A Simple Model of Tumor-Immune Interaction: The Effect of Antigen Delay

被引:0
|
作者
Li, Jianquan [1 ]
Chen, Yuming [2 ]
Cao, Hui [3 ]
Zhang, Dian [4 ]
Zhang, Peijun [1 ]
机构
[1] Xijing Univ, Xian Key Lab Human Machine Integrat & Control Tec, Xian 710123, Peoples R China
[2] Wilfrid Laurier Univ, Dept Math, Waterloo, ON N2L 3C5, Canada
[3] Shaanxi Univ Sci & Technol, Sch Math & Data Sci, Xian 710021, Peoples R China
[4] Xian Med Univ, Dept Immunol, Xian 710021, Peoples R China
来源
基金
加拿大自然科学与工程研究理事会; 中国国家自然科学基金;
关键词
Tumor-immune interaction; tumor antigen; stimulation delay; stability; Hopf bifurcation; BIFURCATION-ANALYSIS; NONLINEAR DYNAMICS; SYSTEM; IMMUNOTHERAPY; STABILITY;
D O I
10.1142/S0218127423501298
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We propose a simple model of tumor-immune interactions, which involves effector cells and tumor cells. In the model, the stimulation delay of tumor antigen in the immune system is incorporated. We investigate the dynamical behavior of the model via theoretic analysis and numerical simulations. The saddle-node bifurcation can occur in both cases with and without delay. In contrast to the case without delay, stimulation delay may result in some complex dynamical behaviors and biological phenomena. In the presence of delay, conditions on absolute/conditional stability of equilibria and the existence of Hopf bifurcations are obtained. We further discuss the effect of the tumor on the switch between absolute stability and conditional stability. Numerical simulations also show the existence of homoclinic bifurcation and the dependence of the asymptotic state of the tumor progression on initial conditions for different delay values. Effects of delay on the dynamics of the model and on the region of tumor extinction are illustrated by simulations with different sets of parameter values. Finally, the corresponding biological implications are demonstrated.
引用
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页数:20
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