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Traveling waves in a delayed SIR epidemic model with nonlinear incidence

Author

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  • Bai, Zhenguo
  • Wu, Shi-Liang

Abstract

We establish the existence and non-existence of traveling wave solutions for a diffusive SIR model with a general nonlinear incidence. The existence proof is shown by introducing an auxiliary system, applying Schauder’s fixed point theorem and then a limiting argument. The nonexistence proof is obtained by two-sided Laplace transform when the speed is less than the critical velocity. Numerical simulations support the theoretical results. We also point out the effects of the delay and the diffusion rate of the infective individuals on the spreading speed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:263:y:2015:i:c:p:221-232
    DOI: 10.1016/j.amc.2015.04.048
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    Citations

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    Cited by:

    1. Vsevolod G. Sorokin & Andrei V. Vyazmin, 2022. "Nonlinear Reaction–Diffusion Equations with Delay: Partial Survey, Exact Solutions, Test Problems, and Numerical Integration," Mathematics, MDPI, vol. 10(11), pages 1-39, May.
    2. Zhang, Zizhen & Kundu, Soumen & Tripathi, Jai Prakash & Bugalia, Sarita, 2020. "Stability and Hopf bifurcation analysis of an SVEIR epidemic model with vaccination and multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    3. Wang, Jinliang & Zhang, Ran & Kuniya, Toshikazu, 2021. "A reaction–diffusion Susceptible–Vaccinated–Infected–Recovered model in a spatially heterogeneous environment with Dirichlet boundary condition," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 848-865.
    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.
    5. Andrei D. Polyanin & Vsevolod G. Sorokin, 2023. "Exact Solutions of Reaction–Diffusion PDEs with Anisotropic Time Delay," Mathematics, MDPI, vol. 11(14), pages 1-19, July.
    6. Kuilin Wu & Kai Zhou, 2019. "Traveling Waves in a Nonlocal Dispersal SIR Model with Standard Incidence Rate and Nonlocal Delayed Transmission," Mathematics, MDPI, vol. 7(7), pages 1-22, July.
    7. Zhu, Peican & Wang, Xinyu & Li, Shudong & Guo, Yangming & Wang, Zhen, 2019. "Investigation of epidemic spreading process on multiplex networks by incorporating fatal properties," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 512-524.
    8. Nan Xu & Yaoqun Xu, 2022. "Research on Tacit Knowledge Dissemination of Automobile Consumers’ Low-Carbon Purchase Intention," Sustainability, MDPI, vol. 14(16), pages 1-26, August.
    9. Zhang, Zizhen & Rahman, Ghaus ur & Gómez-Aguilar, J.F. & Torres-Jiménez, J., 2022. "Dynamical aspects of a delayed epidemic model with subdivision of susceptible population and control strategies," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    10. Andrei D. Polyanin & Vsevolod G. Sorokin, 2023. "Reductions and Exact Solutions of Nonlinear Wave-Type PDEs with Proportional and More Complex Delays," Mathematics, MDPI, vol. 11(3), pages 1-25, January.

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