Colored Noise Enhanced Stability in a Tumor Cell Growth System Under Immune Response

In this paper, we investigate a mathematical model for describing the growth of tumor cell under immune response, which is driven by cross-correlation between multiplicative and additive colored noises as well as the nonzero cross-correlation in between. The expression of the mean first-passage time (MFPT) is obtained by virtue of the steepest-descent approximation. It is found: (i) When the noises are negatively cross-correlated (lambda < 0), then the escape is faster than in the case with no correlation (lambda=0); when the noises are positively cross-correlated (lambda > 0), then the escape is slower than in the case with no correlation. Moreover, in the case of positive cross-correlation, the escape time has a maximum for a certain intensity of one of the noises, i.e., the maximum for MFPT identifies the noise enhanced stability of the cancer state. (ii) The effect of the cross-correlation time tau (3) on the MFPT is completely opposite for lambda > 0 and lambda < 0. (iii) The self-correlation times tau (1) and tau (2) of colored noises can enhance stability of the cancer state, while the immune rate beta can reduce it.