Speaker
Description
We develop and analyze a nonlinear mathematical model for autoimmune-mediated demyelination in multiple sclerosis that captures interactions between healthy myelin, autoreactive immune cells, regulatory immune cells, and neuronal functional capacity. Immune activation is driven by myelin damage through a saturating response function, while regulatory cells suppress pathogenic activity and therapeutic intervention contributes to immune clearance. A fast–slow structure reflects disparate physiological timescales and permits quasi-steady-state reduction to a lower-dimensional immune subsystem. We establish biological well-posedness by proving positivity and global existence of solutions and identifying invariant regions, and we derive a threshold quantity governing autoimmune invasion via linearization about the disease-free equilibrium. The existence and stability of steady states are characterized, including parameter regimes associated with chronic inflammation, remission, and oscillatory immune dynamics, and sufficient conditions ensuring uniform boundedness of immune populations are obtained and interpreted biologically. Numerical simulations illustrate long-term disease trajectories and quantify the impact of therapeutic control on immune regulation and neuronal preservation, providing a mathematically tractable and biologically grounded framework for investigating autoimmune progression and evaluating treatment strategies in multiple sclerosis.
