Mathematical modeling and optimal control of immune responses in multiple sclerosis
- 1Department of Mathematics, Khalifa University, Abu Dhabi, United Arab Emirates.
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.
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BibTeX
@article{alarydah2026mathematical,
title = {{Mathematical modeling and optimal control of immune responses in multiple sclerosis}},
author = {Mo'tassem Al-Arydah},
journal = {PLOS One},
year = {2026},
month = nov,
doi = {10.1371/journal.pone.0349131},
url = {https://doi.org/10.1371/journal.pone.0349131},
note = {CC BY},
}
RIS
TY - JOUR
TI - Mathematical modeling and optimal control of immune responses in multiple sclerosis
AU - Mo'tassem Al-Arydah
PY - 2026
DA - 2026/11/10
JO - PLOS One
DO - 10.1371/journal.pone.0349131
UR - https://doi.org/10.1371/journal.pone.0349131
AB - 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.
SN - 1932-6203
ER -