A chemotaxis reaction-diffusion model for Multiple Sclerosis with Allee effect

TL;DR

This paper introduces a modified reaction-diffusion model for Multiple Sclerosis that incorporates an Allee effect to better understand inflammation dynamics and pattern formation in the brain.

Contribution

It extends previous models by including an Allee effect in macrophage activation, providing new insights into inflammation initiation and pattern emergence.

Findings

Identification of conditions for Turing pattern formation.

Demonstration of the impact of the Allee effect on inflammation dynamics.

Comparison showing differences from previous models.

Abstract

In this paper, we study a modification of the mathematical model describing inflammation and demyelination patterns in the brain caused by Multiple Sclerosis proposed in [Lombardo et al. (2017), Journal of Mathematical Biology, 75, 373--417]. In particular, we hypothesize a minimal amount of macrophages to be able to start and sustain the inflammatory response. Thus, the model function for macrophage activation includes an Allee effect. We investigate the emergence of Turing patterns by combining linearised and weakly nonlinear analysis, bifurcation diagrams and numerical simulations, focusing on the comparison with the previous model.