Mathematical Modeling of Prostate Cancer Dynamics and Therapy

Abstract

This study considers a mathematical model for selecting an optimal chemotherapybased treatment strategy for prostate cancer, with the goal of minimizing the integral of the squared deviation of the PSA tumor marker from its normal value over the entire course of treatment. The optimal strategy is obtained by solving a nonlinear programming problem using the method of local variations. It should be noted that mathematical modeling of biological processes is a complex and not always fully formalizable problem. Verifying the adequacy of such models requires the joint efforts of teams of biologists and physicians and constitutes a separate task. Undoubtedly, the main and decisive role in the fight against cancer belongs to advances in biology and medicine. On the other hand, the success of mathematical methods in many related scientific fields makes it reasonable to hope that the results of mathematical modeling of cancer dynamics, together with appropriate experimental validation, may suggest new ways to choose treatment protocols.