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Traveling Waves in a Nonlocal Dispersal SIR Model with Standard Incidence Rate and Nonlocal Delayed Transmission

Author

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  • Kuilin Wu

    (Department of Mathematics, Guizhou University, Guiyang 550025, China)

  • Kai Zhou

    (School of Mathematics and Computer, Chizhou University, Chizhou 247000, China)

Abstract

In this paper, we study the traveling wave solutions for a nonlocal dispersal SIR epidemic model with standard incidence rate and nonlocal delayed transmission. The existence and nonexistence of traveling wave solutions are determined by the basic reproduction number of the corresponding reaction system and the minimal wave speed. To prove these results, we apply the Schauder’s fixed point theorem and two-sided Laplace transform. The main difficulties are that the complexity of the incidence rate in the epidemic model and the lack of regularity for nonlocal dispersal operator.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:7:p:641-:d:249551
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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.
    2. Kai Zhou & Qi-Ru Wang, 2014. "Existence of Traveling Waves for a Delayed SIRS Epidemic Diffusion Model with Saturation Incidence Rate," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-8, April.
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    Cited by:

    1. Martin Kröger & Reinhard Schlickeiser, 2024. "On the Analytical Solution of the SIRV-Model for the Temporal Evolution of Epidemics for General Time-Dependent Recovery, Infection and Vaccination Rates," Mathematics, MDPI, vol. 12(2), pages 1-19, January.

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