Effects of correlated color noise on the stability and transient property of tumor cell growth system with immune surveillance
WANG Guowei1， FU Yan2
1.School of Education， Nanchang Institute of Science &Technology，Nanchang 330108， China；2.School of Mathematics and Computer Science， Yuzhang Normal Unviersity， Nanchang 330108， China
Abstract：Based on the model of Michaelis-Menten reaction with catalysis， a more comprehensive one dimension Langevin equation of tumor cell growth system with immune monitoring is obtained. Considering the fluctuation of growth rate and mortality caused by the change of growth environment in the process of tumor cell proliferation， the influence of correlated color noise on the system was analyzed. The steady-state probability distribution function and the mean first-passage time of the system are calculated by the linearization approximation and the deepest descent methods， which are used as a window to observe the stability and transient properties of tumor cell growth process， and to analyze the influence of noise on tumor cell growth process. The results show as follows. 1)When the noise intensity D and Q are changed， the structure of the steady-state probability distribution function Pst(x) of tumor cell number can be changed， which leads to the structural transformation between multipole and monopole， and the system produces phase-like transformation. 2)T＋(xu→x＋)is the monotone increasing function of multiplicative noise intensity D， but T－(xu→x－) is the monotone decreasing function of multiplicative noise intensity D. 3)There is a maximum value similar to “resonance peak”in the image of T＋(xu→x＋) verses the change of additive noise intensity Q， and T－(xu→x－) is the monotone decreasing function of Q. 4)When the mean first-passage time T＋(xu→x＋) changes with the correlation time of noises， it shows monotonic decreasing and “resonance peak” transition. However， the mean first-passage time T－(xu→x－) shows a single peak state with the change of noise correlation time τ. 5)The change of the mean first-passage time T＋(xu→x＋) with the correlation intensity λ of noises shows a maximum value similar to the “resonance peak”， and the mean first-passage time T－(xu→x－) is a monotonic decreasing function of λ. The above results are helpful for people to master the growth kinetics characteristics of tumor cells. They can not only provide a theoretical basis for the clinical tumor cell growth research， but also provide theoretical guidance for the clinical cancer detection and treatment in medicine， and have a certain guiding significance for the control and treatment of tumor diseases.
王国威,付 燕. 关联色噪声对具有免疫监视下肿瘤细胞生长系统稳定性和瞬态性质的影响[J]. 华中师范大学学报(自然科学版), 2021, 55(1): 36-45.
WANG Guowei,FU Yan. Effects of correlated color noise on the stability and transient property of tumor cell growth system with immune surveillance. journal1, 2021, 55(1): 36-45.
2021, Vol. 55 
