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目的通过理论方法研究肿瘤生长过程中时间延迟在肿瘤免疫系统中的作用。方法建立肿瘤与免疫系统相互作用的数学模型,在肿瘤Logistic生长函数中引入时间延迟,通过解析和数值的方法研究免疫系统与肿瘤细胞相互作用的过程。分析肿瘤状态与时间延迟的关系,并与肿瘤免疫编辑过程的各阶段相对应。结果理论分析和数值模拟表明,当时间延迟量很小时,肿瘤免疫系统处于稳定状态。当时间延迟量变大时,肿瘤免疫系统进入肿瘤免疫编辑过程中的平衡和逃逸阶段,进而描述了肿瘤的状态从休眠发展为恶性的过程。结论在肿瘤免疫系统相互作用过程中,时间延迟起到关键的作用,不同的时间延迟能够导致不同的肿瘤状态。研究结果有助于加深临床上对肿瘤免疫系统相互作用的理解,为分析肿瘤的状态和治疗提供参考。
Objective To study the role of time delay in the tumor immune system in the process of tumor growth through theoretical methods. Methods The mathematical model of the interaction between tumor and immune system was established. The time delay was introduced into the tumor Logistic growth function. The process of interaction between immune system and tumor cells was studied by analytical and numerical methods. The relationship between tumor status and time delay was analyzed and corresponded to each stage of tumor immunoediting process. Results Theoretical analysis and numerical simulations show that when the time delay is small, the tumor immune system is in a stable state. When the amount of time delay becomes large, the tumor immune system enters the balance and escape phase of the tumor immune editing process, and further describes the process of the tumor’s state from dormancy to malignant. CONCLUSIONS: Time delay plays a key role in tumor immune system interactions. Different time delays can result in different tumor states. The results of the study will help deepen clinical understanding of the interaction of tumor immune system and provide a reference for the analysis of tumor status and treatment.