Deterministic and stochastic stability of a mathematical model of smoking

Statistics and Probability Letters

Volumn 81, Issue 8, 2011, Pages 1276-1284

  Lahrouz, A ^a   Omari, L ^a   Kiouach, D ^a   Belmaati A ^a  

^a SIDI MOHAMED BEN ABDELLAH UNIVERSITY   (Morocco)

Author keywords

Global stability; Lypunov function; Smoking model; Stochastic perturbations; Stochastic stability

Indexed keywords

EID: 79956207923     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spl.2011.03.029     Document Type: Article

References (19)

1. Afanas'ev V.N., Kolmanowskii V.B., Nosov V.R. Mathematical Theory of Control Systems Design 1996, Kluwer Academic, Dordrecht.
2. Bandyopadhyaya M., Saha T., Pal R. Deterministic and stochastic analysis of a delayed allelopathic phytoplankton model within fluctuating environment. Nonlinear Anal. Hybrid Syst. 2008, 2:958-970.
3. Beretta E., Kolmanovskii V., Shaikhet L. Stability of epidemic model with time delay influenced by stochastic perturbations. Math. Comput. Simulation 1998, 45:269-277.
4. Castillo, G.C., Jordan, S.G., Rodriguez, A.H., 2000. Mathematical models for the dynamics of tobacco use, recovery and relapse. Technical Report Series. BU-1505-M, Department of Biometrics, Cornell University.
5. Dalal N., Greenhalgh D., Mao X. A stochastic model for internal HIV dynamics. J. Math. Anal. Appl. 2008, 341:1084-1101.
6. Harrison G.W. Global stability of predator-prey interactions. J. Math. Biol. 1979, 8:159-171.
7. Hasminskii R.Z. Stochastic Stability of Differential Equations 1980, Sijthoof & Noordhoof, Alphen aan den Rijn, The Netherlands.
8. Korobeinikov A. Lyapunov functions and global stability for SIR and SIRS epidemiological models with non-linear transmission. Bull. Math. Biol. 2006, 68:615-626.
9. Korobeinikov A., Maini P.K. Nonlinear incidence and stability of infectious disease models. Math. Med. Biol. 2005, 22:113-128.
10. Lahrouz A., Omari L., Kiouach D. Global analysis of a deterministic and stochastic nonlinear SIRS epidemic model. Nonlinear Anal. Model. Control 2011, 16:59-76.
11. Luo Q., Mao X. Stochastic population dynamics under regime switching. J. Math. Anal. Appl. 2007, 334:69-84.
12. Mackey M.C., Nechaeva I.G. Noise and stability in differential delay equations. J. Differential Equations 1994, 6:395-426.
13. Mao X. Stochastic Differential Equations and Applications 1997, Horwood Publishing Limited, Chichester.
14. Sarkar R.R., Banerjee S. Cancer self remission and tumor stability-a stochastic approach. Math. Biosci. 2005, 196:65-81.
15. Shoromi O., Gumel A.B. Curtailing smoking dynamics: a mathematical modeling approach. Appl. Math. Comput. 2008, 195:475-499.
16. Takeuchi Y., Adachi N. The existence of globally stable equilibria of ecosystems of the generalized volterra type. J. Math. Biol. 1980, 401-415.
17. WHO, 2010a. http://www.emro.who.int/tfi/facts.htm#fact2.
18. WHO, 2010b. http://www.emro.who.int/tfi/facts.htm#fact9.
19. World Health Organization report on the global tobacco epidemic, 2009. http://whqlibdoc.who.int/publications/2009/9789241563918_eng_full.pdf.