Tumor immune escape refers to the inability of the immune system to clear tumor cells, which is one of the major obstacles in designing effective treatment schemes for cancer diseases. Although clinical studies have led to promising treatment outcomes, it is imperative to design theoretical models to investigate the long-term treatment effects. In this paper, we develop a mathematical model to study the interactions among tumor cells, immune escape tumor cells, and T lymphocyte. The chimeric antigen receptor (CAR) T-cell therapy is also described by the mathematical model. Bifurcation analysis shows that there exists backward bifurcation and saddle-node bifurcation when the immune intensity is used as the bifurcation parameter. The proposed model also exhibits bistability when its parameters are located between the saddle-node threshold and backward bifurcation threshold. Sensitivity analysis is performed to illustrate the effects of different mechanisms on the backward bifurcation threshold and basic immune reproduction number. Simulation studies confirm the bifurcation analysis results and predict various types of treatment outcomes using different CAR T-cell therapy strengths. Analysis and simulation results show that the immune intensity can be used to control the tumor size, but it has no effect on the control of the immune escape tumor size. The introduction of the CAR T-cell therapy will reduce the immune escape tumor size and the treatment effect depends on the CAR T-cell therapy strength.

肿瘤免疫逃逸是指免疫系统无法清除肿瘤细胞，这是设计癌症疾病有效治疗方案的主要障碍之一。尽管临床研究已经带来了有希望的治疗结果，但必须设计理论模型来研究长期治疗效果。在本文中，我们开发了一个数学模型来研究肿瘤细胞、免疫逃逸肿瘤细胞和 T 淋巴细胞之间的相互作用。嵌合抗原受体（CAR）T细胞疗法也由数学模型描述。分叉分析表明，当以免疫强度为分叉参数时，存在后向分叉和鞍结分叉。当其参数位于鞍节点阈值和后向分叉阈值之间时，所提出的模型还表现出双稳态。进行敏感性分析来说明不同机制对后向分叉阈值和基本免疫繁殖数的影响。模拟研究证实了分叉分析结果，并预测使用不同 CAR T 细胞治疗强度的各种类型的治疗结果。分析和模拟结果表明，免疫强度可以用来控制肿瘤大小，但对免疫逃逸肿瘤大小的控制没有作用。CAR T细胞疗法的引入将缩小免疫逃逸肿瘤的大小，治疗效果取决于CAR T细胞疗法的强度。