Abstract
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.
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