Abiraterone acetate (AA) has been proven effective for metastatic castration-resistant prostate cancer (mCRPC), and it has been proposed that adaptive AA may reduce toxicity and prolong time to progression, when compared to continuous AA. We developed a simple quantitative model of prostate-specific antigen (PSA) dynamics to evaluate prostate cancer (PCa) stem cell enrichment as a plausible driver of AA treatment resistance. The model incorporated PCa stem cells, non-stem PCa cells and PSA dynamics during adaptive therapy. A leave-one-out analysis was used to calibrate and validate the model against longitudinal PSA data from 16 mCRPC patients receiving adaptive AA in a pilot clinical study. Early PSA treatment response dynamics were used to predict patient response to subsequent treatment. We extended the model to incorporate metastatic burden and also investigated the survival benefit of adding concurrent chemotherapy for patients predicted to become resistant. Model simulations demonstrated PCa stem cell self-renewal as a plausible driver of resistance to adaptive therapy. Evolutionary dynamics from individual treatment cycles combined with metastatic burden measurements predicted patient response with 81% accuracy (specificity=92%, sensitivity=50%). In those patients predicted to progress, simulations of the addition of concurrent chemotherapy suggest a benefit between 1% and 11% reduction in probability of progression when compared to adaptive AA alone. This study developed the first mCRPC patient-specific mathematical model to use early PSA treatment response dynamics to predict subsequent responses to adaptive AA, demonstrating the putative value of integrating mathematical modeling into clinical decision making.