Dynamic Analysis and Optimal Control Strategy for the Impact of Stem Cell Therapy on Type 1 Diabetes

Abstract

Type 1 diabetes (T1D) is a chronic autoimmune disease in which autoreactive effector T cells destroy insulin-producing pancreatic β-cells, leading to impaired insulin production and long-term metabolic complications. This study develops a mathematical model of the interactions among pancreatic β-cells, autoreactive effector T cells, regulatory T cells (Tregs), and stem cell therapy, treating stem cell administration as an immunomodulatory and regenerative strategy that suppresses autoimmune activity and promotes β-cell recovery. The existence, uniqueness, positivity, and boundedness of solutions are established. For the auxiliary subsystem with SE =0 and constant treatment input, the disease-free equilibrium and the threshold quantity R0 are derived, and local asymptotic stability of the DFE is established for R0 <1. For the full model with SE >0, the existence of a unique biologically feasible positive equilibrium is established, together with its local asymptotic stability under constant treatment input. An optimal control problem, formulated using Pontryagin’s Maximum Principle, is used to guide therapeutic dosing, and one-year numerical simulations compare two administration protocols: high-dose pulse injections and continuous infusion. Both reduce autoimmune activity and improve β-cell dynamics, with pulse administration producing stronger transient responses and continuous infusion producing smoother treatment-period dynamics, while both protocols approach similar long-term levels. A local sensitivity analysis identifies immune activation, β-cell destruction, and regulatory T-cell activity as the parameters most strongly shaping disease progression and treatment outcomes. By unifying stem cell therapy, stability analysis, sensitivity analysis, and optimal control, and directly comparing pulse and infusion protocols, this framework offers new insight for designing stem cell-based treatments for autoimmune diabetes.