Dynamics analysis in a tumor-immune system with chemotherapy

doi:10.1088/1674-1056/abcf49

中国物理B ›› 2021, Vol. 30 ›› Issue (5): 58201-058201.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

收稿日期:2020-09-08 修回日期:2020-11-02 接受日期:2020-12-01 出版日期:2021-05-14 发布日期:2021-05-14
通讯作者: Hong-Li Yang E-mail:imuyhl@imu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11762011).

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

Received:2020-09-08 Revised:2020-11-02 Accepted:2020-12-01 Online:2021-05-14 Published:2021-05-14
Contact: Hong-Li Yang E-mail:imuyhl@imu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11762011).

摘要/Abstract

摘要： 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.

关键词: dynamical model, tumor-immune system, chemotherapy, chaos

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.

Key words: dynamical model, tumor-immune system, chemotherapy, chaos

中图分类号: (Oscillations, chaos, and bifurcations)

82.40.Bj

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)

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[J]. 中国物理B, 2021, 30(5): 58201-058201.

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[J]. Chin. Phys. B, 2021, 30(5): 58201-058201.

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Dynamics analysis in a tumor-immune system with chemotherapy

Dynamics analysis in a tumor-immune system with chemotherapy

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