Stability analysis of an SDILR model based on rumor recurrence on social media

Yao, Yao; Xiao, Xi; Zhang, Chengping; Dou, Changsheng; Xia, Shu-Tao

doi:10.1016/j.physa.2019.122236

Cited by 36 publications

(18 citation statements)

References 26 publications

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“…On this basis, Maki and Thompson assumed that when a spreader contacted with other spreader, the spreader would stop spreading rumors and proposed MK model [ 2 ]. Until today, many researchers applied or improved the classical rumor propagation model, such as SI (susceptible–infected), SIR, and applied it in rumor spreading [ 3 – 10 ]. In Ref.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2021

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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.

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Section: Introductionmentioning

confidence: 99%

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

et al. 2021

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“…Huo et al 16 studied the rumor propagation model with two different forms of media reports and used Lyapunov function method to analyze the global stability of the boundary equilibrium point and the positive equilibrium point. Yao et al 17 considered the filtering function of network social media and explored the phenomenon of rumors spreading on social media by using a mathematical model named SDILR. Zhou et al 18 studied the prevention and control measures of online rumors from the perspective of self‐media.…”

Section: Introductionmentioning

confidence: 99%

Analyzing the dynamics of a stochastic rumor propagation model incorporating media coverage

Huo

Dong

2020

Math Methods in App Sciences

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In the age of information globalization, research on the mechanism of propagation will help mitigate the bad influence of rumors. Based on the classical rumor propagation model, this paper further analyzes the internal mechanism of the stochastic rumor propagation model incorporating media coverage with white noise. We investigate the existence of a unique global positive solution to the model and study the dynamic properties of the solutions around the rumor-free and local equilibrium points of the deterministic model. Furthermore, we establish sufficient conditions for the existence of traversal static distribution in the model. Numerical simulation shows that the role of media coverage is crucial to reduce the rumor propagation scale. The larger the coverage rate is, the smaller the rumor propagation scale is. K E Y W O R D Sergodic process, media coverage, rumor propagation, stochastic process

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“…Furthermore, a rumour transmission model with Holling type II functional response was proposed by Huo et al [10] to explain the impact of scientific knowledge on rumour spreading. The phenomenon of rumour-mongering repeatedly on social media was also explored by Yao et al [33] using a susceptible-dangerous-infective-latent-recovered (SDILR) rumour spreading model, and analyses of the local and global asymptotic stabilities were presented. Although the existing models may adequately describe the rumour spreading process, they have yet to consider the impact of uncertain environmental factors on rumour spreading.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic Behaviour of the Stochastic Maki–thompson Model With a Forgetting Mechanism on Open Populations

Yang

2020

ANZIAM J.

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Rumours have become part of our daily lives, and their spread has a negative impact on a variety of human affairs. Therefore, how to control the spread of rumours is an important topic. In this paper, we extend the classic Maki–Thompson model from a deterministic framework to a stochastic framework with a forgetting mechanism, because real-world person-to-person communications are inevitably affected by random factors. By constructing suitable stochastic Lyapunov functions, we show that the asymptotic behaviour of the stochastic rumour model is governed by the basic reproductive number. If this number is less than one, then the solution of the stochastic rumour model oscillates around the rumour-free equilibrium under extra mild conditions, indicating the extinction of the rumour with a probability of one. Otherwise, the solution always fluctuates around the endemic equilibrium under certain parametric restrictions, implying that the rumour will continually persist. In addition, we discuss a possible intervention strategy that stops the spread of rumours by strengthening the intensity of white noise, which is very different from the deterministic rumour model without white noise. Also, numerical simulations are conducted to support our analytical results.

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Stability analysis of an SDILR model based on rumor recurrence on social media

Cited by 36 publications

References 26 publications

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

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

Analyzing the dynamics of a stochastic rumor propagation model incorporating media coverage

Asymptotic Behaviour of the Stochastic Maki–thompson Model With a Forgetting Mechanism on Open Populations

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