A CaputoUFabrizio Fractional-Order Tumor ˝ UImmune Interaction Model with Treatment and ˝ Immunotherapy: Stability, Optimal Control, and Sensitivity Analysis
DOI:
https://doi.org/10.48165/jmmfc.2026.3102Keywords:
Caputo Fabrizio operator, Tumor Model, Stability, Optimal Control, Sensitivity analysisAbstract
We present a fractional-order immune tumor interaction model that captures both tumor progression and treatment effects under Caputo Fabrizio (CF) derivatives (a non-singular kernel fractional derivative). The model divides the system into five key compartments: naive immune cells, effector immune cells, viable tumor cells, treatment-affected tumor cells and dead tumor cells. It incorporates tumor logistic growth, immune activation, proliferation, immunotherapy infusion, drug-mediated cytotoxicity, relapse, and clearance processes. The frac tional formulation reflects memory and hereditary properties inherent in biological interactions. Mathematical analysis establishes equilibrium points, derives the basic reproduction number and determines stability condi tions for tumor-free and coexistence states. Numerical simulations support the theoretical results and reveal the influence of fractional order and therapeutic parameters on tumor suppression and long-term immune control. This framework bridges rigorous mathematical modeling with clinically relevant insights, offering guidance for optimizing immunotherapy and improving treatment strategies.
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