Abstract The application of sliding mode control and piecewise smooth vector fields in cancer is an incipient research area. Here we propose a piecewise dynamics to explore chemoimmunotherapeutic strategies. We investigate the dynamic behavior of the discontinuous mathematical model and we observe the occurrence of typical singularities. The on-off treatment strategies are defined in terms of a time-dependent variable such as the number of cancer or immune cells.

中文翻译：

---

化学免疫疗法数学模型中的滑模控制：典型奇点的出现

摘要 滑模控制和分段平滑矢量场在癌症中的应用是一个新兴的研究领域。在这里，我们提出了一种分段动力学来探索化学免疫治疗策略。我们研究了不连续数学模型的动态行为，并观察了典型奇点的出现。开关治疗策略是根据时间相关变量定义的，例如癌症或免疫细胞的数量。