中国物理B ›› 2023, Vol. 32 ›› Issue (7): 70205-070205.doi: 10.1088/1674-1056/acd2be

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An improved ISR-WV rumor propagation model based on multichannels with time delay and pulse vaccination

Yafang Dong(董雅芳), Liangán Huo(霍良安)†, Xiaoxiao Xie(谢笑笑), and Ming Li(李明)   

  1. Business School, University of Shanghai for Science and Technology, Shanghai 200093, China
  • 收稿日期:2023-02-17 修回日期:2023-04-24 接受日期:2023-05-05 出版日期:2023-06-15 发布日期:2023-07-05
  • 通讯作者: Liangán Huo E-mail:huohuolin@yeah.net
  • 基金资助:
    This work was partially supported by the Project for the National Natural Science Foundation of China (Grant Nos. 72174121 and 71774111), the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning, and the Project for the Natural Science Foundation of Shanghai (Grant No. 21ZR1444100).

An improved ISR-WV rumor propagation model based on multichannels with time delay and pulse vaccination

Yafang Dong(董雅芳), Liangán Huo(霍良安)†, Xiaoxiao Xie(谢笑笑), and Ming Li(李明)   

  1. Business School, University of Shanghai for Science and Technology, Shanghai 200093, China
  • Received:2023-02-17 Revised:2023-04-24 Accepted:2023-05-05 Online:2023-06-15 Published:2023-07-05
  • Contact: Liangán Huo E-mail:huohuolin@yeah.net
  • Supported by:
    This work was partially supported by the Project for the National Natural Science Foundation of China (Grant Nos. 72174121 and 71774111), the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning, and the Project for the Natural Science Foundation of Shanghai (Grant No. 21ZR1444100).

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摘要： The rapid development of the Internet has broadened the channels of dissemination of information, it has also led to the rapid and widespread propagation of rumors, which can have a serious negative impact socially. In this paper, an improved ISR-WV rumor propagation model integrating multichannels is proposed by considering the system's time delay, and the influence of different channels of propagation on the dynamic process is further analyzed. Moreover, the basic reproduction number R0 , rumor-free equilibrium, and rumor-prevailing equilibrium, as well as their stability, are deduced. Then, an optimal control problem with pulse vaccination is designed. Finally, the validity of the model and theoretical results is verified by numerical simulations and a practical application. The results show that the rumor propagation threshold R0 is more sensitive to the rate of the propagation of the information base channel. The shorter the thinking time τ1 required for the ignorant to react after obtaining the information, the larger the final scale of propagation. Under this condition, the time delay τ2 spent by a spreader in producing a video is negatively related to the final scale of the propagation; conversely, a longer τ1 implies that the person tends to more cognizant, which can suppress the spread of rumors. Under this condition, τ2 has little effect on the final scale of propagation. In addition, the results also prove that timely implementation of the pulse vaccination control strategy of popular science education can effectively control the propagation of rumors and reduce their negative impact.

关键词: rumor propagation, propagation channels, pulse vaccination control, time delay, information base

Abstract: The rapid development of the Internet has broadened the channels of dissemination of information, it has also led to the rapid and widespread propagation of rumors, which can have a serious negative impact socially. In this paper, an improved ISR-WV rumor propagation model integrating multichannels is proposed by considering the system's time delay, and the influence of different channels of propagation on the dynamic process is further analyzed. Moreover, the basic reproduction number R0 , rumor-free equilibrium, and rumor-prevailing equilibrium, as well as their stability, are deduced. Then, an optimal control problem with pulse vaccination is designed. Finally, the validity of the model and theoretical results is verified by numerical simulations and a practical application. The results show that the rumor propagation threshold R0 is more sensitive to the rate of the propagation of the information base channel. The shorter the thinking time τ1 required for the ignorant to react after obtaining the information, the larger the final scale of propagation. Under this condition, the time delay τ2 spent by a spreader in producing a video is negatively related to the final scale of the propagation; conversely, a longer τ1 implies that the person tends to more cognizant, which can suppress the spread of rumors. Under this condition, τ2 has little effect on the final scale of propagation. In addition, the results also prove that timely implementation of the pulse vaccination control strategy of popular science education can effectively control the propagation of rumors and reduce their negative impact.

Key words: rumor propagation, propagation channels, pulse vaccination control, time delay, information base

中图分类号:  (Delay and functional equations)

  • 02.30.Ks
02.30.Hq (Ordinary differential equations) 02.30.Yy (Control theory) 02.30.-f (Function theory, analysis)