Caputo fractional-order tumor–immune–checkpoint inhibitor modeling: chaos-enhanced particle swarm optimization, ANFIS-driven adaptation, and large-scale in silico simulation for personalized cancer immunotherapy

Abstract

The interplay between tumors and the immune system during immunotherapeutic interventions is characterized by highly nonlinear, individualized dynamics that conventional integer-order mathematical representations are inadequate to describe. The present work introduces a Caputo fractional-order three-compartment model coupling tumor cell populations, immune effector cells, and checkpoint inhibitor drug concentrations, whose parameters are identified through a chaos-augmented particle swarm optimization (CE-PSO) strategy utilizing logistic-map-based stochastic perturbations. An adaptive neuro-fuzzy inference system (ANFIS) component performs online adjustment of both the fractional differentiation order and immune responsiveness, driven by IL-2 and IFN-γ cytokine-inspired signal inputs. Rigorous proof of global asymptotic stability at the tumor-free steady state is provided through the fractional-order Lyapunov direct approach. Broad computational evaluation across a virtual cohort of fifty simulated patients yields RMSE = 0.066, reflecting an 83.2% accuracy gain relative to classical integer-order alternatives, along with a 16% enhancement in tumor suppression under ANFIS-guided individualized dosing. The full simulation pipeline—encompassing the Adams-Bashforth-Moulton numerical integrator and both the CE-PSO and ANFIS components—is structured for maximal reproducibility. To the authors’ knowledge, this represents the inaugural stability-certified platform to concurrently unify cytokine-responsive real-time ANFIS tuning, CE-PSO parameter optimization, and Caputo fractional-order system dynamics within a single computational environment for patient-tailored cancer immunotherapy.