Uniform boundedness of solutions to a multiple sclerosis chemotaxis model with regulatory T cell response

Multiple sclerosis (MS) is an autoimmune disease in which autoreactive T cells attack the myelin sheath while regulatory T cells (Tregs) migrate chemotactically toward lesion sites to suppress inflammation. In this paper, a two-component chemotaxis system coupling autoreactive T cells and Tregs is proposed, in which the chemotactic signal is produced by the autoreactive population itself. Under sufficiently weak chemotaxis, the system is shown to possess a unique globally defined nonnegative classical solution which is uniformly bounded in time, in any space dimension n≥ 1. The proof combines a comparison argument exploiting the cubic saturation of the activation term, an L¹-estimate based on an exact cancellation structure, and the self-mapping approach. Linear stability analysis reveals that chemoattraction is linearly stabilizing whereas chemorepulsion can destabilize the homogeneous coexistence steady state, providing a possible mechanism for focal plaque formation in MS.