-free networks, on the other hand, this threshold becomes vanishingly small in the limit of infinite system size. We find that the initial rate at which a rumour spreads is much higher in scale-free networks than in random graphs, and that the rate at which the spreading proceeds on scale-free networks is further increased when assortative degree correlations are introduced. The impact of degree correlations on the final fraction of nodes that ever hears a rumour, however, depends on the interplay between network topology and the rumour spreading rate. Our results show that scale-free social networks are prone to the spreading of rumours, just as they are to the spreading of infections. They are relevant to the spreading dynamics of chain emails, viral advertising and large-scale information dissemination algorithms on the Internet.     

An interplay model for authorities’ actions and rumor spreading in emergency event

Rumor spreading influences how rational individuals assess risks and evaluate needs, especially, it affects authorities to make decisions in an emergency-affected environments. Conversely, authorities’ response to emergency will induct public opinions as well. In this paper, we present a simple model to describe the interplay between rumor spreading and authorities’ actions in emergency situation based on utility theory. By drawing from differential equations we found that it is possible to minimize negative social utility of rumor spreading in the control of situation. At the same time, authorities’ proactive actions can improve rumor management in emergency situation and yield positive social utility. Finally, we outline strategies for authorities that can contribute to rumor management in an emergency event.     

Periodic Wave of Epidemic Spreading in Community Networks

It was reported by Cummings ef al. [Nature 427 （2004） 344] that there are periodic waves in the spatiotemporal data of epidemics. For understanding the mechanism, we study the epidemic spreading on community networks by both the SIS model and the SIRS model. We find that with the increase of infection rate, the number of total infected nodes may be stabilized at a fixed point, oscillatory waves, and periodic cycles. Moreover, the epidemic spreading in the SIS model can be explained by an analytic map.