Controlling the number of tumor cells remains a fundamental challenge in oncology due to the complex, nonlinear dynamics of tumor-immune interactions, extreme parameter scaling, and clinical constraints such as drug toxicity and the unidirectional nature of therapeutic interventions. To address these difficulties, this paper introduces a novel methodology for tumor growth control by leveraging the space of hyperbolic functions (HFs). We investigate a nonlinear model describing the dynamic interaction between effector cells and tumor cells. First, we design a stabilizing feedback control within the HFs framework, formulated as a hyperbolic tangent state feedback law. A Lyapunovbased analysis rigorously proves that this controller ensures global asymptotic stability of the desired equilibrium, where the tumor cell population is eradicated. Numerical simulations demonstrate that the proposed stabilizer drives divergent tumor growth to zero with a rapid convergence rate across various initial conditions. Furthermore, we formulate and solve an optimal control problem to simultaneously minimize the tumor cell population and the dose of a chemotherapeutic agent. The resulting optimality system, derived from Pontryagin’s Minimum Principle, is efficiently discretized and solved using a numerical scheme based on hyperbolic function approximations and Legendre-Gauss-Lobatto collocation points. Simulation results confirm the efficacy of this approach, illustrating a trade-off between tumor eradication and drug usage that can be tuned via the objective function’s weighting parameters. The findings collectively establish the space of hyperbolic functions as a powerful and efficient tool for both stabilization and optimal control in complex, nonlinear oncological models, offering a promising framework for designing therapeutic strategies.