Stochastic Properties Of Tumor Growth Driven By Noise

Since the biologic theory of immune system can control tumor cell infinite growth,transformation and metastasis, a tumor growth model under immune surveillance isobtained by using the methods of nonlinear dynamics and statistical physics. The effects ofnon-Gaussian noise and Lévy noise on the dynamical behavior of tumor growth arediscussed. The results of this paper provide a theoretical basis to restrain the tumor growthand to obtain more therapy time.Firstly, the effect of tumor cell growth with coupling between non-Gaussian andGaussian noise terms is investigated. The expression of the Fokker-Planck equation and thesteady state distribution function is derived through the path integral approach and thefunctional approximation. It is found that the obtaining of the minimum average tumor cellpopulation mainly depends on the increase of the departure from the Gaussian noise andthe decrease of Gaussian noise strength. And the increase of mean first passage time whichindicates the transition between active and inactive state mainly depends on the decrease ofthe departure from the Gaussian noise and the Gaussian noise strength is obtained bytheoretical analysis and numerical simulation.Besides, the stochastic property of tumor growth driven by Lévy noise is analyzed. Bynumerical simulation, the mean first passage time for tumor model driven by Lévy noise isdiscussed. In order to check the validity of the numerical simulation, we compare theresults of steady-state probability distribution driven by Lévy noise when the stabilityindex α=2and the skewness β=0with the results driven by Gaussian noise. And theresults of the mean first passage time which indicates the transition between active andinactive state can illuminate that more time of therapy can be obtained when the stabilityindex α is increasing while the scaling σ <1and the skewness βâ†'0.