Final Rumor Size Research Articles

Spread and control of medical rumors in a social network: A generalized diffusion model with a highly asymmetric network structure

Medical rumors have become a threat to modern society. To study the spread and control of rumors, nonlinear differential equations modeling with the well‐mixed assumption is commonly used. However, this approach ignores the underlying network structure which plays an important role in information spreading. We establish a generalized differential equations model to study the spread and control of medical rumors in a highly asymmetric social network. In our model, each node represents a group of people and a “weighted” and “directed” network describes the communications between these nodes. This network can be generated from real‐world data by community detection algorithms. We provide methods to numerically calculate the final size of a rumor in each node and its derivatives with respect to each parameter. With these methods, if the government has resources to influence the parameters subject to certain constraints or cost functions, one can obtain the optimal resources allocation easily through nonlinear programming algorithms. We show that the implications on the government's resources allocation from the well‐mixed special case in the literature or conventional wisdom may become inapplicable in the general situation. Therefore, the underlying network should not be ignored. Because the final size of a medical rumor is not always the best measure of its damage, we extend our results to a wide class of objectives and show that different objectives result in very different implications. While the lack of a rule of thumb may sound negative, our flexible framework provides a powerful workhorse for interested parties to work out the details in their specific situations. Finally, we provide a sufficient condition for no outbreak of rumors. This condition can serve as a heuristic that a government with abundant resources can use to prevent the outbreak of rumors.

A novel complex social network rumor stochastic model: Convergence in distribution to a final rumor size

We introduce a chain-binomial model in a heterogeneous complex social network (HCSN) to investigate the spread of a rumor. A novel formulation of the state of the Markov chain (MC) for the SEIR (susceptible-exposed-infected-removed) rumor epidemic model is obtained, where two discrete time measures represent individuals in their disease states both instantaneously, and also the total time duration in each state. The general MC is characterized in the HCSN, for both the mean-field and global levels of the network rumor epidemic dynamics. The convergence in distribution of the MC to the final size of the rumor epidemic random variable is fully characterized. Moreover, the algorithm to obtain the expected final number of nodes that ever hear the rumor is given. An example to demonstrate the algorithm is presented.

Official long-term and short-term strategies for preventing the spread of rumors

<abstract> <p>Recently, public security incidents caused by rumor spreading have frequently occurred, leading to public panic, social chaos and even casualties. Therefore, how governments establish strategies to restrain rumor spreading is important for judging their governance capacity. Herein, we consider one long-term strategy (education) and two short-term strategies (isolation and debunking) for officials to intervene in rumor spreading. To investigate the effects of these strategies, an improved rumor-spreading model and a series of mean-field equations are proposed. Through theoretical analysis, the effective thresholds of three rumor-prevention strategies are obtained, respectively. Finally, through simulation analysis, the effectiveness of these strategies in preventing rumor spreading is investigated. The results indicate that long-term and short-term strategies are effective in suppressing rumor spreading. The greater the efforts of governments to suppress rumors, the smaller the final rumor size. The study also shows that the three strategies are the best when applied simultaneously. The government can adopt corresponding measures to suppress rumor spreading effectively.</p> </abstract>

Effect of Global and Local Refutation Mechanism on Rumor Propagation in Heterogeneous Network

In the process of rumors propagation, the behavior of individuals to propagation or refutation is not only influenced by the surrounding global environment but also the local environment. In this paper, a modified rumor propagation model is proposed considering the global and local effects of the rumor refutation mechanism and the activity rate of individuals in a heterogeneous network, and the dynamics process of the rumor propagation is derived by using the mean-field equation. Combining theoretical proving and simulation analysis, it shows that the critical threshold of rumor propagation has a great relationship with individual activity rates and global and local effects of the rumor refutation mechanism. The greater the government’s efforts to refute rumors, the lower the critical threshold of rumor propagation and the smaller the final rumor size. While relatively, people are much more likely to believe the global rumor refutation information taken with official information, local rumor refutation information has little influence on rumor propagation.

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.

Dynamical behaviors and spatial diffusion in a psychologically realistic rumor spreading model

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.

The influence of oblivion-recall mechanism and loss-interest mechanism on the spread of rumors in complex networks

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 [Formula: see text] and the recall factor [Formula: see text] 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 [Formula: see text], [Formula: see text] and the propagation critical thresholds [Formula: see text] is investigated. It shows that [Formula: see text] is directly proportional to [Formula: see text], which indicates that the loss-interest mechanism makes [Formula: see text] exist, and the oblivion-recall mechanism increases the value of [Formula: see text]. 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.

SE2IR Invest Market Rumor Spreading Model Considering Hesitating Mechanism

Abstract According to the actual situation of investor network, a SE2IR rumor spreading model with hesitating mechanism is proposed, and the corresponding mean-field equations is obtained on scale-free network. In this paper, we first combine the theory of spreading dynamics and find out the basic reproductive number R0. And then analyzes the stability of the rumor-free equilibrium and the final rumor size. Finally, we discuss random immune strategies and target immune strategies for the rumor spreading, respectively. Through numerical simulation, we can draw the following conclusions: Reducing the fuzziness and attractiveness of invest market rumor can effectively reduce the impact of rumor. And the target immunization strategy is more effective than the random immunization strategy for the communicators in the invest investor network.

Rumor and authoritative information propagation model considering super spreading in complex social networks

The research of rumor spreading and controlling has become an important issue in social networks. In this paper, we propose a novel rumor and authoritative information propagation model considering the super spreading mechanism. We derive mean-field equations to describe the dynamics of the rumor and authoritative information propagation model. Then the basic reproduction number and the final size of rumor and authoritative information are estimated. Simulations are conducted in a Barabási–Albert scale-free network to verify the effectiveness by comparing the proposed model with real data in Sina Weibo and to analyze the dynamics of the model. The results show that the influence of super spreading mechanism on rumor is greater than that on authoritative information. The presence of the super spreading mechanism only on rumor will cause explosive growth of the final rumor spreading size. Besides, the stronger the force of authoritative information, the smaller the final rumor spreading size and the larger the final authoritative information size. What is more, the influence of the force of authoritative information to attract individuals to spread it has greater influence on the final rumor and authoritative information spreading size than the force to forbid spreading rumors. The results are useful to understand better the mechanism of rumor propagation and refutation in complex social networks.

Rumor spreading model considering hesitating mechanism in complex social networks

The study of rumor spreading has become an important issue on complex social networks. On the basis of prior studies, we propose a modified ​susceptible–exposed–infected–removed (SEIR) model with hesitating mechanism by considering the attractiveness and fuzziness of the content of rumors. We derive mean-field equations to characterize the dynamics of SEIR model on both homogeneous and heterogeneous networks. Then a steady-state analysis is conducted to investigate the spreading threshold and the final rumor size. Simulations on both artificial and real networks show that a decrease of fuzziness can effectively increase the spreading threshold of the SEIR model and reduce the maximum rumor influence. In addition, the spreading threshold is independent of the attractiveness of rumor. Simulation results also show that the speed of rumor spreading obeys the relation “BA network > WS network”, whereas the final scale of spreading obeys the opposite relation.

SIR Rumor Spreading Model with Network Medium in Complex Social Networks

In this paper, taking into consideration the influence of the network medium, we propose a novel susceptible-infected-removed (SIR) model to study rumor spreading, and discuss by means of mean-field theory the dynamical behaviors of the SIR model on homogeneous networks and inhomogeneous networks, respectively. Theoretical analysis and simulation results show that, in both networks, the existence of the network medium greatly reduces the critical thresholds and increases the final rumor size. By numerical simulations, we also find that rumor spreading obviously accelerates with an increase of the infectivity between persons and the network medium, but the influence of the network medium on homogeneous networks is greater than on inhomogeneous networks. Therefore, to effectively control rumor spreading, it will not only be necessary to control the rumor spreading rate among different individuals, but one also needs to control the infectivity between persons and the network medium.

2SI2R rumor spreading model in homogeneous networks

Similarities exist between the rumor spreading and the infectious disease transmission. Some researches on the disease spreading involve two or more diseases which are cross-infection propagation. Similarly, two or several kinds of rumors may spread at the same time. In this paper, we study a rumor spreading model called 2SI2R model, in which two types of rumors spread simultaneously among the crowd. Derived from mean-field equations, the dynamics of the 2SI2R rumor spreading model in homogeneous networks is elucidated. Employing the method on infectious diseases, the basic reproduction number, the stability of the disease-free equilibrium, and the final size of rumor are investigated and discussed. In the numerical simulation part, the interaction of two rumors and the impact of different parameters on the rumor spreading are discussed.

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.