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The periodic traveling waves in a diffusive periodic SIR epidemic model with nonlinear incidence

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  • Wu, Weixin
  • Teng, Zhidong

Abstract

In this paper, a reaction-diffusion SIR epidemic model is proposed. It takes into account the individuals mobility, the time periodicity of the infection rate and recovery rate, and the general nonlinear incidence function, which contains a number of classical incidence functions. In our model, due to the introduction of the general nonlinear incidence function, the boundedness of the infected individuals can not be obtained, so we study the existence and nonexistence of periodic traveling wave solutions of original system with the aid of auxiliary system. The basic reproduction number R0 and the critical wave speed c* are given. We obtained the existence and uniqueness of periodic traveling waves for each wave speed c>c* using the Schauder’s fixed points theorem when R0>1. The nonexistence of periodic traveling waves for two cases (i) R0>1 and 0

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:144:y:2021:i:c:s0960077921000369
    DOI: 10.1016/j.chaos.2021.110683
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    References listed on IDEAS

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    1. 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.
    2. Shan Wang & Youhua Peng & Feng Wang, 2020. "Stability and Asymptotic Behavior of a Regime-Switching SIRS Model with Beddington–DeAngelis Incidence Rate," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-12, July.
    3. Yu, Zhixian & Yuan, Rong, 2012. "Existence and asymptotics of traveling waves for nonlocal diffusion systems," Chaos, Solitons & Fractals, Elsevier, vol. 45(11), pages 1361-1367.
    4. 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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    Cited by:

    1. Li, Wenjie & Zhang, Ying & Cao, Jinde & Wang, Dongshu, 2023. "Large time behavior in a reaction diffusion epidemic model with logistic source," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).

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