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

William Barker

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 239, issue C, 245-262

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.

Keywords: Traveling waves; Reaction–diffusion equations; Delay; SIR model (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:239:y:2026:i:c:p:245-262

DOI: 10.1016/j.matcom.2025.04.027

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