 Traveling waves in delayed lattice systems: Effects of case report delays and pathogen detectionXin Wu, Zeyu Ding, Rong Yuan and Fangyuan Chen Mathematics and Computers in Simulation (MATCOM), 2025, vol. 238, issue C, 516-535 Abstract: This paper presents a delayed lattice dynamical system derived from a diffusive disease model, where the delay arises from case reporting lags and the time required for pathogen detection. The system accounts for discrete diffusion, reflecting the real-world scenario where cases are reported by discrete monitoring points, such as sentinel hospitals. By applying Schauder’s fixed point theorem, the Lyapunov–LaSalle theorem, and Lebesgue’s dominated convergence theorem, the existence of super-critical and critical traveling waves is established. Additionally, the non-existence of such waves is demonstrated using the bilateral Laplace transform. The paper concludes with a discussion and numerical simulation on how spatial movement patterns among infected individuals and time delays affect the determination of critical velocity, emphasizing the significance of these factors in disease spread dynamics. Keywords: Traveling waves; Diffusive SIR epidemic model; Lattice dynamical system; Report delay; Lyapunov–LaSalle theorem (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:238:y:2025:i:c:p:516-535 DOI: 10.1016/j.matcom.2025.06.024 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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