Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (6): 1969-1979.

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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;
  • Supported by:
    the NSFC(11971281);the NSFC(12071268);the Scientific Research Fund of Xi'an Medical University(2018GJFY05)


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

CLC Number: 

  • O175.1