Optimal Control of Prostate Cancer Progression via Androgen Suppression Therapy: Deterministic and Stochastic Modeling

Source abstract

Prostate cancer progression is strongly influenced by androgens, and androgen suppression therapy (AST) is among the most effective approaches for managing the disease. In this study, we develop and investigate both deterministic and stochastic models of prostate cancer dynamics under AST to develop strategies that effectively reduce tumor burden. The deterministic model consists of nonlinear ordinary differential equations capturing the interactions among androgen-sensitive and androgen-resistant tumor cells, androgen levels, and prostate-specific antigen (PSA). The control parameter corresponds to the intensity of androgen suppression, and the optimal control problem is solved via Pontryagin's Maximum Principle to generate treatment schedules that minimize tumor size while limiting drug exposure over a finite period. To account for biological variability and random fluctuations in treatment response, a stochastic version of the model is introduced by adding Brownian noise to key state variables. This stochastic optimal control problem is solved numerically using an Euler–Maruyama scheme coupled with a dynamic optimization algorithm. Numerical simulations reveal marked differences between deterministic and stochastic treatment outcomes. In particular, while continuous full-scale therapy emerges in the deterministic setting, the stochastic framework naturally yields an intermittent and adaptive control strategy, alternating periods of intensive and partial treatment. This behavior reflects clinically relevant intermittent androgen suppression protocols and leads to a more balanced and realistic therapeutic schedule, highlighting the importance of stochastic modeling in the design of effective and sustainable AST strategies.