Dynamics of a non-smooth model of prostate cancer with intermittent androgen deprivation therapy

Abstract

Intermittent androgen deprivation therapy (IADT) is widely used in the clinic treatment for prostate cancer. We propose a Filippov system in this paper, which defines the following threshold policy: the androgen deprivation therapy (ADT) is implemented once the concentration of androgen-dependent (AD) cells exceeds the threshold level ET and it is suspended otherwise. To better understand the effect of the IADT on the evolution of prostate cancer, we perform a comprehensive qualitative analysis of global dynamics of the targeted model. As the threshold value varies, our model admits multistability of three equilibria, bistability of two equilibria, stability of the regular equilibrium or the pseudo-equilibrium, and the boundary equilibrium bifurcation. The steady-state regimes include high concentration, low concentration and no androgen-independent cells. This highlights the critical role of threshold values and the initial condition of prostate cancer cells of patients. The main results indicate that the concentration of AD cells and AI cells can be contained at a relatively satisfactory level, which can help to make treatment schedule and improve treatment outcomes for patients with prostate cancer.