The stationary properties and the state transition of the tumor cell growth mode

Abstract

We study the stationary properties and the state transition of the tumor cell growth model (the logistic model) in presence of correlated noises for the case of nonzero correlation time. We derived an approximative Fokker-Planck equation and the stationary probability distribution (SPD) of the model. Based the SPD, we investigated the effects of both correlation strength ( $\lambda$ ) and correlation time ( $\tau$ ) of cross-correlated noises on the SPD, the mean of the tumor cell population and the normalized variance ( $\lambda_2$ ) of the system, and calculated the state transition rate of the system between two stable states. Our results indicate that: (i) $\lambda$ and $\tau$ play opposite roles in the stationary properties and the state transition of the system, i.e. increase of $\lambda$ can produce a smaller mean value of the cell population and slow down the state transition, but increase of $\tau$ can produce a larger mean value of the cell population and enhance state transition; (ii) For large $\lambda$ , there a peak structure on both $\lambda_2$ - $\lambda$ plot and $\lambda_2$ - $\tau$ plot. For the small $\lambda$ , $\lambda_2$ increases with increasing $\lambda$ , but $\lambda_2$ increases with decreasing $\tau$ .