具NK细胞的溶瘤病毒疗法的模型分析

Analysis of Oncolytic Virotherapy Model with the Natural Killer Cells

本文建立了一类包含自然杀伤细胞(NK细胞)免疫反应的肿瘤病毒相互作用模型。首先分析了系统的边界性态,将系统的平衡点进行完整的分类,讨论了边界平衡点的局部稳定性,并从数值上验证了周期解的存在性,最后讨论了NK细胞在病毒治疗中所起到的作用。数值结果表明:a)整体肿瘤大小与病毒感染率成反比,与肿瘤生长速率成正比;b)对于NK细胞相关参数,NK细胞从淋巴结的流入速率越大,最终肿瘤越小;若产生NK细胞增殖,当增殖速率比较小时,相较于无NK增殖时,最终肿瘤变大,即较小的NK细胞增殖对治疗产生负面的影响,但当NK细胞的增殖速率过高时,将会导致肿瘤和病毒的完全清除。

In this paper,a tumor-virus interaction model that contains the immune response of the natural killer cells(NK cells)was established.Firstly,the boundary behavior of the system was analyzed,the equilibria of the system were completely classified,the local stability of the equilibria were discussed,and the existence of periodic solution was verified numerically.Finally,the role of NK cells on oncolytic virotherapy was examined.The numerical simulation results are as follows.a)The whole tumor population is inversely proportional to the viral infection rate,proportional to the tumor growth rate.b)For the parameters related to NK cells,the larger the inflow rate of NK cells from lymph nodes,the smaller the final tumor;if the proliferation of NK cells is produced,the tumor will eventually become larger compared with no NK proliferation when the proliferation rate is relatively small,which implies that small proliferation rate of NK cells has a negative effect on treatment.However,the tumor and oncolytic viruses will be completely eliminated when the proliferation rate of NK cells is too high.