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 in | Communications in theoretical physics Vol. 61; no. 5; pp. 571 - 577 |
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Format | Journal Article |
Language | English |
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01.05.2014
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Abstract | 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. |
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AbstractList | 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. |
Author | 郝孟丽 徐伟 李东喜 刘迪 |
AuthorAffiliation | Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710129, China School of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China |
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CitedBy_id | crossref_primary_10_1142_S0219493721500167 crossref_primary_10_1016_j_cnsns_2021_105883 |
Cites_doi | 10.1016/j.physa.2013.06.010 10.1016/j.amc.2011.06.068 10.1017/CBO9780511809781 10.1088/0253-6102/40/1/120 10.1109/TNN.2008.2005610 10.1016/0305-0491(80)90326-0 10.1142/S0218127412500903 10.1016/j.jtbi.2005.06.037 10.1140/epjb/e2008-00246-2 10.1103/PhysRevE.73.060902 10.1023/A:1008705820024 10.1007/s002850050127 10.1038/ni1102-991 10.1103/PhysRevE.74.041904 10.1007/s10955-010-0068-8 10.1103/PhysRevE.74.011916 10.1063/1.4732102 10.1142/S0217984912501497 10.1016/0022-5193(78)90150-9 10.1016/j.physleta.2010.12.066 10.1088/0253-6102/52/3/16 10.1016/j.physleta.2012.04.006 10.1007/BF02107618 10.4171/JEMS/231 10.1007/BF02458325 |
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Notes | 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 |
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References | 22 23 24 26 29 B.Q. Ai (6) 2003; 40 W. Horsthemke (7) 1984 T. Gao (25) 2014 K.I. Sato (28) 1999 C.J. Wang (20) 2009; 52 31 10 11 12 13 14 15 16 17 18 R.T. Prehn (19) 1971; 7 1 2 H.J. Qiao (27) 2013; 34 3 4 5 8 9 21 Z. Schuss (30) 1980 |
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SubjectTerms | 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 |
Title | Extinction Effects of Multiplicative Non-Gaussian Levy Noise in a Tumor Growth System with Immunization |
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