Spreading Properties of a City-Road Reaction-Diffusion Model on One-Dimensional Lattice
Abstract
We propose and study a new model to describe biological invasions constrained on infinite homogeneous one dimensional metric graphs. Our model consists of an infinite PDE-ODE system where, at each vertex of the one-dimensional lattice ℤ, we have a logistic equation, and connections between vertices are given by diffusion equations on the edges supplemented with Robin like boundary conditions at the vertices. We establish the main properties of the system and study the long time behavior of the solutions, especially by characterizing an asymptotic spreading speed for the system. In the fast diffusion regime, we derive a novel asymptotic model which exhibits similar propagation properties as the classical discrete Fisher-KPP on the one-dimensional lattice ℤ.
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BibTeX
@article{faye2026spreading,
title = {{Spreading Properties of a City-Road Reaction-Diffusion Model on One-Dimensional Lattice}},
author = {Grégory Faye and Jean-Michel Roquejoffre and Min Zhao},
journal = {Journal of Mathematical Biology},
year = {2026},
month = sep,
doi = {10.1007/s00285-026-02466-3},
eprint = {2511.16157},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05372596v2},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Spreading Properties of a City-Road Reaction-Diffusion Model on One-Dimensional Lattice
AU - Grégory Faye
AU - Jean-Michel Roquejoffre
AU - Min Zhao
PY - 2026
DA - 2026/09/21
JO - Journal of Mathematical Biology
DO - 10.1007/s00285-026-02466-3
UR - https://hal.science/hal-05372596v2
AB - We propose and study a new model to describe biological invasions constrained on infinite homogeneous one dimensional metric graphs. Our model consists of an infinite PDE-ODE system where, at each vertex of the one-dimensional lattice ℤ, we have a logistic equation, and connections between vertices are given by diffusion equations on the edges supplemented with Robin like boundary conditions at the vertices. We establish the main properties of the system and study the long time behavior of the solutions, especially by characterizing an asymptotic spreading speed for the system. In the fast diffusion regime, we derive a novel asymptotic model which exhibits similar propagation properties as the classical discrete Fisher-KPP on the one-dimensional lattice ℤ.
SN - 0303-6812
SN - 1432-1416
ER -