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Wave propagation in a nonlocal diffusion epidemic model with nonlocal delayed effects

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  • Zhen, Zaili
  • Wei, Jingdong
  • Zhou, Jiangbo
  • Tian, Lixin

Abstract

A nonlocal diffusion epidemic model with nonlocal delayed effects is investigated. The existence and non-existence of the non-trivial and non-negative traveling wave solutions for the model are obtained, respectively. It is found that the threshold dynamics of the model is determined by the basic reproduction number of the corresponding reaction system and minimal wave speed.

Suggested Citation

  • Zhen, Zaili & Wei, Jingdong & Zhou, Jiangbo & Tian, Lixin, 2018. "Wave propagation in a nonlocal diffusion epidemic model with nonlocal delayed effects," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 15-37.
    • Handle: RePEc:eee:apmaco:v:339:y:2018:i:c:p:15-37
    DOI: 10.1016/j.amc.2018.07.007
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    References listed on IDEAS

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    1. Bai, Zhenguo & Wu, Shi-Liang, 2015. "Traveling waves in a delayed SIR epidemic model with nonlinear incidence," Applied Mathematics and Computation, Elsevier, vol. 263(C), pages 221-232.
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    Cited by:

    1. Guo, Zun-Guang & Sun, Gui-Quan & Wang, Zhen & Jin, Zhen & Li, Li & Li, Can, 2020. "Spatial dynamics of an epidemic model with nonlocal infection," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    2. Wei, Jingdong & Zhou, Jiangbo & Zhen, Zaili & Tian, Lixin, 2019. "Super-critical and critical traveling waves in a two-component lattice dynamical model with discrete delay," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    3. Wu, Weixin & Teng, Zhidong, 2021. "The periodic traveling waves in a diffusive periodic SIR epidemic model with nonlinear incidence," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).

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