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Turing instability in a network-organized epidemic model with delay

Author

Listed:
  • Zheng, Qianqian
  • Shen, Jianwei
  • Pandey, Vikas
  • Guan, Linan
  • Guo, Yantao

Abstract

In this paper, we show the impact of both network and time delays on Turing instability and demarcate the role of diffusion in the epidemic. The stability and bifurcation of equilibrium points are analyzed to reveal the epidemic state, which is the precondition of pattern formation. The network could lead to the transition from the endemic to the periodic outbreak via negative wavenumber, which provides a way to prevent significant harm or decrease the damage of the epidemic to humans by the delay, the connection rate, and the infection rate. Also, the threshold value of time delay is proportional to the minimum eigenvalue of the network matrix, which provides a way to control the periodic behavior. Finally, numerical simulations validate these analytical results and the mechanisms of frequent outbreaks.

Suggested Citation

  • Zheng, Qianqian & Shen, Jianwei & Pandey, Vikas & Guan, Linan & Guo, Yantao, 2023. "Turing instability in a network-organized epidemic model with delay," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    • Handle: RePEc:eee:chsofr:v:168:y:2023:i:c:s0960077923001066
    DOI: 10.1016/j.chaos.2023.113205
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    References listed on IDEAS

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    1. Wei, Wei & Xu, Wei & Song, Yi & Liu, Jiankang, 2021. "Bifurcation and basin stability of an SIR epidemic model with limited medical resources and switching noise," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    2. Zheng, Qianqian & Shen, Jianwei & Xu, Yong & Pandey, Vikas & Guan, Linan, 2022. "Pattern mechanism in stochastic SIR networks with ER connectivity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    3. Hua Liu & Yong Ye & Yumei Wei & Weiyuan Ma & Ming Ma & Kai Zhang, 2019. "Pattern Formation in a Reaction-Diffusion Predator-Prey Model with Weak Allee Effect and Delay," Complexity, Hindawi, vol. 2019, pages 1-14, November.
    4. Yansu Ji & Jianwei Shen, 2020. "Turing Instability of Brusselator in the Reaction-Diffusion Network," Complexity, Hindawi, vol. 2020, pages 1-12, October.
    5. Huang, Yi-Jie & Li, Chun-Hsien, 2019. "Backward bifurcation and stability analysis of a network-based SIS epidemic model with saturated treatment function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 527(C).
    6. Li, Jing & Sun, Gui-Quan & Jin, Zhen, 2014. "Pattern formation of an epidemic model with time delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 403(C), pages 100-109.
    7. Spricer, Kristoffer & Britton, Tom, 2019. "An SIR epidemic on a weighted network," Network Science, Cambridge University Press, vol. 7(4), pages 556-580, December.
    8. Zheng, Qianqian & Shen, Jianwei, 2020. "Turing instability induced by random network in FitzHugh-Nagumo model," Applied Mathematics and Computation, Elsevier, vol. 381(C).
    9. Li, Jinhui & Teng, Zhidong & Wang, Guangqing & Zhang, Long & Hu, Cheng, 2017. "Stability and bifurcation analysis of an SIR epidemic model with logistic growth and saturated treatment," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 63-71.
    10. Malbor Asllani & Joseph D. Challenger & Francesco Saverio Pavone & Leonardo Sacconi & Duccio Fanelli, 2014. "The theory of pattern formation on directed networks," Nature Communications, Nature, vol. 5(1), pages 1-9, December.
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    Cited by:

    1. Liu, Tongtao & Zhang, Yongping, 2024. "Tracking problem of the Julia set for the SIS model with saturated treatment function under noise," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).

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