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Dynamic Analysis and Optimal Control of ISCR Rumor Propagation Model with Nonlinear Incidence and Time Delay on Complex Networks

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  • Zhongxue Chang
  • Haijun Jiang
  • Shuzhen Yu
  • Shanshan Chen
  • Giulio E. Cantarella

Abstract

An Innocents-Spreaders-Calmness-Removes (ISCR) rumor propagation model is established with nonlinear incidence and time delay on complex networks in this paper. Based on the mean-field theory, the spreading dynamics of the ISCR model are discussed in detail. Firstly, the basic reproduction number R0 is obtained by the next generation matrix method to ensure the existence of rumor-prevailing equilibrium. Secondly, by utilizing the Routh–Hurwitz criterion and LaSalle’s invariance principle, the local stability and global stability of rumor equilibria are proved. Moreover, the optimal control is presented via Pontryagin’s minimum principle, which is to effectively restrain rumor diffusion. Finally, the theoretical results are verified by numerical simulations.

Suggested Citation

  • Zhongxue Chang & Haijun Jiang & Shuzhen Yu & Shanshan Chen & Giulio E. Cantarella, 2021. "Dynamic Analysis and Optimal Control of ISCR Rumor Propagation Model with Nonlinear Incidence and Time Delay on Complex Networks," Discrete Dynamics in Nature and Society, Hindawi, vol. 2021, pages 1-20, September.
    • Handle: RePEc:hin:jnddns:3935750
    DOI: 10.1155/2021/3935750
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    Cited by:

    1. Xuefeng Yue & Liangan Huo, 2022. "Analysis of the Stability and Optimal Control Strategy for an ISCR Rumor Propagation Model with Saturated Incidence and Time Delay on a Scale-Free Network," Mathematics, MDPI, vol. 10(20), pages 1-20, October.

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