How optimal control of cellular cost shapes population-level tumor growth dynamics

Tumor progression is often modeled as a passive response to external therapy or immune pressure, but tumor populations may also exhibit population-level regulation of proliferation and apoptosis. We develop a continuous-time Markov decision framework in which a controlled birth--death process represents a tumor population modulating the balance between proliferation and susceptibility to apoptosis in the presence of extrinsic death pressure. We examine threshold and quadratic costs, an unbounded linear reward, and constrained linear and quadratic formulations to determine how objective structure shapes optimal policies and induced population drift. Threshold and quadratic penalties generate restoring dynamics, with transitions from growth to suppression and regions of near-neutral drift associated with regulated or near-dormant behavior. An unbounded linear reward instead produces sustained or near-neutral growth without a restoring regime. Under constraints, a linear reward expands the region of positive drift as capacity increases, whereas a quadratic reward generates restoring, logistic-like drift around an interior population scale. These results show that regulated tumor dynamics depend on how growth incentives, extrinsic death pressure, penalties, and constraints scale with population size.