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Chin. Phys. B, 2021, Vol. 30(5): 058201    DOI: 10.1088/1674-1056/abcf49

Dynamics analysis in a tumor-immune system with chemotherapy

Hai-Ying Liu(刘海英), Hong-Li Yang(杨红丽), and Lian-Gui Yang(杨联贵)
School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China
Abstract  An ordinary differential equation (ODE) model of tumor growth with the effect of tumor-immune interaction and chemotherapeutic drug is presented and studied. By analyzing the existence and stability of equilibrium points, the dynamic behavior of the system is discussed elaborately. The chaotic dynamics can be obtained in our model by equilibria analysis, which show the existence of chaos by calculating the Lyapunov exponents and the Lyapunov dimension of the system. Moreover, the action of the infusion rate of the chemotherapeutic drug on the resulting dynamics is investigated, which suggests that the application of chemotherapeutic drug can effectively control tumor growth. However, in the case of high-dose chemotherapeutic drug, chemotherapy-induced effector immune cells damage seriously, which may cause treatment failure.
Keywords:  dynamical model      tumor-immune system      chemotherapy      chaos  
Received:  08 September 2020      Revised:  02 November 2020      Accepted manuscript online:  01 December 2020
PACS:  82.40.Bj (Oscillations, chaos, and bifurcations)  
  87.10.Ed (Ordinary differential equations (ODE), partial differential equations (PDE), integrodifferential models)  
  87.15.A- (Theory, modeling, and computer simulation)  
  87.19.xj (Cancer)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11762011).
Corresponding Authors:  Hong-Li Yang     E-mail:

Cite this article: 

Hai-Ying Liu(刘海英), Hong-Li Yang(杨红丽), and Lian-Gui Yang(杨联贵) Dynamics analysis in a tumor-immune system with chemotherapy 2021 Chin. Phys. B 30 058201

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