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Synchronization of Epidemic Systems with Neumann Boundary Value under Delayed Impulse

Author

Listed:
  • Ruofeng Rao

    (Department of Mathematics, Chengdu Normal University, Chengdu 611130, China)

  • Zhi Lin

    (Department of Mathematics, Chengdu Normal University, Chengdu 611130, China
    School of Mathematical and Computational Science, Hunan University of Science and Technology, Xiangtan 411201, China)

  • Xiaoquan Ai

    (Department of Mathematics, Chengdu Normal University, Chengdu 611130, China)

  • Jiarui Wu

    (Department of Mathematics, Chengdu Normal University, Chengdu 611130, China)

Abstract

This paper reports the construction of synchronization criteria for the delayed impulsive epidemic models with reaction–diffusion under the Neumann boundary value. Different from the previous literature, the reaction–diffusion epidemic model with a delayed impulse brings mathematical difficulties to this paper. In fact, due to the existence of second-order partial derivatives in the reaction–diffusion model with a delayed impulse, the methods of first-order ordinary differential equations from the previous literature cannot be effectively applied in this paper. However, with the help of the variational method and an appropriate boundedness assumption, a new synchronization criterion is derived, and its effectiveness is illustrated by numerical examples.

Suggested Citation

  • Ruofeng Rao & Zhi Lin & Xiaoquan Ai & Jiarui Wu, 2022. "Synchronization of Epidemic Systems with Neumann Boundary Value under Delayed Impulse," Mathematics, MDPI, vol. 10(12), pages 1-10, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:12:p:2064-:d:839182
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    References listed on IDEAS

    as
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    2. Rihan, F.A. & Al-Mdallal, Q.M. & AlSakaji, H.J. & Hashish, A., 2019. "A fractional-order epidemic model with time-delay and nonlinear incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 97-105.
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    4. Cao, Wenping & Zhu, Quanxin, 2021. "Stability analysis of neutral stochastic delay differential equations via the vector Lyapunov function method," Applied Mathematics and Computation, Elsevier, vol. 405(C).
    5. Yan Ji & Jinde Cao, 2022. "Parameter Estimation Algorithms for Hammerstein Finite Impulse Response Moving Average Systems Using the Data Filtering Theory," Mathematics, MDPI, vol. 10(3), pages 1-16, January.
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