Numerical Simulations of Kinetic Models for chemotaxis

TL;DR

This paper introduces a new Cartesian mesh algorithm for simulating kinetic models of chemotaxis, analyzing how geometry affects bacterial behavior and validating the method through numerical experiments and experimental comparisons.

Contribution

The paper presents a novel numerical scheme for kinetic chemotaxis models on arbitrary geometries, demonstrating its accuracy, stability, and ability to replicate biological phenomena.

Findings

The scheme accurately captures bacterial aggregation and wave propagation.

Geometry significantly influences collective bacterial behavior.

Numerical results align well with experimental data.

Abstract

We present a new algorithm based on a Cartesian mesh for the numerical approximation of kinetic models for chemosensitive movements set in an arbitrary geometry. We investigate the influence of the geometry on the collective behavior of bacteria described by a kinetic equation interacting with nutrients and chemoattractants. Numerical simulations are performed to verify accuracy and stability of the scheme and its ability to exhibit aggregation of cells and wave propagations. Finally some comparisons with experiments show the robustness and accuracy of such kinetic models.