A Mathematical Modeling Framework for a Periodic Subcutaneous Tolerogenic Immune Training Vaccine (LSTIV) to Promote Donor-Specific Tolerance in Solid Organ Transplantation: A Hypothesis-Generating Theoretical Study with Explicit Assumptions and Limitations

Background: Chronic immunosuppression in solid organ transplantation is associated with substantial morbidity. Antigen-specific tolerogenic strategies represent a promising alternative but lack quantitative frameworks to guide dosing and predict long-term dynamics. Methods: We propose a conceptual framework for a periodic subcutaneous tolerogenic immune training vaccine (LSTIV) and develop a multi-compartment ordinary differential equation (ODE) model to explore its theoretical dynamics. The model incorporates periodic forcing, regulatory feedback, and graft health coupling. Parameters are calibrated using ranges reported in peer-reviewed literature. Simulations employ scipy.integrate.solve_ivp with adaptive stepping and positivity constraints. Global sensitivity analysis (Monte Carlo sampling, partial rank correlation coefficients, Sobol indices), Bayesian uncertainty quantification, and explicit falsifiability criteria are included. All code, data, and derivations are embedded within this manuscript for complete reproducibility. Results: Under the stated model assumptions, periodic LSTIV administration is predicted to support a Treg-to-effector T cell ratio exceeding 8-10 and a graft health index G(730) approaching 0.90 (monthly dosing) versus approximately 0.25 (no intervention). Sensitivity analyses identify vaccine dosing amplitude and Treg-mediated suppression as the most influential parameters. Bayesian calibration of key parameters yields posterior distributions consistent with prior biological knowledge. Complete numerical results, convergence diagnostics, and parameter uncertainty ranges are provided in supplementary tables. Conclusions: This hypothesis-generating theoretical framework provides a reproducible, mathematically grounded platform to explore periodic tolerogenic vaccination. All results are conditional on model structure and parameter choices; they are not proof of clinical efficacy. Explicit limitations, falsifiability criteria, and a translational roadmap are provided to guide future empirical validation. Keywords: mathematical modeling, transplant immunology, tolerogenic vaccine, ordinary differential equations, sensitivity analysis, hypothesis generation, reproducible research