The properties of the anti-tumor model with coupling non-Gaussian noise and Gaussian colored noise

• The non-Gaussian noise has a dual role in the development of tumor.
• A minimum of the mean value can be obtained by choosing proper parameters.
• The cross-correlated degree can slow down the transition of tumors.
• The correlation time can enhance the stability of the disease state.

The anti-tumor model with correlation between multiplicative non-Gaussian noise and additive Gaussian-colored noise has been investigated in this paper. The behaviors of the stationary probability distribution demonstrate that the multiplicative non-Gaussian noise plays a dual role in the development of tumor and an appropriate additive Gaussian colored noise can lead to a minimum of the mean value of tumor cell population. The mean first passage time is calculated to quantify the effects of noises on the transition time of tumors between the stable states. An increase in both the non-Gaussian noise intensity and the departure from the Gaussian noise can accelerate the transition from the disease state to the healthy state. On the contrary, an increase in cross-correlated degree will slow down the transition. Moreover, the correlation time can enhance the stability of the disease state.