A nonlinear competitive model of the prostate tumor growth under intermittent androgen suppression

Hormone suppression has been the primary modality of treatment for prostate cancer. However long-term androgen deprivation may induce androgen-independent (AI) recurrence. Intermittent androgen suppression (IAS) is a potential way to delay or avoid the AI relapse. Mathematical models of tumor growth and treatment are simple while they are capable of capturing the essence of complicated interactions. Game theory models have analyzed that tumor cells can enhance their fitness by adopting genetically determined survival strategies. In this paper, we consider the survival strategies as the competitive advantage of tumor cells and propose a new model to mimic the prostate tumor growth in IAS therapy. Then we investigate the competition effect in tumor development by numerical simulations. The results indicate that successfully IAS-controlled states can be achieved even though the net growth rate of AI cells is positive for any androgen level. There is crucial difference between the previous models and the new one in the phase diagram of successful and unsuccessful tumor control by IAS administration, which means that the suggestions from the models for medication can be different. Furthermore we introduce quadratic logistic terms to the competition model to simulate the tumor growth in the environment with a finite carrying capacity considering the nutrients or inhibitors. The simulations show that the tumor growth can reach an equilibrium state or an oscillatory state with the net growth rate of AI cells being androgen independent. Our results suggest that the competition and the restraint of a limited environment can enhance the possibility of relapse prevention.