期刊
JOURNAL OF STATISTICAL PHYSICS
卷 141, 期 5, 页码 889-908出版社
SPRINGER
DOI: 10.1007/s10955-010-0068-8
关键词
Correlation times; Mean first-passage time; Tumor cell growth system
资金
- National Nature Science Foundation [50906035]
- Key Foundation [90610035]
- United Foundation of China [U0937604]
- Natural Science Foundation of Yunnan Province [2010CD031]
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.
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