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Time periodic travelling waves for an advection–reaction–diffusion SIR epidemic model with seasonality and bilinear incidence

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  • Jiang, Xibei
  • Wu, Weixin

Abstract

In order to investigate the influence of spatial convection effect and the periodic environment on the spreading behaviour of epidemic, in this paper, an SIR epidemic model with time varying coefficients and diffusion advection is proposed. The periodic travelling waves satisfying certain boundary conditions are discussed by constructing operators on bounded closed convex sets consisting of periodic upper and lower solutions, utilizing the twice fixed point theorem and some limit techniques. The results show that the existence of travelling waves depends on the reproduction number R0 and the critical wave speed c∗. Specifically, when R0>1 and c>c∗, the existence of periodic travelling waves satisfying some boundary condition is obtained, and the nonexistence of such travelling waves for two cases (i) R0>1 and 0

Suggested Citation

  • Jiang, Xibei & Wu, Weixin, 2025. "Time periodic travelling waves for an advection–reaction–diffusion SIR epidemic model with seasonality and bilinear incidence," Chaos, Solitons & Fractals, Elsevier, vol. 191(C).
    • Handle: RePEc:eee:chsofr:v:191:y:2025:i:c:s0960077924013754
    DOI: 10.1016/j.chaos.2024.115823
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    References listed on IDEAS

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    1. 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).
    2. F. N. Si & Q. X. Liu & J. Z. Zhang & L. Q. Zhou, 2007. "Propagation of travelling waves in sub-excitable systems driven by noise and periodic forcing," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 60(4), pages 507-513, December.
    3. 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.
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