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

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Abstract

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 (λ<0), then the escape is faster than in the case with no correlation (λ=0); when the noises are positively cross-correlated (λ>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 τ 3 on the MFPT is completely opposite for λ>0 and λ<0. (iii) The self-correlation times τ 1 and τ 2 of colored noises can enhance stability of the cancer state, while the immune rate β can reduce it.

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Authors and Affiliations

  1. Faculty of Science, Kunming University of Science and Technology, Kunming, 650093, China

    Chunhua Zeng

  2. Province Engineering Research Center of Industrial Energy Conservation and New Technology, Kunming University of Science and Technology, Kunming, Yunnan, 650093, China

    Chunhua Zeng & Hua Wang

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  1. Chunhua Zeng
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  2. Hua Wang
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Correspondence to Chunhua Zeng.

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Zeng, C., Wang, H. Colored Noise Enhanced Stability in a Tumor Cell Growth System Under Immune Response. J Stat Phys 141, 889–908 (2010). https://doi.org/10.1007/s10955-010-0068-8

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