Describing the anti-tumour immune response as a series of cellular kinetic reactions from known immunological mechanisms, we create a mathematical model that shows the CD4\(^{+}\)/CD8\(^{+}\) T-cell ratio, T-cell infiltration and the expression of MHC-I to be interacting factors in tumour elimination. Methods from dynamical systems theory and non-equilibrium statistical mechanics are used to model the T-cell dependent anti-tumour immune response. Our model predicts a critical level of MHC-I expression which determines whether or not the tumour escapes the immune response. This critical level of MHC-I depends on the helper/cytotoxic T-cell ratio. However, our model also suggests that the immune system is robust against small changes in this ratio. We also find that T-cell infiltration and the specificity of the intra-tumour TCR repertoire will affect the critical MHC-I expression. Our work suggests that the functional form of the time evolution of MHC-I expression may explain the qualitative behaviour of tumour growth seen in patients.

将抗肿瘤免疫反应描述为来自已知免疫学机制的一系列细胞动力学反应，我们创建了一个数学模型，显示了 CD4 \(^{+}\) /CD8 \(^{+}\)T 细胞比率、T 细胞浸润和 MHC-I 的表达是肿瘤消除的相互作用因素。来自动态系统理论和非平衡统计力学的方法用于模拟 T 细胞依赖性抗肿瘤免疫反应。我们的模型预测 MHC-I 表达的临界水平，这决定了肿瘤是否逃避免疫反应。MHC-I 的这一临界水平取决于辅助细胞/细胞毒性 T 细胞的比例。然而，我们的模型还表明，免疫系统对这一比率的微小变化具有强大的抵抗力。我们还发现 T 细胞浸润和肿瘤内 TCR 库的特异性将影响关键的 MHC-I 表达。我们的工作表明，MHC-I 表达时间演变的功能形式可以解释患者体内肿瘤生长的定性行为。