Table of Contents
ISRN Applied Mathematics
Volume 2014, Article ID 847075, 7 pages
http://dx.doi.org/10.1155/2014/847075
Research Article

Global Dynamics of a Mathematical Model on Smoking

Department of Mathematics, King Abdulaziz University, Jeddah 21551, Saudi Arabia

Received 17 November 2013; Accepted 17 December 2013; Published 6 February 2014

Academic Editors: A. Bairi and S. W. Gong

Copyright © 2014 Zainab Alkhudhari et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. M. M. Bassiony, “Smoking in Saudi Arabia,” Saudi Medical Journal, vol. 30, no. 7, pp. 876–881, 2009. View at Google Scholar · View at Scopus
  2. “World Health Organization report on tobacco,” 2012, http://www.who.int/mediacentre/factsheets/fs339/en/.
  3. C. Castillo-Garsow, G. Jordan-Salivia, and A. R. Herrera, “Mathematical models for the dynamics of tobacco use, recovery, and relapse,” Technical Report Series BU-1505-M, Cornell University, Ithaca, NY, USA, 1997. View at Google Scholar
  4. O. Sharomi and A. B. Gumel, “Curtailing smoking dynamics: a mathematical modeling approach,” Applied Mathematics and Computation, vol. 195, no. 2, pp. 475–499, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. A. Lahrouz, L. Omari, D. Kiouach, and A. Belmaâti, “Deterministic and stochastic stability of a mathematical model of smoking,” Statistics & Probability Letters, vol. 81, no. 8, pp. 1276–1284, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. G. Zaman, “Qualitative behavior of giving up smoking models,” Bulletin of the Malaysian Mathematical Sciences Society, vol. 34, no. 2, pp. 403–415, 2011. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. G. Zaman, “Optimal campaign in the smoking dynamics,” Computational and Mathematical Methods in Medicine, vol. 2011, Article ID 163834, 9 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. V. S. Ertürk, G. Zaman, and S. Momani, “A numeric-analytic method for approximating a giving up smoking model containing fractional derivatives,” Computers & Mathematics with Applications, vol. 64, no. 10, pp. 3065–3074, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. P. van den Driessche and J. Watmough, “Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,” Mathematical Biosciences, vol. 180, pp. 29–48, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. F. Brauer, P. van den Driessche, and J. Wu, Mathematical Epidemiology, vol. 1945 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  11. L. Perko, Differential Equations and Dynamical Systems, vol. 7 of Texts in Applied Mathematics, Springer, New York, NY, USA, 1991. View at Publisher · View at Google Scholar · View at MathSciNet
  12. L. Cai, X. Li, M. Ghosh, and B. Guo, “Stability analysis of an HIV/AIDS epidemic model with treatment,” Journal of Computational and Applied Mathematics, vol. 229, no. 1, pp. 313–323, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. C. C. McCluskey and P. van den Driessche, “Global analysis of two tuberculosis models,” Journal of Dynamics and Differential Equations, vol. 16, no. 1, pp. 139–166, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. J. Arino, C. C. McCluskey, and P. van den Driessche, “Global results for an epidemic model with vaccination that exhibits backward bifurcation,” SIAM Journal on Applied Mathematics, vol. 64, no. 1, pp. 260–276, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. X. Ge and M. Arcak, “A sufficient condition for additive D-stability and application to reaction-diffusion models,” Systems & Control Letters, vol. 58, no. 10-11, pp. 736–741, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  16. M. W. Hirsch, S. Smale, and R. L. Devaney, Differential Equations, Dynamical Systems, and an Introduction to Chaos, vol. 60 of Pure and Applied Mathematics, Elsevier/Academic Press, Amsterdam, The Netherlands, 2nd edition, 2004. View at MathSciNet
  17. S. Busenberg and P. van den Driessche, “Analysis of a disease transmission model in a population with varying size,” Journal of Mathematical Biology, vol. 28, no. 3, pp. 257–270, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet