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

TL;DR

This paper derives reaction-diffusion models for Multiple Sclerosis from kinetic theory, analyzes pattern formation and stability using weakly nonlinear analysis, and supports findings with numerical simulations.

Contribution

It introduces a novel derivation of MS-related reaction-diffusion models from kinetic theory and investigates pattern formation mechanisms.

Findings

Conditions for Turing instability identified

Two-dimensional pattern shapes and stability analyzed

Numerical simulations confirm theoretical predictions

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.