一类具有抗原性的肿瘤-免疫系统的定性分析

数学物理学报 ›› 2021, Vol. 41 ›› Issue (6): 1969-1979.

一类具有抗原性的肿瘤-免疫系统的定性分析

谢鑫¹(),李建全^1,*(),王玉萍¹,张典²

¹ 陕西科技大学数学系西安 710021
² 西安医学院医学免疫教研室西安 710021

收稿日期:2020-11-17 出版日期:2021-12-26 发布日期:2021-12-02
通讯作者: 李建全 E-mail:1424967994@qq.com;jianq_li@263.net
作者简介:谢鑫, E-mail: 1424967994@qq.com
基金资助:
国家自然科学基金(11971281);国家自然科学基金(12071268);西安医学院科研基金(2018GJFY05)

A Qualitative Analysis of a Tumor-Immune System with Antigenicity

Xin Xie¹(),Jianquan Li^1,*(),Yuping Wang¹,Dian Zhang²

¹ Department of Mathematics, Shaanxi University of Science and Technology, Xi'an 710021
² Department of Immunology, Xi'an Medical University, Xi'an 710021

Received:2020-11-17 Online:2021-12-26 Published:2021-12-02
Contact: Jianquan Li E-mail:1424967994@qq.com;jianq_li@263.net
Supported by:
the NSFC(11971281);the NSFC(12071268);the Scientific Research Fund of Xi'an Medical University(2018GJFY05)

摘要/Abstract

摘要：

该文提出并研究了一类具有抗原性的肿瘤与免疫系统相互作用的动力学模型，得到了模型有瘤平衡点的存在性，并分析了各可行平衡点的局部动力学性态，通过排除周期解的存在性得到了模型的全局动力学性态，发现模型在一定条件下会发生鞍结点分支以及双稳定现象，即肿瘤的增长发展结局会依赖其初始状态.相应的理论分析结果得到数值模拟的验证.

关键词: 肿瘤-免疫系统, 抗原性, 稳定性, 鞍结点分支

Abstract:

In this paper, we propose and investigate a tumor-immune system interaction model with antigenicity. The existence of equilibria of the model is determined, and the local dynamics of each feasible equilibrium is analyzed. The global dynamics of the model is obtained by excluding the existence of periodic solutions. It is found that, under certain conditions, the saddle-node bifurcation and the bi-stability of strong equilibrium with tumor and equilibrium without tumor may occur for the model, which imply that the growth and development of the tumor will depend on its initial state. The obtained theoretical analysis results are verified by numerical simulations.

Key words: Tumor-immune system, Antigenicity, Stability, Saddle-node bifurcation

中图分类号:

O175.1

谢鑫,李建全,王玉萍,张典. 一类具有抗原性的肿瘤-免疫系统的定性分析[J]. 数学物理学报, 2021, 41(6): 1969-1979.

Xin Xie,Jianquan Li,Yuping Wang,Dian Zhang. A Qualitative Analysis of a Tumor-Immune System with Antigenicity[J]. Acta mathematica scientia,Series A, 2021, 41(6): 1969-1979.

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