Weakly nonlinear analysis of a reaction-diffusion model for demyelinating lesions in Multiple Sclerosis

Multiple Sclerosis is a chronic autoimmune disorder characterized by the degradation of the myelin sheath in the central nervous system, leading to neurological impairments. In this work, we analyze a reaction-diffusion model derived from kinetic theory to study the formation of demyelinating lesions. We perform a Turing instability analysis and a weakly nonlinear analysis to investigate different spatial patterns that may emerge. Our study examines how key parameters, including the squeezing probability of immune cells and the chemotactic response, impact pattern formation. Numerical simulations confirm the analytical results, revealing the emergence of distinct spatial structures.