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Traveling waves for a diffusive SIR epidemic model with delay in the diffusion term

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  • Barker, William

Abstract

This paper investigates the existence of traveling waves in a diffusive SIR model with delay incorporated in the diffusion terms and a nonlinear incidence rate with delay. By employing a cross-iteration scheme and partial monotonicity conditions, we establish that the existence of quasi-upper and lower solutions, along with suitable super and sub-solutions, provides sufficient conditions for the existence of a traveling wavefront. This existence result is obtained via Schauder’s fixed-point theorem. Furthermore, given an appropriate basic reproduction number, the traveling wavefront transitions from the disease-free steady state to the endemic steady state. To illustrate our approach, we explicitly construct super- and sub-solutions for a specific model.

Suggested Citation

  • Barker, William, 2026. "Traveling waves for a diffusive SIR epidemic model with delay in the diffusion term," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 239(C), pages 245-262.
    • Handle: RePEc:eee:matcom:v:239:y:2026:i:c:p:245-262
    DOI: 10.1016/j.matcom.2025.04.027
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    1. repec:plo:pone00:0021128 is not listed on IDEAS
    2. 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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