Abstract This paper focuses on a class of stochastic systems describing tumor-immune dynamics. The underlying systems are given by stochastic differential equations. Our study concentrates on longtime behavior. A sharp threshold-type condition is obtained, which characterizes the dynamic systems, and pinpoints sufficient and nearly necessary conditions for persistence and extinction. Examples and numerical results are provided to illustrate our findings.

中文翻译：

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一类随机肿瘤免疫系统的长期行为

摘要 本文重点研究一类描述肿瘤免疫动力学的随机系统。底层系统由随机微分方程给出。我们的研究集中在长期行为上。获得了一个尖锐的阈值类型条件，它表征了动态系统，并确定了持久性和灭绝性的充分和几乎必要的条件。提供了示例和数值结果来说明我们的发现。