Intermittent androgen deprivation therapy is often used to treat prostate cancer, but there are few mathematical modelling studies of it. To explore the mechanisms of such therapy, we describe intermittent therapy with impulsive differential equations, then we propose a novel mathematical model of intermittent androgen deprivation therapy with white noise. We first studied the model’s basic properties including the existence and uniqueness of the solution. By using the theory of stochastic differential equations, we investigated the thresholds for the extinction and persistence of prostate cancer cells, which are markedly affected by the antigenicity of tumours and noise parameters. Moreover, sufficient conditions for the stationary distribution and ergodicity of the system are provided. The results show that reducing the period of pulsed interventions or increasing the dosages (or frequencies) of the therapy will be helpful for curing prostate cancer.

间歇性雄激素剥夺疗法通常用于治疗前列腺癌，但很少有数学模型研究。为了探索这种疗法的机理，我们用脉冲微分方程描述了间歇疗法，然后我们提出了一种带有白噪声的间歇性雄激素剥夺疗法的新型数学模型。我们首先研究了模型的基本属性，包括解决方案的存在性和唯一性。通过使用随机微分方程的理论，我们研究了前列腺癌细胞的灭绝和持久性的阈值，这些阈值受肿瘤的抗原性和噪声参数的影响明显。而且，为系统的平稳分布和遍历性提供了充分的条件。