Turing pattern induced by the directed ER network and delay

Qianqian Zheng; Jianwei Shen; Lingli Zhou; Linan Guan; Qianqian Zheng; Jianwei Shen; Lingli Zhou; Linan Guan

doi:10.3934/mbe.2022553

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 12: 11854-11867. doi: 10.3934/mbe.2022553

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Research article Special Issues

Turing pattern induced by the directed ER network and delay

1.
School of Science, Xuchang University; Henan Joint International Research Laboratory of High Performance Computation for Complex Systems, Xuchang 461000, China
2.
School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou 450046, China
3.
School of Mathematical Sciences, Soochow University, Suzhou 215006, China

Academic Editor: Masaki Ogura

Received: 01 June 2022 Revised: 24 July 2022 Accepted: 02 August 2022 Published: 17 August 2022

Infectious diseases generally spread along with the asymmetry of social network propagation because the asymmetry of urban development and the prevention strategies often affect the direction of the movement. But the spreading mechanism of the epidemic remains to explore in the directed network. In this paper, the main effect of the directed network and delay on the dynamic behaviors of the epidemic is investigated. The algebraic expressions of Turing instability are given to show the role of the directed network in the spread of the epidemic, which overcomes the drawback that undirected networks cannot lead to the outbreaks of infectious diseases. Then, Hopf bifurcation is analyzed to illustrate the dynamic mechanism of the periodic outbreak, which is consistent with the transmission of COVID-19. Also, the discrepancy ratio between the imported and the exported is proposed to explain the importance of quarantine policies and the spread mechanism. Finally, the theoretical results are verified by numerical simulation.
- SIR,
- pattern formation,
- network,
- turing instability,
- delay
Citation: Qianqian Zheng, Jianwei Shen, Lingli Zhou, Linan Guan. Turing pattern induced by the directed ER network and delay[J]. Mathematical Biosciences and Engineering, 2022, 19(12): 11854-11867. doi: 10.3934/mbe.2022553

Related Papers:

Abstract

Infectious diseases generally spread along with the asymmetry of social network propagation because the asymmetry of urban development and the prevention strategies often affect the direction of the movement. But the spreading mechanism of the epidemic remains to explore in the directed network. In this paper, the main effect of the directed network and delay on the dynamic behaviors of the epidemic is investigated. The algebraic expressions of Turing instability are given to show the role of the directed network in the spread of the epidemic, which overcomes the drawback that undirected networks cannot lead to the outbreaks of infectious diseases. Then, Hopf bifurcation is analyzed to illustrate the dynamic mechanism of the periodic outbreak, which is consistent with the transmission of COVID-19. Also, the discrepancy ratio between the imported and the exported is proposed to explain the importance of quarantine policies and the spread mechanism. Finally, the theoretical results are verified by numerical simulation.

References

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