基于关联噪声下具有免疫监视的肿瘤生长系统稳定性及逃逸率研究  

Stability and Escape Rate of Tumor Growth System with Immune Surveillance Based on Correlated Noise

作　　者：付燕 王国威[2] FU Yan;WANG Guo-wei(School of Mathematics and Computer Science,Yuzhang Normal University,Nanchang 330103,China;School of Education,Nanchang Institute of Science and Technology,Nanchang 330108,China)

机构地区：[1]豫章师范学院数学与计算机学院,江西南昌330103 [2]南昌工学院教育学院,江西南昌330108

出　　处：《数学的实践与认识》2021年第22期99-111,共13页Mathematics in Practice and Theory

基　　金：江西省教育厅科学技术研究项目(GJJ191108,GJJ203111);豫章师范学院校级科研课题(YZYB-21-17);南昌工学院科技计划课题(NGKJ-19-03)。

摘　　要：在具有催化作用的Michaelis-Menten反应模型的基础之上,得到具有免疫监视下肿瘤细胞生长模型的随机微分方程.考虑肿瘤细胞增殖过程中环境等因素的变化对肿瘤细胞生长率和死亡率的影响,以关联噪声的形式引入系统,通过对一维朗之万方程的线性化近似,利用最快下降法等方法计算系统的稳态概率分布函数、平均首次通过时间和逃逸率,分析关联噪声对肿瘤细胞生长过程的稳定性以及逃逸率的影响。结果表明:(1)系统的一阶矩是噪声间关联强度的单调减函数,且稳态概率分布函数的曲线呈现出双峰结构,特异性免疫系数可以改变肿瘤细胞数概率分布的结构;(2)逃逸率W+(xu→x+)作为噪声强度D的函数,其图像会随着噪声间关联强度的变化由单极值转换为单调曲线,发生“类相变”现象;逃逸率W_(xu→x-)随噪声强度D变化的函数,其图像会出现具有“共振峰”特征的极大值,且噪声间关联强度入越大,其峰值的位置越向右移动;(3)如果加性噪声强度维持不变,则存在一个最适合的噪声关联强度,可以使系统的跃迁概率W+(xu→x+)达到最大值;(4)W+(xn→x+)是噪声强度Q的单调减函数.上述研究结果可以帮助人们对肿瘤细胞的随机生长特性产生更全面的认识,在科学研究中可以为肿瘤细胞的生长提供理论基础,在临床医学中可以为肿瘤检测和治疗提供理论指导,对预防、控制和治疗肿瘤疾病具有指导意义.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 analyze the influence of noise on tumor cell growth process.The results show that:(1)The first moment of the system is the monotone decreasing function of the correlation intensity between the noise,and the curve of the steady-state probability distribution function presents a bimodal structure,and the specific immune coefficient can change the structure of the probability distribution of tumor cell number.(2)As a function of the noise intensity,the image of changes from monopole value to monotone curve with the change of the correlation intensity between noises,thus the phenomenon of“phase-like transformation”occurs.(3)If the additive noise intensity is fixed,there exists a most suitable noise correlation intensity,which can make the transition probability of the system reach the maximum value.If the noise correlation intensity is less than 0.6,the system escape rate will appear a suppression platform,and the system transition rate is O.When,the escape rate increases with the increase of correlation intensity,indicating that the noise correlation intensity induces the system transition from metastable to stable state.(4)is the monotone subtraction function of noise intensity.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

关 键 词：噪声 肿瘤细胞 免疫监视 朗之万方程 稳定性 逃逸率 

分 类 号：O211.63[理学—概率论与数理统计] R730.2[理学—数学]