International journal of

ADVANCED AND APPLIED SCIENCES

EISSN: 2313-3724, Print ISSN:2313-626X

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 Volume 5, Issue 2 (February 2018), Pages: 71-75

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 Original Research Paper

 Title: Dynamical transmission and effect of smoking in society

 Author(s): Aqeel Ahmad, Muhammad Farman *, Faisal Yasin, M. O. Ahmad

 Affiliation(s):

 Department of Mathematics and Statistics, University of Lahore, Lahore, Pakistan

 https://doi.org/10.21833/ijaas.2018.02.012

 Full Text - PDF          XML

 Abstract:

Smoking is a large problem in the entire world. Despite overwhelming facts about smoking, it is still a very bad habit which is widely spread and accepted socially. Among smokers, often the desire to quit smoking arises. A large number of smokers attempt to quit, but only a few of them are successful. In this research, the nonstandard finite difference scheme is applied on system which is dynamically consistent, easy to implement and show a good agreement to control the bad impact of smoking for long period of time and to eradicate a death killer factor in the world spread by smoking. We have discussed the qualitative behavior of the model and numerical simulations are carried out to support the analytical results. 

 © 2017 The Authors. Published by IASE.

 This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

 Keywords: Epidemic model, Stability analysis, Qualitative analysis, Sensitivity analysis, NSFD

 Article History: Received 27 September 2017, Received in revised form 6 December 2017, Accepted 10 December 2017

 Digital Object Identifier: 

 https://doi.org/10.21833/ijaas.2018.02.012

 Citation:

 Ahmad A, Farman M, Yasin F, and Ahmad MO (2018). Dynamical transmission and effect of smoking in society. International Journal of Advanced and Applied Sciences, 5(2): 71-75

 Permanent Link:

 http://www.science-gate.com/IJAAS/2018/V5I2/Aqeel.html

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 References (27)

  1. Alkhudhari Z, Al-Sheikh S, and Al-Tuwairqi S (2014). Global dynamics of a mathematical model on smoking. Hindawi Publishing Corporation, ISRN Applied Mathematics, 2014: Article ID 847075, 7 pages. http://doi.org/10.1155/2014/847075 
  2. Anguelov R and Lubuma JMS (2001). Contributions to the mathematics of the nonstandard finite difference method and applications. Numerical Methods for Partial Differential Equations, 17(5): 518-543. https://doi.org/10.1002/num.1025 
  3. Anguelov R, Dumont Y, Lubuma JS, and Shillor M (2014). Dynamically consistent nonstandard finite difference schemes for epidemiological models. Journal of Computational and Applied Mathematics, 255: 161-182. https://doi.org/10.1016/j.cam.2013.04.042 
  4. Arafa AAM, Rida SZ, and Khalil M (2012). Fractional modeling dynamics of HIV and CD4+ T-cells during primary infection. Nonlinear Biomedical Physics, 6(1): 1-7. https://doi.org/10.1186/1753-4631-6-1  PMid:22214194 PMCid:PMC3275462 
  5. Biazar J (2006). Solution of the epidemic model by Adomian decomposition method. Applied Mathematics and Computation, 173(2): 1101-1106. https://doi.org/10.1016/j.amc.2005.04.036 
  6. Buonomo B and Lacitignola D (2008). On the dynamics of an SEIR epidemic model with a convex incidence rate. Ricerche Di Matematica, 57(2): 261-281. https://doi.org/10.1007/s11587-008-0039-4 
  7. Busenberg S and Van den Driessche P (1990). Analysis of a disease transmission model in a population with varying size. Journal of Mathematical Biology, 28(3): 257-270. https://doi.org/10.1007/BF00178776  PMid:2332704 
  8. El-Sayed AMA, Rida SZ, and Arafa AAM (2009). On the solutions of time-fractional bacterial chemotaxis in a diffusion gradient chamber. International Journal of Nonlinear Science, 7(4): 485-492.     
  9. Erturk VS, Zaman G, and Momani S (2012). A numeric–analytic method for approximating a giving up smoking model containing fractional derivatives. Computers and Mathematics with Applications, 64(10): 3065-3074. https://doi.org/10.1016/j.camwa.2012.02.002 
  10. Garsow CC, Salivia GJ, and Herrera AR (2000). Mathematical models for the dynamics of tobacoo use, recovery and relapse. Technical Report Series BU-1505-M, Cornell University, UK.     
  11. Gumel A (2014). Mathematics of Continuous and Discrete Dynamical Systems. Vol. 618, American Mathematical Society, Providence, Rhode Island. https://doi.org/10.1090/conm/618 
  12. Haq F, Shah K, ur Rahman G, and Shahzad M (2017). Numerical solution of fractional order smoking model via laplace Adomian decomposition method. Alexandria Engineering Journal. https://doi.org/10.1016/j.aej.2017.02.015 
  13. Kribs-Zaleta CM (1999). Structured models for heterosexual disease transmission. Mathematical Biosciences, 160(1): 83-108. https://doi.org/10.1016/S0025-5564(99)00026-7 
  14. Liu X and Wang C (2010). Bifurcation of a predator prey model with disease in the prey. Nonlinear Dynamics, 62(4): 841-850. https://doi.org/10.1007/s11071-010-9766-7 
  15. Lubin JH and Caporaso NE (2006). Cigarette smoking and lung cancer: modeling total exposure and intensity. Cancer Epidemiology and Prevention Biomarkers, 15(3): 517-523. https://doi.org/10.1158/1055-9965.EPI-05-0863  PMid:16537710 
  16. Lubuma JMS and Patidar KC (2007). Non-standard methods for singularly perturbed problems possessing oscillatory/layer solutions. Applied Mathematics and Computation, 187(2): 1147-1160. https://doi.org/10.1016/j.amc.2006.09.011 
  17. Makinde OD (2007). Adomian decomposition approach to a SIR epidemic model with constant vaccination strategy. Applvcied Mathematics and Computation, 184(2): 842-848. https://doi.org/10.1016/j.amc.2006.06.074 
  18. Mickens RE (1989). Exact solutions to a finite‐difference model of a nonlinear reaction‐advection equation: Implications for numerical analysis. Numerical Methods for Partial Differential Equations, 5(4): 313-325. https://doi.org/10.1002/num.1690050404 
  19. Mickens RE (1994). Nonstandard finite difference models of differential equations. World Scientific, Singapore, Singapore.     
  20. Mickens RE (2000). Applications of nonstandard finite difference schemes. World Scientific, Singapore, Singapore. https://doi.org/10.1142/4272 
  21. Mickens RE (2002). Nonstandard finite difference schemes for differential equations. The Journal of Difference Equations and Applications, 8(9): 823-847. https://doi.org/10.1080/1023619021000000807 
  22. Mickens RE (2005). Advances in the applications of nonstandard finite difference schemes. World Scientific, Singapore, Singapore. https://doi.org/10.1142/5884 
  23. Sharomi O and Gumel AB (2008). Curtailing smoking dynamics: a mathematical modeling approach. Applied Mathematics and Computation, 195(2): 475-499. https://doi.org/10.1016/j.amc.2007.05.012 
  24. Singh J, Kumar D, Al Qurashi M, and Baleanu D (2017). A new fractional model for giving up smoking dynamics. Advances in Difference Equations, 2017(1): 88-102. https://doi.org/10.1186/s13662-017-1139-9 
  25. Zaman G (2011a). Qualitative behavior of giving up smoking models. Bulletin of the Malaysian Mathematical Sciences Society, 34(2): 403-415.     
  26. Zaman G (2011b). Optimal campaign in the smoking dynamics. Hindawi Publishing Corporation, Computational and Mathematical Methods in Medicine, 2011: Article ID 163834, 9 pages. https://doi.org/10.1155/2011/163834 
  27. Zeb A, Chohan MI, and Zaman G (2012). The homotopy analysis method for approximating of giving up smoking model in fractional order. Applied Mathematics, 3(8): 914-919. https://doi.org/10.4236/am.2012.38136