Modeling the Effects of Chemotherapeutic Dose Response on a Stochastic Tumor-Immune Model of Prostate Cancer with Androgen Deprivation Therapy

The periodical application of androgen deprivation therapy, immunotherapy, or chemotherapy is an effective method for cancer treatment, but few studies combine them. To explore such comprehensive treatment mechanisms, this paper establishes a pulsed stochastic hybrid dynamics model considering tumor antigenicity and density-dependent mortality. In addition to analyzing the basic properties of solutions such as the tumor-free periodic solution and global attraction of the model, the threshold conditions for the persistence and extinction of prostate cancer cells and effector cells are obtained by using stochastic differential equation theory. Besides, sufficient conditions for the existence of stationary distribution of the system are established. The results reveal that comprehensive therapy or white noise can determine tumor dynamics and suggest that the treatment of prostate cancer should be individualized according to the state of tumor development. Finally, biological significance is discussed and conclusions are given.