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Chin. Phys. B, 2014, Vol. 23(9): 090501    DOI: 10.1088/1674-1056/23/9/090501
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Effects of Lévy noise and immune delay on the extinction behavior in a tumor growth model

Hao Meng-Li (郝孟丽), Xu Wei (徐伟), Gu Xu-Dong (谷旭东), Qi Lu-Yuan (戚鲁媛)
Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710129, China
Abstract  The combined effects of Lévy noise and immune delay on the extinction behavior in a tumor growth model are explored. The extinction probability of tumor with certain density is measured by exit probability. The expression of the exit probability is obtained using the Taylor expansion and the infinitesimal generator theory. Based on numerical calculations, it is found that the immune delay facilitates tumor extinction when the stability index α<1, but inhibits tumor extinction when the stability index α>1. Moreover, larger stability index and smaller noise intensity are in favor of the extinction for tumor with low density. While for tumor with high density, the stability index and the noise intensity should be reduced to promote tumor extinction.
Keywords:  exit probability            vy noise      immune delay      tumor growth model  
Received:  17 January 2014      Revised:  09 March 2014      Accepted manuscript online: 
PACS:  05.40.Fb (Random walks and Levy flights)  
  82.39.-k (Chemical kinetics in biological systems)  
  02.50.-r (Probability theory, stochastic processes, and statistics)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11172233, 11272258, and 11302170).
Corresponding Authors:  Xu Wei     E-mail:  weixu@nwpu.edu.cn

Cite this article: 

Hao Meng-Li (郝孟丽), Xu Wei (徐伟), Gu Xu-Dong (谷旭东), Qi Lu-Yuan (戚鲁媛) Effects of Lévy noise and immune delay on the extinction behavior in a tumor growth model 2014 Chin. Phys. B 23 090501

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