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

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.

References in corpus (3)

• Mathematical modeling of glioma invasion and therapy approaches via kinetic theory of active particles
• Reaction-diffusion systems derived from kinetic theory for Multiple Sclerosis
• A reaction-diffusion model for relapsing-remitting multiple sclerosis with a treatment term

Cited by in corpus (1)

• Turing instability and 2-D pattern formation in reaction-diffusion systems derived from kinetic theory