Noise-Driven Tipping in a Tumor-Immune Model with Optimal Combination Therapy

Cancer mortality remains high in part because tumor-immune interactions can be unpredictable and may exhibit multistability, making malignant progression difficult to anticipate. We develop and analyze a tumor-immune model incorporating chemotherapy-induced toxicity and a Norton-Simon type tumor response, and show via deterministic analysis and continuation that increasing toxicity can generate hysteresis and bistability separating tumor dormancy from an uncontrolled full-growth state, so that small perturbations may precipitate abrupt progression. To capture uncertainty, we study environmental and demographic stochasticity and observe noise-induced switching in both cases; however, demographic noise sustains higher resilience of the tumor-dominant state under bistability, whereas stronger environmental noise tends to suppress uncontrolled tumor growth. We further assess early-warning signals using single and composite rolling-window indicators and find that they can provide advance warning of transitions from dormancy to full growth, with composite measures offering greater robustness across noise levels. Finally, we formulate an optimal control problem for combination immunotherapy and radiotherapy and demonstrate that appropriately timed treatment can substantially reduce tumor burden when initiated from either dormancy or full-growth conditions, highlighting how stochasticity-aware monitoring and optimized interventions may help prevent catastrophic tumor progression.