Stochastic responses of tumor-immune system with periodic treatment

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.