Extinction Effects of Multiplicative Non-Gaussian Levy Noise in a Tumor Growth System with Immunization

The extinction phenomenon induced by multiplicative non-Gaussian Levy noise in a tumor growth model with immune response is discussed. Under the influence of the stochastic immune rate, the model is analyzed in terms of a stochastic differential equation with multiplicative noise. By means of the th...

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Published inCommunications in theoretical physics Vol. 61; no. 5; pp. 571 - 577
Main Author 郝孟丽 徐伟 李东喜 刘迪
Format Journal Article
LanguageEnglish
Published 01.05.2014
Subjects
Density
Extinction
Mathematical models
Noise
Non-Gaussian
Stability
Stochasticity
Tumors
乘法
免疫应答
征收
消光效果
生长系统
肿瘤细胞
随机微分方程
非高斯噪声
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Summary:The extinction phenomenon induced by multiplicative non-Gaussian Levy noise in a tumor growth model with immune response is discussed. Under the influence of the stochastic immune rate, the model is analyzed in terms of a stochastic differential equation with multiplicative noise. By means of the theory of the infinitesimal generator of Hunt processes, the escape probability, which is used to measure the noise-induced extinction probability of tumor cells, is explicitly expressed as a function of initial tumor cell density, stability index and noise intensity. Based on the numerical calculations, it is found that for different initial densities of tumor cells, noise parameters play opposite roles on the escape probability. The optimally selected values of the multiplicative noise intensity and the stability index are found to maximize the escape probability.
Bibliography:HAO Meng-Li , XU Wei , LI Dong-Xi,LIU Di （ 1 Department of Applied Mathematics, Northwestern Polytechnical University, Xi＇an 710129, China 2School of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China）
The extinction phenomenon induced by multiplicative non-Gaussian Levy noise in a tumor growth model with immune response is discussed. Under the influence of the stochastic immune rate, the model is analyzed in terms of a stochastic differential equation with multiplicative noise. By means of the theory of the infinitesimal generator of Hunt processes, the escape probability, which is used to measure the noise-induced extinction probability of tumor cells, is explicitly expressed as a function of initial tumor cell density, stability index and noise intensity. Based on the numerical calculations, it is found that for different initial densities of tumor cells, noise parameters play opposite roles on the escape probability. The optimally selected values of the multiplicative noise intensity and the stability index are found to maximize the escape probability.
model of tumor growth, stochastic immune rate, non-Gaussian L6vy motion, noise-induced ex-tinction probability
11-2592/O3
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:0253-6102
1572-9494
DOI:10.1088/0253-6102/61/5/05