Dynamics of the Rumor‐Spreading Model with Control Mechanism in Complex Network

Abstract

The spread of rumors has a great impact on social order, people’s psychology, and life. In recent years, the application of rumor-spreading models in complex networks has received extensive attention. Taking the management and control of rumors by relevant departments in real life into account, the SIDRQ rumor-spreading model that combines forgetting mechanism, immune mechanism, and suspicion mechanism and guides on a uniform network is established in this paper. Then, the basic reproductive number of the system and the unique existence of the solution are discussed, and the stability of the system is analyzed using the basic reproductive number, Lyapunov function, and Lienard and Chipart theorem; furthermore, the basic reproductive number may not be able to deduce the stability of the system and a counterexample is given. Finally, the influence of different parameters on the spread of rumors is studied, and the validity of the theoretical results is verified.

SEIOR Rumor Propagation Model Considering Hesitating Mechanism and Different Rumor-Refuting Ways in Complex Networks

“…Wang et al [20] considered a containment mechanism and forgetting mechanism in the propagation of network information and believed that infected nodes would become immune nodes due to the containment mechanism. Since then, more and more scholars have proposed different rumor propagation mechanisms, such as the hesitating mechanism [21,22], trust mechanism [23], counterattack mechanism [24,25], recurrence mechanism [26], and propagation mechanism integrating multiple mechanisms [27].…”

“…Zhao et al studied the rumor propagation characteristics on the homogeneous network [52], scale-free network [18], and Barrat-Barthelemy-Vespignani (BBV) weighted network [53], and deduced the rumor propagation thresholds on different networks. Since then, more and more scholars have studied the dynamic behavior of rumor propagation models with different propagation mechanisms in complex networks [21,24,27,[54][55][56][57][58][59]. These studies show that complex networks can more truly reflect real social networks and that many real social networks are very close to heterogeneous networks whose topologies are more complex than homogeneous networks.…”

Study on an SIR rumor propagation model with an interaction mechanism on WeChat networks

“…Considering the heterogeneity of the network, a 2SIH2R model was studied with the mechanisms of discernment and confrontation in a heterogeneous network to examine the dissemination of the rumor and the truth [19]. Taking the management and control of rumors by relevant departments in real life into account, the SIDRQ rumor-spreading model with the forgetting mechanism, immune mechanism, and suspicion mechanism and guides on a uniform network was established [20]. A novel susceptible-exposed-infected-recovered (SEIR)-delayed rumor propagation model with saturation incidence on heterogeneous networks was devoted to investigation [21].…”

Dynamic Analysis and Optimal Control of Rumor Propagation Model with Reporting Effect

“…By studying the above influencing factors, many scholars have further considered the influence of the forgetting mechanism [25][26][27] and other communication mechanisms [28,29], proportion of wise people [30], and vigilance [31] of rumor spread on the process of rumor spread. Gu et al [25] considered the influence of forgetting and memory mechanisms on the spread process of rumors and proposed that under certain conditions, forgetting and memory mechanisms would terminate the propagation process of rumors.…”

“…In 2011, Zhao et al [26], combined with the forgetting mechanism, established the rumor propagation model on the online social blog platform Livejournal. On this basis, Zhao et al [27] discussed the influence of the new state of the hibernator on the rumor propagation process and proposed a rumor propagation model. Considering the different personal attitudes toward the propagation of rumors, Hu et al [28] proposed the hypothesis that the public has three attitudes toward rumor propagation: They like the propagation of rumors, they do not like the propagation of rumors, and they are hesitant (or neutral) about the propagation of rumors.…”