The Extinction and Persistence of Tumor Evolution Influenced by External Fluctuations and Periodic Treatment
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This paper investigates the extinction and persistence of tumor evolution influenced by external fluctuations and periodic treatment. Firstly, a mathematical model describing the evolution of tumor cells with immunization under external fluctuations and periodic treatment is established based on stochastic differential equation. Then, making use of the methods of Ito’s formula, the sufficient conditions for extinction and persistence are derived by rigorous mathematical proofs. Finally, numerical simulations are applied to illustrate and verify the conclusions. 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.
KeywordsExtinction Persistence External fluctuations Periodic treatment
This work was supported by the Shanxi Scholarship Council of China (Grant No. 2015-032), Technological Innovation Programs of Higher Education Institutions in Shanxi (Grant No. 2015121) and Applied Basic Research Programs of Shanxi Province (Grant No. 201601D021013).
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