Abstract: According to the interaction mechanism between probiotics and prostate cancer cells, a three-dimensional stochastic cancer dynamic model composed of probiotics, androgen-dependent prostate cancer cells and androgen-independent prostate cancer cells was constructed. The sufficient conditions for the persistence and extinction of prostate cancer cells were obtained by constructing an appropriate V function. The therapeutic effect of probiotic-assisted androgen deprivation therapy against prostate cancer was simulated and predicted. The study found that probiotics’ inhibitory effect on prostate cancer cells and noise intensity played an important role in the persistence and extinction of prostate cancer cells. In particular, further studies have shown that enhancing noise or improving the inhibitory effect of beneficial bacteria on androgen-independent cancer cells can not only effectively eradicate cancer cells but also effectively prevent the occurrence of drug resistance.

Key words: random model of prostate cancer, extinction, persistence, drug resistance