具时滞的肿瘤免疫扩散模型的动力学性质分析

Dynamics Analysis of Delayed Tumor-Immune Model With Diffusion

考虑到肿瘤细胞会发生扩散和免疫细胞识别肿瘤细胞存在滞后现象这两个因素,基于KADDAR和ALAOUI的模型,建立了一个带有时滞的肿瘤免疫扩散模型.研究结果表明:当免疫细胞识别肿瘤细胞时间较短时,免疫系统清除肿瘤细胞的能力较强,这时系统存在很少的肿瘤细胞,治疗肿瘤相对容易.反之,免疫系统衰竭,肿瘤细胞疯狂增长,变成了不受机体控制的恶性肿瘤,治疗变得困难.通过分析免疫细胞识别肿瘤细胞时间的阈值,可判断肿瘤的最佳治疗时间,减少患者因肿瘤导致的死亡率.

Considering the factors that,the diffusion of tumor cells and the delay of immune cells recognizing tumor cells,a tumor-immune model with delay and diffusion terms was established based on the model of Kaddar and Alaoui.The research results show that:when the immune cells recognize tumor cells for a short time,the immune system has a strong ability to eliminate tumor cells,and there are few tumor cells in the system at this time,it is relatively easy to treat tumors;on the contrary,the immune system fails and the tumor cells grow wildly,turning into a malignant tumor that is not controlled by the body,and treatment becomes difficult.By analyzing the threshold of the time for immune cells to recognize tumor cells,the best treatment time for tumors can be judged,and the mortality of patients due to tumors can be reduced.