Stochastic responses of tumor—immune system with periodic treatment

doi:10.1088/1674-1056/26/9/090203

中国物理B ›› 2017, Vol. 26 ›› Issue (9): 90203-090203.doi: 10.1088/1674-1056/26/9/090203

Stochastic responses of tumor—immune system with periodic treatment

Dong-Xi Li(李东喜), Ying Li(李颖)

1 College of Data Science, Taiyuan University of Technology, Taiyuan 030024, China;
2 College of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China

收稿日期:2017-02-26 修回日期:2017-05-09 出版日期:2017-09-05 发布日期:2017-09-05
通讯作者: Dong-Xi Li E-mail:dxli0426@126.com
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11402157 and 11571009), Shanxi Scholarship Council of China (Grant No. 2015-032), Technological Innovation Programs of Higher Education Institutions in Shanxi, China (Grant No. 2015121), and Applied Basic Research Programs of Shanxi Province, China (Grant No. 2016021013).

Stochastic responses of tumor—immune system with periodic treatment

Dong-Xi Li(李东喜)¹, Ying Li(李颖)²

1 College of Data Science, Taiyuan University of Technology, Taiyuan 030024, China;
2 College of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China

Received:2017-02-26 Revised:2017-05-09 Online:2017-09-05 Published:2017-09-05
Contact: Dong-Xi Li E-mail:dxli0426@126.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11402157 and 11571009), Shanxi Scholarship Council of China (Grant No. 2015-032), Technological Innovation Programs of Higher Education Institutions in Shanxi, China (Grant No. 2015121), and Applied Basic Research Programs of Shanxi Province, China (Grant No. 2016021013).

摘要/Abstract

摘要： We investigate the stochastic responses of a tumor-immune system competition model with environmental noise and periodic treatment. Firstly, a mathematical model describing the interaction between tumor cells and immune system under external fluctuations and periodic treatment is established based on the stochastic differential equation. Then, sufficient conditions for extinction and persistence of the tumor cells are derived by constructing Lyapunov functions and Ito's formula. Finally, numerical simulations are introduced to illustrate and verify the results. The results of this work provide the theoretical basis for designing more effective and precise therapeutic strategies to eliminate cancer cells, especially for combining the immunotherapy and the traditional tools.

关键词: stochastic responses, environmental noise, tumor-immune system, extinction

Abstract: We investigate the stochastic responses of a tumor-immune system competition model with environmental noise and periodic treatment. Firstly, a mathematical model describing the interaction between tumor cells and immune system under external fluctuations and periodic treatment is established based on the stochastic differential equation. Then, sufficient conditions for extinction and persistence of the tumor cells are derived by constructing Lyapunov functions and Ito's formula. Finally, numerical simulations are introduced to illustrate and verify the results. The results of this work provide the theoretical basis for designing more effective and precise therapeutic strategies to eliminate cancer cells, especially for combining the immunotherapy and the traditional tools.

Key words: stochastic responses, environmental noise, tumor-immune system, extinction

中图分类号: (Probability theory, stochastic processes, and statistics)

02.50.-r

05.40.-a (Fluctuation phenomena, random processes, noise, and Brownian motion)

李东喜, 李颖. Stochastic responses of tumor—immune system with periodic treatment[J]. 中国物理B, 2017, 26(9): 90203-090203.

Dong-Xi Li(李东喜), Ying Li(李颖). Stochastic responses of tumor—immune system with periodic treatment[J]. Chin. Phys. B, 2017, 26(9): 90203-090203.

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Stochastic responses of tumor—immune system with periodic treatment

Stochastic responses of tumor—immune system with periodic treatment

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