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Smoking dynamics with health education effect

1 Department of Mathematics, University of Evansville, Evansville, IN 47722, USA
2 Department of Computer Science and Engineering, The University of Texas at Arlington, Arlington, TX 76019, USA
3 Department of Applied Mathematics, Western University, London, Ontario, N6A 5B7, Canada
4 Department of Information and Statistics, Guangxi University of Finance and Economics, Nanning,Guangxi, 750003, China

Topical Section: Mathematical modeling

This paper provides a mathematical study for analyzing the dynamics of smoking with health education campaigns involved. The method of next generation matrix is used to derive the basic reproduction number $R_0$. We prove that the smoking-free equilibrium is both locally and globally asymptotically stable if $R_0 < 1$; and the smoking-present equilibrium is globally asymptotically stable if $R_0 > 1$. By comparing with smoking dynamics without health education involved, we conclude that health education can decrease smoking population. Numerical simulations are used to support our conclusions.
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References

1. World Health Organization, WHO global report on trends in prevalence of tobacco smoking 2015, World Health Organization, 2015.

2. V. Bilano, S. Gilmour, T. Moffet, et al. Global trends and projections for tobacco use, 1990–2025: an analysis of smoking indicators from the WHO Comprehensive Information Systems for Tobacco Control, The Lancet, 385 (2015), 966–976.    

3. I. D. Bier, J. Wilson, P. Studt, et al. Auricular acupuncture, education, and smoking cessation: a randomized, sham-controlled trial, Am. J. Public Health, 92 (2002), 1642–1647.    

4. D. de Walque, Does education affect smoking behaviors?: Evidence using the Vietnam draft as an instrument for college education, J. Health Econ., 26 (2007), 877–895.

5. S. Durkin, E. Brennan and M. Wakefield, Mass media campaigns to promote smoking cessation among adults: an integrative review, Tob. control, 21 (2012), 127–138.    

6. O. Sharomi and A. B. Gumel, Curtailing smoking dynamics: a mathematical modeling approach, Appl. Math. Comput., 195 (2008), 475–499.    

7. Z. Alkhudhari, S. Al-Sheikh and S. Al-Tuwairqi, Global dynamics of a mathematical model on smoking, International Scholarly Research Notices, 2014 (2014), 1–7.    

8. D. Qamar, O. Muhammad, H. Takasar, et al. Qualitative behavior of a smoking model, Adv. Differ. Equ-NY, 2016 (2016), 96.    

9. J. W. McEvoy, M. J. Blaha, J. J. Rivera, et al. Mortality rates in smokers and nonsmokers in the presence or absence of coronary artery calcification, JACC-CARDIOVASC IMAG., 5 (2012), 1037–1045.    

10. G. Zaman, Qualitative behavior of giving up smoking models, B. Malays. Math. Sci. So., 34 (2009), 403–415.

11. H. Xiang, N. N. Song and H. F. Huo, Modeling effects of public health educational campaigns on drinking dynamics, J. Biol. Dynam., 10 (2016), 164–178.    

12. H. Xiang, C. C. Zhu and H. F. Huo, Modelling the effect of immigration on drinking behaviour, J. Biol. Dynam., 11 (2017), 275–298.    

13. H. F. Huo and C. C. Zhu, Influence of relapse in a giving up smoking model, Abstr. Appl. Anal., 2013 (2013), 1–12.    

14. H. F. Huo and N. N. Song, Global stability for a binge drinking model with two-stage, Discrete Dyn. Nat. Soc., 2012 (2012), 1–15.    

15. H. F. Huo, Y. L. Chen and H. Xiang, Stability of a binge drinking model with delay, J. Biol. Dynam., 11 (2017), 210–225.    

16. P. Van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29–48.    

17. H. T. Zhao and M. C. Zhao, Global Hopf bifurcation analysis of an susceptible-infective-removed epidemic model incorporating media coverage with time delay, J. Biol. Dynam., 11 (2017), 8–24.    

© 2018 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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