Dynamic behavior of stochastic prostate cancer system with comprehensive therapy under regime switching

The random volatility, including continuous perturbation and regime switching, inevitably occurs in tumor microenvironment. In this paper, by introducing Gaussian white noise and regime switching, the combination of the two environmental disturbances is consid-ered in the prostate cancer (PCa) model with comprehensive treatment. The Ito's formula, Lyapunov function method and ergodicity of Markov chain are employed to research the extinction-persistence behavior of PCa cells and the existence of a unique ergodic station-ary distribution. Our results show high-intensity Gaussian white noise type of continuous perturbation can suppress PCa development and that when the regime switching is on, patients can obtain a good quality of life and improve the survival rate by improving im-munity and then maintaining in such high-intensity noise state for a long time.(c) 2022 Elsevier Inc. All rights reserved.