A nonlinear model with competition between prostate tumor cells and its application to intermittent androgen suppression therapy of prostate cancer

The recurrence of a tumor is a crucial problem in hormonal therapy of prostate cancer. Recent studies suggest that intermittent androgen suppression administration may prolong or hopefully prevent the progression to the recurrence. It was shown that a simple mathematical model is useful to understand how and why intermittent administration can be effective and to seek a better medication scheme. In this paper, we propose a new model for the intermittent androgen suppression therapy. What is central in the new model is that the competitive effect between androgen-dependent and independent cancer cells is assumed to be essential for the decrease of androgen-independent cells under a normal androgen level. In the newly proposed model, the separatrix in the phase space for a normal androgen level plays an important role. There is crucial difference between the previous model and the new one in the phase diagram of success and failure of the permanent tumor control by intermittent androgen suppression administration. That means that the suggestions from the models for clinical problems can be different. We also consider the combined model of the previous and newly proposed models, which can smoothly bridge two models.