中文摘要：

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。

英文摘要：

Objective To study the effect of time delay on tumor-immune system during tumor growth through theoretical approaches.Methods A mathematical model of the tumor-immune system interaction was established,and a time delay in the logistic growth term was introduced to investigate the processes of the interaction between immune system and tumor cells through qualitative analysis and numerical simulations.The relationship between the states of tumor and time delay was analyzed and the results were compared with the stages of the cancer immunoediting.Results Qualitative analysis and numerical simulations indicated that the tumor-immune system was a stable equilibrium state if the time delay was small.With the time delay increasing,the tumor-immune system entered equilibrium and escape stages of the cancer immunoediting,which described the alteration from dormant state to malignant state.Conclusions The time delay plays a key role in the interaction between immune system and tumor cells.The different time delays can result in different behaviors of tumor.The results will help to deepen clinical understanding of the tumor-immune system and provide references for the analysis and treatment of tumor.