A Numerical Prediction on the Smoking Habits

Ayşe Beler

doi:10.17776/csj.1786746

A Numerical Prediction on the Smoking Habits

Abstract

The goal of this study is to predict the smoking habits of individuals that belong to different kinds of groups, namely: potential smokers/non-smokers, light smokers, heavy smokers, and smokers who temporarily and permanently quit smoking. The interactions between these groups are modeled by five ordinary differential equations representing each group. The governing system of differential equations is solved by using the Gegenbauer polynomials. Since the model does not have an analytical solution, numerical results are compared by the fourth order Runge Kutta method and Mathematica default solver to validate the accuracy and efficiency of the method. We simulate the long-term behavior of these individuals and show the interaction among the groups.

Keywords

: Gegenbauer polynomials, Smoking problem, Ordinary differential equations

References

World Health Organization. (2025, June 25). Tobacco. World Health Organization. https://www.who.int/news-room/fact-sheets/detail/tobacco
Zaman, G. (2011). Qualitative behavior of giving up smoking models. Bulletin of the Malaysian Mathematical Sciences Society, 34(2), 403–415.
Zaman, G. (2011). Optimal campaign in the smoking dynamics. Computational and Mathematical Methods in Medicine, 2011, Article 163834. https://doi.org/10.1155/2011/163834
Ertürk, V. S., Zaman, G., & Momani, S. (2012). A numeric–analytic method for approximating a giving up smoking model containing fractional derivatives. Computers & Mathematics with Applications, 64(10), 3065–3074. https://doi.org/10.1016/j.camwa.2012.02.002
Alkhudhari, Z., Al-Sheikh, S., & Al-Tuwairqi, S. (2014). The effect of occasional smokers on the dynamics of a smoking model. International Mathematical Forum, 9(25), 1207–1222. https://doi.org/10.12988/imf.2014.46120
Alkhudhari, Z., Al-Sheikh, S., & Al-Tuwairqi, S. (2014). Global dynamics of a mathematical model on smoking. ISRN Applied Mathematics, 2014, Article 847075. https://doi.org/10.1155/2014/847075
Alkhudhari, Z., Al-Sheikh, S., & Al-Tuwairqi, S. (2015). The effect of heavy smokers on the dynamics of a smoking model. International Journal of Differential Equations and Applications, 14(4), 343–356.
Khalid, M., Khan, F. S., & Iqbal, A. (2016). Perturbation-iteration algorithm to solve fractional giving up smoking mathematical model. International Journal of Computer Applications, 142(9), 1–6. https://doi.org/10.5120/ijca2016909891
Zeb, A., Zaman, G., Ertürk, V. S., Alzalg, B., Yousafzai, F., & Khan, M. (2016). Approximating a giving up smoking dynamic on adolescent nicotine dependence in fractional order. PLOS ONE, 11(4), Article e0103617. https://doi.org/10.1371/journal.pone.0103617
Singh, J., Kumar, D., Al Qurashi, M., & Baleanu, D. (2017). A new fractional model for giving up smoking dynamics. Advances in Difference Equations, 2017, Article 88. https://doi.org/10.1186/s13662-017-1139-9

Haq, F., Shah, K., ur Rahman, G., & Shahzad, M. (2018). Numerical solution of fractional order smoking model via Laplace Adomian decomposition method. Alexandria Engineering Journal, 57(2), 1061–1069. https://doi.org/10.1016/j.aej.2017.02.015
Uçar, S., Uçar, E., Özdemir, N., & Hammouch, Z. (2019). Mathematical analysis and numerical simulation for a smoking model with Atangana–Baleanu derivative. Chaos, Solitons & Fractals, 118, 300–306. https://doi.org/10.1016/j.chaos.2018.12.003
ur Rahman, G., Agarwal, R. P., & Din, Q. (2019). Mathematical analysis of giving up smoking model via harmonic mean type incidence rate. Applied Mathematics and Computation, 354, 128–148. https://doi.org/10.1016/j.amc.2019.01.053
Sofia, I. R., Bandekar, S. R., & Ghosh, M. (2023). Mathematical modeling of smoking dynamics in society with impact of media information and awareness. Results in Control and Optimization, 11, Article 100233. https://doi.org/10.1016/j.rico.2023.100233
Haidong, Q., Rahman, M. u., & Arfan, M. (2023). Fractional model of smoking with relapse and harmonic mean type incidence rate under Caputo operator. Journal of Applied Mathematics and Computing, 69, 403–420. https://doi.org/10.1007/s12190-022-01747-6
Addai, E., Adeniji, A., Peter, O. J., Agbaje, J. O., & Oshinubi, K. (2023). Dynamics of age-structure smoking models with government intervention coverage under fractal-fractional order derivatives. Fractal and Fractional, 7(5), Article 370. https://doi.org/10.3390/fractalfract7050370
Zhang, S., Meng, Y., Chakraborty, A. K., & Wang, H. (2024). Controlling smoking: A smoking epidemic model with different smoking degrees in deterministic and stochastic environments. Mathematical Biosciences, 368, Article 109132. https://doi.org/10.1016/j.mbs.2023.109132
Pavani, K., & Raghavendar, K. (2024). A novel technique to study the solutions of time fractional nonlinear smoking epidemic model. Scientific Reports, 14, Article 4159. https://doi.org/10.1038/s41598-024-54492-0
Özaltun Şimşek, G., Beler, A., & Gümgüm, S. (2024). Gegenbauer wavelet solutions of the SIR and SITR systems of the COVID-19 disease. International Journal of Biomathematics, Article 2450143. https://doi.org/10.1142/S1793524524501432
Özaltun, G., Konuralp, A., & Gümgüm, S. (2023). Gegenbauer wavelet solutions of fractional integro-differential equations. Journal of Computational and Applied Mathematics, 420, Article 114830. https://doi.org/10.1016/j.cam.2022.114830
Özdek, D. (2024). Gegenbauer parameter effect on Gegenbauer wavelet solutions of Lane-Emden equations. Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 29(1), 144–156. https://doi.org/10.53433/yyufbed.1330540
Gegenbauer, L. (1884). Zur Theorie der Functionen Cnν(x)Cnν (x). Denkschriften der Kaiserlichen Akademie der Wissenschaften zu Wien, Mathematisch-Naturwissenschaftliche Classe, 48, 293–316.

Details

Primary Language

English

Subjects

Biological Mathematics

Journal Section

Research Article

Authors

Ayşe Beler ^*
0000-0003-4414-3727
Türkiye

Publication Date

June 29, 2026

Submission Date

September 19, 2025

Acceptance Date

May 18, 2026

Published in Issue

Year 2026 Volume: 47 Number: 3

DOI

https://doi.org/10.17776/csj.1786746

IZ

https://izlik.org/JA97EE48ZC

APA

Beler, A. (2026). A Numerical Prediction on the Smoking Habits. Cumhuriyet Science Journal, 47(3), 618-628. https://doi.org/10.17776/csj.1786746

AMA

1.Beler A. A Numerical Prediction on the Smoking Habits. CSJ. 2026;47(3):618-628. doi:10.17776/csj.1786746

Chicago

Beler, Ayşe. 2026. “A Numerical Prediction on the Smoking Habits”. Cumhuriyet Science Journal 47 (3): 618-28. https://doi.org/10.17776/csj.1786746.

EndNote

Beler A (June 1, 2026) A Numerical Prediction on the Smoking Habits. Cumhuriyet Science Journal 47 3 618–628.

IEEE

[1]A. Beler, “A Numerical Prediction on the Smoking Habits”, CSJ, vol. 47, no. 3, pp. 618–628, June 2026, doi: 10.17776/csj.1786746.

ISNAD

Beler, Ayşe. “A Numerical Prediction on the Smoking Habits”. Cumhuriyet Science Journal 47/3 (June 1, 2026): 618-628. https://doi.org/10.17776/csj.1786746.

JAMA

1.Beler A. A Numerical Prediction on the Smoking Habits. CSJ. 2026;47:618–628.

MLA

Beler, Ayşe. “A Numerical Prediction on the Smoking Habits”. Cumhuriyet Science Journal, vol. 47, no. 3, June 2026, pp. 618-2, doi:10.17776/csj.1786746.

Vancouver

1.Ayşe Beler. A Numerical Prediction on the Smoking Habits. CSJ. 2026 Jun. 1;47(3):618-2. doi:10.17776/csj.1786746

As of 2026, Cumhuriyet Science Journal will be published in six issues per year, released in February, April, June, August, October, and December

A Numerical Prediction on the Smoking Habits

Abstract

Keywords

References

Details

Primary Language

Subjects

Journal Section

Authors

Publication Date

Submission Date

Acceptance Date

Published in Issue

DOI

IZ

Cite