Stochastic responses of tumor—immune system with periodic treatment

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

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.

Keywords: stochastic responses environmental noise tumor-immune system extinction

Received: 26 February 2017
Revised: 09 May 2017
Accepted manuscript online:

PACS:	02.50.-r	(Probability theory, stochastic processes, and statistics)
	05.40.-a	(Fluctuation phenomena, random processes, noise, and Brownian motion)

Fund: 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).

Corresponding Authors: Dong-Xi Li
E-mail: dxli0426@126.com

Cite this article:

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

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