Derivation from kinetic theory and 2-D pattern analysis of chemotaxis models for Multiple Sclerosis

2025/01/20 by Marzia Bisi, Maria Groppi, Bisi, Marzia +5 · 1 voice · 3 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · #Mathematical Biology Tumor Growth #q-bio.QM

paper · pdf · doi:10.48550/arxiv.2501.13119

arxiv published 2025/01/20 · arxiv updated 2026/01/02

Abstract

In this paper, a class of reaction-diffusion equations for Multiple Sclerosis is presented. These models are derived by means of a diffusive limit starting from a proper kinetic description, taking account of the underlying microscopic interactions among cells. At the macroscopic level, we discuss the necessary conditions for Turing instability phenomena and the formation of two-dimensional patterns, whose shape and stability are investigated by means of a weakly nonlinear analysis. Some numerical simulations, confirming and extending theoretical results, are proposed for a specific scenario.

Cited by

• Turing instability and 2-D pattern formation in reaction-diffusion systems derived from kinetic theory
• Nonclassical Turing instabilities induced by superdiffusive transport in FitzHugh-Nagumo dynamics
• Weakly nonlinear analysis of a reaction-diffusion model for demyelinating lesions in Multiple Sclerosis

Discussions

• Derivation from kinetic theory and 2-D pattern analysis of chemotaxis models for Multiple Sclerosis #NeuroDegeneration 🧪🧠 https://arxiv.org/abs/2501.13119 [bsky, 0 points, 0 comments]

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