In prostate cancer treatment, intermittent androgen deprivation therapy can delay the emergence of drug resistance, yet its efficacy is influenced by environmental fluctuations, treatment parameters, and competition among tumor cell populations. To investigate the mechanisms underlying resistance during intermittent therapy, we developed a stochastic impulsive differential equation model. First, a global analysis of the model without environmental noise is conducted. Subsequently, sufficient conditions for tumor extinction and persistence are established based on stochastic stability theory. Numerical simulations further demonstrate that moderate noise suppresses tumor growth, and an optimal... More >