Dynamic analysis of a rumor propagation model with Lévy noise

Jia, Fangju; Lv, Guangying; Zou, Guang‐an

doi:10.1002/mma.4694

Cited by 14 publications

(8 citation statements)

References 13 publications

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“…The models used in the above studies to describe rumor propagation behavior are mostly deterministic models, whereas the random models used to study rumor propagation are few 19–21 . But in the real world, rumor models are often affected by environmental noise.…”

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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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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“…Jia et al. [24] , [25] , [26] compared and analyzed the threshold difference between deterministic model and stochastic model with white noise fluctuation, and concluded that the basic reproduction number

of stochastic model was less than that of deterministic system. Jain et al.…”

Section: Introductionmentioning

confidence: 99%

Rumor spreading in complex networks under stochastic node activity

Cheng

Huo

Zhao

2020

Physica A: Statistical Mechanics and its Applications

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The research on rumor spreading has a long history, and its wanton flooding has brought huge impact on people’s life. In the process of its spreading, the individual’s activity plays an important role. However, in the complex and changeable environment, randomness cannot be ignored, not to mention its influence on individual activity Based on the model of individual activity, this paper explores the stochastic version of the rumor model including fluctuations in the activity. Then, the influence of Stratonovich stochastic noise on the asymptotic behavior of non-linear rumor spreading model is studied. Through the mathematical analysis, we get the critical values to measure whether the deterministic and stochastics models spread or not, as well as the threshold conditions for rumor to spread wantonly. At the same time, the effects of Stratonovich stochastic noise on the asymptotic behavior of rumor-free equilibrium point and endemic equilibrium point are obtained respectively, and the condition that the rumor-free equilibrium is globally asymptotically stable in the presence of noise is given. Finally, the theoretical results are verified by numerical simulation.

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“…Jia and Lv [14] formulated a stochastic rumour propagation model with Gaussian white noise and investigated the sufficient conditions related to extinction and persistence of rumour. They also explored a stochastic rumour model with Levy noise [15]. On the other hand, recent studies have revealed the impact of stochastic factors on complex social networks [13,38].…”

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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Dynamic analysis of a rumor propagation model with Lévy noise

Cited by 14 publications

References 13 publications

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

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

Rumor spreading in complex networks under stochastic node activity

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

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