具有双线性刺激率和饱和抑制率的肿瘤免疫模型的全局分析

Global Analysis of Tumor-Immune Models with Bilinear Stimulation Rate and Saturation Inhibition Rate

假设肿瘤细胞对效应细胞具有双线性刺激率和饱和抑制率,建立了肿瘤细胞和效应细胞相互作用的数学模型,讨论了该模型平衡点的存在性,利用稳定性理论讨论了无瘤平衡点和有瘤平衡点的局部渐近稳定性,并用中心流形定理分析了该模型产生鞍结点分支的条件.同时,利用数值模拟进一步验证了理论分析结果的正确性,展示了模型复杂的全局动力学性态.最后,研究了效应细胞的常数输入率,或肿瘤细胞对效应细胞的刺激率改变时,模型动力学性态的变化趋势.

In this paper,a tumor-immune model was constructed under the assumption that the tumor cells have bilinear stimulation rate and saturation inhibition rate on the effect cells,we discuss the existence of the equilibria and the local asymptotic stability of tumor equilibrium and tumor-free equilibrium by stability theory,analysis the conditions when the saddle node bifurcation is generated by center manifold theory.At the same time,the correctness of theoretical analysis results is verified furtherly by numerical simulations and the complex global dynamic behavior of the model is shown.Finally,we investigate the trend of model dynamics when the constant input rate of effect cells or the stimulation rate of tumor cells on effect cells were changed.