Fractional-order optimal control for personalized chemotherapy scheduling in hematological malignancies

Résumé

The clinical management of hematological malignancies requires a delicate balance between tumor cytotoxicity, immune preservation, and toxicity. Traditional integer-order models fail to capture the memory-dependent dynamics of cancer-immune interactions, leading to suboptimal dosing schedules. We present a comprehensive optimal control framework based on fractional-order differential equations that incorporates memory effects through Caputo derivatives with patient-specific parameter α ∈ (0,1]. The model tracks tumor cells, immune response, normal tissue damage, and drug concentration. We formulate a quadratic optimal control problem balancing tumor burden, drug exposure, and normal-cell preservation. The resulting personalized schedules vary dramatically with α: strong memory (α = 0.5) patients benefit from pulsed therapy (5 days on / 9 days off, 4 cycles), while weak memory (α = 0.9) require metronomic continuous low-dose therapy. The framework reduces total cost by 39–63% versus no treatment and improves immune preservation by 27–36% over standard CHOP/R-CHOP. Validation against 8 cohorts (n = 1,020 patients) yields mean error 2.4% (95% CI: 1.8–3.0%) and R² = 0.96. The Pareto "knee" occurs at tumor weight A = 0.5–0.7 (71–82% reduction with acceptable toxicity). Monthly re-optimisation provides the best clinical benefit-to-burden trade-off. Robustness analysis shows α is the most robust parameter (4–6% performance drop for ±10% perturbation), while δC requires re-optimisation. Cost-effectiveness analysis shows optimal strategies are dominant (lower cost, higher QALYs) for strong-memory patients. A practical 7-day clinical workflow is provided, with open-source code for implementation. These results demonstrate that fractional-order modelling captures essential biological memory effects, enabling truly personalised, clinically actionable chemotherapy schedules.