MATHEMATICAL MODELING AND BIFURCATION ANALYSIS FOR A BIOLOGICAL MECHANISM OF CANCER DRUG RESISTANCE

doi:10.1007/s10473-024-0321-x

数学物理学报(英文版) ›› 2024, Vol. 44 ›› Issue (3): 1165-1188.doi: 10.1007/s10473-024-0321-x

• • 上一篇

MATHEMATICAL MODELING AND BIFURCATION ANALYSIS FOR A BIOLOGICAL MECHANISM OF CANCER DRUG RESISTANCE

Kangbo Bao^1,2, Guizhen LIANG³, Tianhai TIAN^4,*, Xinan ZHANG^2,*

1. School of Information Engineering and Artificial Intelligence, Lanzhou University of Finance and Economics, Lanzhou 730020, China;
2. School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China;
3. School of Mathematics and Information Science, Xinxiang University, Xinxiang 453003, China;
4. School of Mathematical Sciences, Monash University, Melbourne VIC 3800, Australia

收稿日期:2022-11-22 修回日期:2023-10-07 出版日期:2024-06-25 发布日期:2024-05-21

MATHEMATICAL MODELING AND BIFURCATION ANALYSIS FOR A BIOLOGICAL MECHANISM OF CANCER DRUG RESISTANCE

Kangbo Bao^1,2, Guizhen LIANG³, Tianhai TIAN^4,*, Xinan ZHANG^2,*

1. School of Information Engineering and Artificial Intelligence, Lanzhou University of Finance and Economics, Lanzhou 730020, China;
2. School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China;
3. School of Mathematics and Information Science, Xinxiang University, Xinxiang 453003, China;
4. School of Mathematical Sciences, Monash University, Melbourne VIC 3800, Australia

Received:2022-11-22 Revised:2023-10-07 Online:2024-06-25 Published:2024-05-21
Contact: *Tianhai TIAN, E-mail:tianhai.tian@monash.edu; Xinan ZHANG, E-mail:xinanzhang@mail.ccnu.edu.cn
About author:Kangbo Bao, E-mail:baokangbo@163.com; Guizhen LIANG, E-mail:lgz3361@163.com
Supported by:
National Natural Science Foundation of China (11871238, 11931019, 12371486).

摘要/Abstract

摘要： Drug resistance is one of the most intractable issues in targeted therapy for cancer diseases. It has also been demonstrated to be related to cancer heterogeneity, which promotes the emergence of treatment-refractory cancer cell populations. Focusing on how cancer cells develop resistance during the encounter with targeted drugs and the immune system, we propose a mathematical model for studying the dynamics of drug resistance in a conjoint heterogeneous tumor-immune setting. We analyze the local geometric properties of the equilibria of the model. Numerical simulations show that the selectively targeted removal of sensitive cancer cells may cause the initially heterogeneous population to become a more resistant population. Moreover, the decline of immune recruitment is a stronger determinant of cancer escape from immune surveillance or targeted therapy than the decay in immune predation strength. Sensitivity analysis of model parameters provides insight into the roles of the immune system combined with targeted therapy in determining treatment outcomes.

关键词: mathematical model, drug resistance, cancer heterogeneity, immune system, targeted therapy

Abstract: Drug resistance is one of the most intractable issues in targeted therapy for cancer diseases. It has also been demonstrated to be related to cancer heterogeneity, which promotes the emergence of treatment-refractory cancer cell populations. Focusing on how cancer cells develop resistance during the encounter with targeted drugs and the immune system, we propose a mathematical model for studying the dynamics of drug resistance in a conjoint heterogeneous tumor-immune setting. We analyze the local geometric properties of the equilibria of the model. Numerical simulations show that the selectively targeted removal of sensitive cancer cells may cause the initially heterogeneous population to become a more resistant population. Moreover, the decline of immune recruitment is a stronger determinant of cancer escape from immune surveillance or targeted therapy than the decay in immune predation strength. Sensitivity analysis of model parameters provides insight into the roles of the immune system combined with targeted therapy in determining treatment outcomes.

Key words: mathematical model, drug resistance, cancer heterogeneity, immune system, targeted therapy

中图分类号:

37N25

Kangbo Bao, Guizhen LIANG, Tianhai TIAN, Xinan ZHANG. MATHEMATICAL MODELING AND BIFURCATION ANALYSIS FOR A BIOLOGICAL MECHANISM OF CANCER DRUG RESISTANCE[J]. 数学物理学报(英文版), 2024, 44(3): 1165-1188.

Kangbo Bao, Guizhen LIANG, Tianhai TIAN, Xinan ZHANG. MATHEMATICAL MODELING AND BIFURCATION ANALYSIS FOR A BIOLOGICAL MECHANISM OF CANCER DRUG RESISTANCE[J]. Acta mathematica scientia,Series B, 2024, 44(3): 1165-1188.

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MATHEMATICAL MODELING AND BIFURCATION ANALYSIS FOR A BIOLOGICAL MECHANISM OF CANCER DRUG RESISTANCE

MATHEMATICAL MODELING AND BIFURCATION ANALYSIS FOR A BIOLOGICAL MECHANISM OF CANCER DRUG RESISTANCE

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