Modeling, Control, and Management of a Nonlinear Tumor–Immune Biological System via Adaptive Smooth Sliding Mode Radiochemotherapy

Nonlinear biological systems exhibit complex interactions, uncertain parameters, and strong treatment-dependent dynamics, making mathematical modeling and control essential for designing reliable therapeutic intervention strategies. This study proposes a multi-input adaptive smooth sliding mode control (AMIS-SMC) framework for regulating combined radiotherapy and chemotherapy in a nonlinear tumor–immune dynamical system described by ordinary differential equations. The proposed controller integrates a hyperbolic tangent smoothing mechanism with adaptive parameter-estimation laws to compensate for uncertainty in tumor and healthy-cell growth dynamics. In this way, the method explicitly links biological-system modeling, feedback control, treatment-dose management, and parameter adaptation within a single mathematically analyzable framework. Fundamental closed-loop properties are established analytically, including positivity and boundedness of all biological state variables, asymptotic convergence of the sliding surfaces, and explicit upper bounds on the administered radiation and chemotherapeutic drug dosages. Lyapunov-based stability analysis is used to guarantee boundedness of the closed-loop signals and convergence of the sliding manifold. Numerical simulations based on a brain-tumor case study demonstrate that the proposed AMIS-SMC algorithm achieves rapid tumor suppression while administering substantially lower treatment intensities than conventional and integral SMC approaches. Under nominal conditions, the proposed controller reduces cumulative radiation and chemotherapy dosages while maintaining effective tumor mitigation. Under mismatched parameter conditions, AMIS-SMC consistently drives the tumor-cell population toward the desired equilibrium across all tested scenarios, whereas conventional and integral SMC show limited adaptability. Statistical analysis using Mann–Whitney U and Fisher’s tests further indicates that AMIS-SMC provides an effective mathematical-control and treatment-management strategy for tumor suppression in a simplified nonlinear tumor–immune biological system under parameter uncertainty.