Mathematical modeling and optimal control of immune responses in multiple sclerosis.

Authors

Mo'tassem Al-Arydah

Published in

PloS one. Volume 21. Issue 11. Pages e0349131. Epub Nov 10, 2026.

Abstract

Multiple sclerosis (MS) is a chronic autoimmune disease characterized by immune-mediated destruction of the myelin sheath in the central nervous system. In this work, we develop and analyze a mathematical model describing the interactions among myelin, autoreactive immune cells, regulatory immune cells, and treatment. A fast-time reduction of the slow-fast model yields an analytically tractable immune subsystem that captures the principal immune interactions. We establish the existence and stability properties of the immune-free and interior equilibria and derive the autoimmune activation number R0 governing immune persistence. The analysis reveals a treatment-dependent threshold structure separating two distinct dynamical regimes. For R0>1, the reduced immune subsystem admits an interior equilibrium that is a nonlinear center surrounded by closed periodic orbits, whereas for R0<1, the immune-free equilibrium is globally asymptotically stable. Numerical simulations of the full model exhibit recurrent inflammatory oscillations under insufficient treatment and suppression of autoimmune activity under sufficiently strong treatment. Analytical sensitivity indices and global sensitivity analysis using LHS-PRCC identify immune activation and autoreactive immune-cell removal as the dominant mechanisms influencing the autoimmune activation threshold. An optimal control framework is developed to balance autoimmune suppression, cumulative treatment intensity, and treatment adjustment costs. Numerical results indicate that the computed treatment strategies can reduce autoimmune burden while accounting for treatment-related costs. Overall, the proposed framework provides insights into the interplay between immune regulation, myelin damage, and treatment, highlighting the role of treatment-dependent thresholds and optimized interventions in controlling autoimmune activity in multiple sclerosis.

PMID:
43008080
Bibliographic data and abstract were imported from PubMed on 11 Nov 2026.

Read full publication at:
Please sign in to see all details.

Stats

1-terrible, 9-excellent. How would you rate this publication? Sign in in to submit your rating.

Post a comment

You need to be signed in to post comments. You can sign in here.

Comments

There are no comments yet.