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Traveling waves in delayed lattice systems: Effects of case report delays and pathogen detection

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  • Wu, Xin
  • Ding, Zeyu
  • Yuan, Rong
  • Chen, Fangyuan

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.

Suggested Citation

  • Wu, Xin & Ding, Zeyu & Yuan, Rong & Chen, Fangyuan, 2025. "Traveling waves in delayed lattice systems: Effects of case report delays and pathogen detection," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 238(C), pages 516-535.
    • Handle: RePEc:eee:matcom:v:238:y:2025:i:c:p:516-535
    DOI: 10.1016/j.matcom.2025.06.024
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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. Kelly Charniga & Sang Woo Park & Andrei R Akhmetzhanov & Anne Cori & Jonathan Dushoff & Sebastian Funk & Katelyn M Gostic & Natalie M Linton & Adrian Lison & Christopher E Overton & Juliet R C Pulliam, 2024. "Best practices for estimating and reporting epidemiological delay distributions of infectious diseases," PLOS Computational Biology, Public Library of Science, vol. 20(10), pages 1-21, October.
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