Identifying optimal adaptive therapeutic schedules for prostate cancer through combining mathematical modeling and dynamic optimization.

• A new framework based on a dynamic optimization problem identifies the adaptive therapeutic schedule for prostate cancer. • A competitive model between drug-sensitive and drug-resistant cells is established and validated using available data. • The stability of equilibrium points and existence of a periodic solution indicate the feasibility of adaptive therapy. • Our therapeutic framework is superior to the current approaches in the total drug dose and the survival time. Adaptive therapy, a new therapeutic strategy, is increasingly applied in the treatment of cancer. According to the evolutionary game theory of cancer cells, adaptive therapy is understood as the dynamic regulation of cancer cells. However, it is a great challenge to identify the therapeutic period and dose in adaptive therapy. In this study, we establish a competitive model between drug-sensitive and drug-resistant cancer cells. Theoretical analysis, including the stability of equilibrium points and the existence of periodic solutions, validates the interpretability of the model. The available data for prostate cancers are used to identify the model parameters. Furthermore, we propose a new dynamic optimization problem with constraints to establish the adaptive therapeutic schedule for prostate cancer, and an optimal set of decisions in this optimization problem represents the therapeutic period and dose in adaptive therapy. Through numerical simulations and quantitative analysis, we compare our therapeutic schedule and current adaptive therapeutic schedules in patients with prostate cancer in three aspects: the total drug dose, the peak number of drug-resistant cancer cells and the survival time. These results demonstrate that our therapeutic framework is superior to the current adaptive therapeutic schedules. The proposed therapeutic framework could provide an identifiable adaptive therapy to achieve personal and precise treatment for prostate cancer. [ABSTRACT FROM AUTHOR]