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

• 论文 • 上一篇    下一篇

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. 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 Li1,*(),Yuping Wang1,Dian Zhang2   

  1. 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:

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