癌症新抗原疫苗已成为刺激免疫系统抗击癌症的有希望的方法。我们提出了一个简单的模型，包括肿瘤免疫互作的关键要素，并进行相位平面分析，以理解癌症新抗原疫苗的免疫机制。我们对代表免疫细胞杀伤肿瘤细胞的两种广泛使用的函数形式得出了分析结果:质量作用定律（LMA）和德皮利斯 - 拉杜斯卡亚定律（LPR）。使用LMA，我们的结果表明，缓慢生长的肿瘤可以逃避免疫监视，并存在唯一的周期解。LPR提供了更丰富的动力学，其中肿瘤消除和不受控制的肿瘤生长都存在。我们表明，肿瘤消除需要足够数量的初级激活的T细胞与恶性细胞有关，这支持在手术切除或使用放射治疗治疗初级肿瘤后，使用新抗原癌症疫苗作为辅助治疗。我们还推导出了在LPR假设下不受控制的肿瘤生长的充分条件。对这两种不同选择的杀伤率函数进行分析的并置强调了它们对模型行为和生物学意义的重要性，我们希望通过这种方式激发进一步的理论和实验工作，以了解不同功能形式背后的机制。 版权© 2023 Elsevier公司。保留所有权利。

Cancer neoantigen vaccines have emerged as a promising approach to stimulating the immune system to fight cancer. We propose a simple model including key elements of cancer-immune interactions and conduct a phase plane analysis to understand the immunological mechanisms of cancer neoantigen vaccines. Analytical results are obtained for two widely used functional forms that represent the killing rate of tumor cells by immune cells: the law of mass action (LMA) and the dePillis-Radunskaya Law (LPR). Using the LMA, our results reveal that a slowly growing tumor can escape the immune surveillance and that there is a unique periodic solution. The LPR offers richer dynamics, in which tumor elimination and uncontrolled tumor growth are both present. We show that tumor elimination requires sufficient number of initial activated T cells in relationship to the malignant cells, which lends support to using the neoantigen cancer vaccine as an adjuvant therapy after the primary tumor is surgically removed or treated using radiotherapy. We also derive a sufficient condition for uncontrolled tumor growth under the assumption of the LPR. The juxtaposition of analyses with these two different choices for the killing rate function highlights their importance on model behavior and biological implications, by which we hope to spur further theoretical and experimental work to understand mechanisms underlying different functional forms for the killing rate.Copyright © 2023 Elsevier Inc. All rights reserved.