Cross-correlation enhanced stability in a tumor cell growth model with immune surveillance driven by cross-correlated noises

The transient properties of a tumor cell growth model with immune surveillance driven by cross-correlated multiplicative and additive noises are investigated. The explicit expression of extinction rate from the state of a stable tumor to the state of extinction is obtained. Based on the numerical computations, we find the following: (i) the intensity of multiplicative noise D and the intensity of additive noise alpha enhance the extinction rate for the case of lambda <= 0 (i. e. lambda denotes cross-correlation intensity between two noises), but for the case of lambda > 0, a critical noise intensity D or alpha exists at which the extinction rate is the smallest; D and alpha at first weaken the extinction rate and then enhance it. (ii) The immune rate beta and the cross-correlation intensity lambda play opposite roles on the extinction rate, i. e. beta enhances the extinction rate of the tumor cell, while lambda weakens the extinction rate of the tumor cell. Namely, the immune rate can enhance the extinction of the tumor cell and the cross-correlation between two noises can enhance stability of the cancer state.