Citation: | ZHANG Xue-kang, ZHANG Zhen-zhong. Permanence and extinction of stochastic smoking model[J]. Journal of East China Normal University (Natural Sciences), 2017, (4): 71-88. doi: 10.3969/j.issn.1000-5641.2017.04.007 |
[1] |
World Health Organization. Tobacco fact sheet [EB/OL]. [2016-03-01]. http://www.who.int/mediacentre/fact-sheets/fs339/en/.
|
[2] |
CASTILLO-GARSOW C, JORDAN-SALIVIA G, RODRIGUEZ-HERRERA A. Mathematical models for the dynamics of tobacco use, recovery and relapse [EB/OL]. [2016-03-01]. https://ecommons.cornell.edu/handle/1813/32095.
|
[3] |
SHAROMI O, GUMEL A. Curtailing smoking dyanamics: A mathematical modeling approach [J]. Applied Mathematics and Computation, 2008, 195(2): 475-499. doi: 10.1016/j.amc.2007.05.012
|
[4] |
ZAMAN G. Qualitative behavior of giving up smoking models [J]. Bulletin of the Malaysian Mathematical Sciences Sciences Society, 2011, 34(2): 403-415. https://www.researchgate.net/profile/Gul_Zaman/publication/228472006_Qualitative_Behavior_of_Giving_Up_Smoking_Models/links/0deec53573c48e0444000000.pdf?origin=publication_detail
|
[5] |
ALKHUDHARI Z, SHEIKH S, TUWAIRQI S. Global dynamics of a mathematical model on smoking [J]. ISRN Applied Mathematics, 2014, Article ID 847075. https://www.researchgate.net/profile/Salma_Al-Tuwairqi/publication/262886946_Research_Article_Global_Dynamics_of_a_Mathematical_Model_on_Smoking/links/0c96053918c681a8af000000.pdf?inViewer=true&pdfJsDownload=true&disableCoverPage=true&origin=publication_detail
|
[6] |
GARD T C. Persistence in stochastic food web models [J]. Bulletin of Mathematical Biology, 1984, 46(3): 357-370. doi: 10.1007/BF02462011
|
[7] |
GRAY A, GREENHALGH D, HU L, et al. A stochastic differential equations SIS epidemic model [J]. Siam Journal on Applied Mathematics, 2011, 71(3): 876-902. doi: 10.1137/10081856X
|
[8] |
BAO J, YUAN C. Stochastic population dynamics driven by Lévy noise [J]. Journal of Mathematical Analysis and Applications, 2012, 391(2): 363-375. doi: 10.1016/j.jmaa.2012.02.043
|
[9] |
LAHROUZ A, OMARI L, KIOUACH D, et al. Deterministic and stochastic stability of a mathematical model of smoking [J]. Statistics and Probability Letters, 2011, 81(8): 1276-1284. doi: 10.1016/j.spl.2011.03.029
|
[10] |
MAO X. Exponential Stability of Stochastic Differential Equations [M]. New York: Marcel Dekker, 1994.
|
[11] |
MAO X. Stochastic Differential Equations and Applications [M]. Chichest: Horwood Publishing Limited, 1999.
|
[12] |
LIU H, MA Z. The threshold of survival for system of two species in a polluted environment [J]. Journal of Mathematical Biology, 1991, 30(1): 49-61. doi: 10.1007/BF00168006
|
[13] |
MAO X, YUAN C. Stochastic Differential Equations with Markovian Switching [M]. London: Imperial College Press, 2006: 74.
|
[14] |
JIANG D, SHI N, LI X. Global stability and stochastic permanence of a non-autonomous logistic equation with random perturbation [J]. Journal of Mathematical Analysis and Applications, 2008, 340(1): 588-597. doi: 10.1016/j.jmaa.2007.08.014
|
[15] |
LI X, GRAY A, JING D, et al. Sufficient and necessary conditions of stochastic permanence and exctinction for stochastic logistic populations under regime switching [J]. Journal of Mathematical Analysis and Applications, 2011, 376(1): 11-28. doi: 10.1016/j.jmaa.2010.10.053
|
[16] |
KARATZAS I, SHREVE S. Brownian Motion and Stochastic Calculus [M]. Second edition. Berlin: Springer, 2007: 293.
|
[17] |
ZHANG X, ZHANG Z, TONG J, et al. Ergodicity of stochastic smoking model and parameter estimation [J]. Advances in Difference Equations, 2016, 274: 1-20. https://www.researchgate.net/publication/309444899_Ergodicity_of_stochastic_smoking_model_and_parameter_estimation
|
[18] |
KLEBANER F C. Introduction to Stochastic Calculus with Applications [M]. Second edition. London: Imperial College Press, 2005: 219.
|