The purpose of this research is to carry out a quantitative study of prostate-specific antigen dynamics for patients with prostatic diseases, such as benign prostatic hyperplasia (BPH) and localized prostate cancer (LPC). The proposed PSA mathematical model was implemented using clinical data of 218 Japanese patients with histological proven BPH and 147 Japanese patients with LPC (stages T2a and T2b). For prostatic diseases (BPH and LPC) a nonlinear equation was obtained and solved in a close form to predict PSA progression with patients' age. The general solution describes PSA dynamics for patients with both diseases LPC and BPH. Particular solutions allow studying PSA dynamics for patients with BPH or LPC. Analytical solutions have been obtained and solved in a close form to develop nomograms for a better understanding of PSA dynamics in patients with BPH and LPC. This study may be useful to improve the diagnostic and prognosis of prostatic diseases.