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Modelling collective invasion with reaction-diffusion equations: When does domain curvature matter?

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Neglecting curved geometry in reaction-diffusion models can lead to inaccuracies. This study quantifies when it

Keywords:
AnnulusCellular invasionFisher-KPPReaction–diffusion

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Area of Science:

  • Mathematical Biology
  • Computational Science
  • Physics

Background:

  • Cellular invasion often occurs in curved environments.
  • Simplifying models by ignoring curvature can introduce prediction errors.

Purpose of the Study:

  • To determine criteria for validly neglecting curved geometry in reaction-diffusion models.
  • To analyze the impact of curvature on invasion dynamics.

Main Methods:

  • Analytical exploration of reaction-diffusion equations (RDEs) on an annular geometry.
  • Asymptotic expansion to derive conditions for ignoring curvature.
  • Numerical simulations of the Fisher-KPP model on annular and rectangular domains.

Main Results:

  • Derived conditions for when domain curvature can be ignored in RDEs.
  • Quantified deviations in invasion dynamics between curved and flat geometries.
  • Showcased how deviations vary across annulus width and with geometric parameters (r0, δ).

Conclusions:

  • Provides crucial insights into the validity of simplifying assumptions in reaction-diffusion modeling.
  • Offers guidance on when to account for curved geometries in studying traveling wave phenomena.
  • Highlights the importance of geometric considerations in biological invasion models.