Stability Analysis of Conventional and E-Cigarette Smokers Behavior Model with Saturation Effects

Binti Mu'alafi Suryantini, Budi Priyo Prawoto

Abstract


Smoking behavior is a harmful habit that poses serious health risks and has been regarded as a lifestyle by certain segments of society, regardless of age, gender, or social status. This study develops and analyzes a mathematical model of smoking behavior that classifies between conventional smokers and e-cigarette smokers, incorporates interaction with lung cancer patients, and considers the saturation effect on potential smokers as the number of smokers in the population increases. The method is determining assumptions to create a compartment diagram and construct the model. This model has four equilibrium points. The results show that when R01 < 1, R02 < 1, the smoker-free equilibrium point is asymptotically stable. When R01 < 1, R02 > 1, the endemic equilibrium point of e-cigarette smokers becomes stable. When R01 > 1 and R02 < 1, the endemic equilibrium point of conventional smokers becomes stable. Meanwhile, when R01 > 1 and R02 > 1, the endemic equilibrium point of coexistence of conventional and e-cigarette smokers becomes stable. Numerical simulations show that the intensity of smoking transmission affects the dynamics of the system. The lower the transmission rate by conventional and e-cigarette smokers, the faster the transition to a smoker-free population. The saturation effect plays a role in limiting excessive contact between potential smokers and smokers.

Keywords


e-cigarate; lung cancer; saturation effects; smoking; stability analysis

Full Text:

PDF

References


[1] Badan Pusat Statistik, Percentage of population aged 15 years and over who smoked tobacco within the last month by province (percent), 2025, [Online]. Available: https://www.bps.go.id, 2025.

[2] Global Adult Tobacco Survey, “Global adult tobacco survey (gats) indonesia report 2021,” Kementerian Kesehatan Republik Indonesia, World Health Organization, Tech. Rep., 2021. Available online.

[3] S. Glantz, A. Jeffers, and J. P. Winickoff, “Nicotine addiction and intensity of e-cigarette use by adolescents in the us, 2014 to 2021,” JAMA Network Open, vol. 5, no. 11, pp. 1–12, 2022. doi: 10.1001/jamanetworkopen.2022.40671

[4] F. Hafidah, A. Apriningsih, C. Simanjorang, and L. Hanifah, “Determinants of electronic smoking behavior among adolescents in indonesia (analysis of global youth tobacco survey 2019),” Public Health of Indonesia, vol. 10, no. 2, pp. 133–142, 2024. doi: 10.36685/phi.v10i2.787

[5] T. Jerzyński and G. V. Stimson, “Estimation of the global number of vapers: 82 million worldwide in 2021,” Drugs, Habits and Social Policy, vol. 24, no. 2, pp. 91–103, 2023. doi: 10.1108/DHS-07-2022-0028

[6] S. Sapru, M. Vardhan, Q. Li, Y. Guo, X. Li, and D. Saxena, “E-cigarettes use in the united states: Reasons for use, perceptions, and effects on health,” BMC Public Health, vol. 20, no. 1, pp. 1–10, 2020. doi: 10.1186/s12889-020-09572-x

[7] Y. Y. Zhang et al., “The effect of e-cigarettes on smoking cessation and cigarette smoking initiation: An evidence-based rapid review and meta-analysis,” Tobacco Induced Diseases, vol. 19, no. 1, pp. 1–15, 2021. doi: 10.18332/TID/131624

[8] A. O. Armencia et al., “Associations between smoking, stress, quality of life, and oral health among dental students in romania: A cross-sectional study,” Medicina, pp. 1–21, 2025. doi: 10.3390/medicina61081394

[9] Global Cancer Observatory, Cancer today globocan 2022 indonesia, 2022. Available online.

[10] K. C. Thandra, A. Barsouk, K. Saginala, J. S. Aluru, and A. Barsouk, “Epidemiology of lung cancer,” Wspolczesna Onkologia, vol. 25, no. 1, pp. 45–52, 2021. doi: 10.5114/wo.2021.103829

[11] A. Kundu et al., “Evidence update on the cancer risk of vaping e-cigarettes: A systematic review,” Tobacco Induced Diseases, vol. 23, no. 1, pp. 1–13, 2025. doi: 10.18332/tid/192934

[12] J. D. Murray, Mathematical Biology: I. An Introduction (3rd ed.) Springer-Verlag, 2002.

[13] A. Zakiyyah, S. Bahri, and A. R. Putri, “Mathematical analysis of sexual violence dynamics with recidivist perpetrators,” Jurnal Matematika UNAND, vol. 14, no. 4, pp. 411–423, 2025. doi: 10.25077/jmua.14.4.411-423.2025

[14] J. Juhari, Z. A. Fikrina, E. Alisah, and I. Sujarwo, “Dynamical analysis of modified mathematical model of social media addiction,” CAUCHY: Jurnal Matematika Murni dan Aplikasi, vol. 9, no. 2, pp. 310–319, 2024. doi: 10.18860/ca.v9i2.29225

[15] Z. Zulaikha and D. M. Putri, “Mathematical stability analysis of bullying’ s impact on student’ s mental health,” CAUCHY: Jurnal Matematika Murni dan Aplikasi, vol. 10, no. 2, pp. 1043–1053, 2025. doi: 10.18860/cauchy.v10i2.33212

[16] F. Meghatria and O. Belhamiti, “Predictive model of smoking social network intervention in development of lung cancer,” pp. 1–22, 2024. doi: 10.22541/au.172446203.32150944/v1

[17] F. I. Permatasari, “Analisis kestabilan model seitr pada penyebaran penyakit kanker paru paru akibat asap rokok,” MATHunesa: Jurnal Ilmiah Matematika, vol. 13, no. 1, pp. 73–87, 2025. doi: 10.26740/mathunesa.v13n1.p73-87

[18] A. Noersena, Fatmawati, C. Alfiniyah, and A. Abidemi, “Mathematical modelling of smoking behavior: Treatment and prevention optimal control,” Barekeng, vol. 19, no. 3, pp. 2003–2016, 2025. doi: 10.30598/barekengvol19iss3pp2003-20167

[19] R. K. Naji and A. A. Thirthar, “Stability and bifurcation of an sis epidemic model with saturated incidence rate and treatment function,” Iranian Journal of Mathematical Sciences and Informatics, vol. 15, no. 2, pp. 129–146, 2020. doi: 10.29252/ijmsi.15.2.129

[20] F. Brauer, P. v. d. Driessche, and J. Wu, Mathematical Epidemiology. Springer-Verlag, 2008.

[21] S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos (2nd ed.) Springer-Verlag, 2003.

[22] W. E. Boyce and R. C. DiPrima, Elementary Differential Equations and Boundary Value Problems (11th ed.) John Wiley & Sons, Inc, 2017.

[23] P. Zhang et al., “Association of smoking and polygenic risk with the incidence of lung cancer: A prospective cohort study,” British Journal of Cancer, vol. 126, no. 11, pp. 1637–1646, 2022. doi: 10.1038/s41416-022-01736-3

[24] P. N. Lee, K. J. Coombs, and J. S. Fry, “Estimating lung cancer risk from e-cigarettes and heated tobacco products: Applications of a tool based on biomarkers of exposure and of potential harm,” Harm Reduction Journal, vol. 22, no. 1, pp. 1–22, 2025. doi: 10.1186/s12954-025-01188-x

[25] J. Ahmed and M. H. A. Biswas, “Mathematical modeling and analysis the effect of smoking for the dynamics of lung cancer,” Proceedings of the International Conference on Industrial Engineering and Operations Management, pp. 1241–1252, 2021. doi: 10.46254/an11.20210251




DOI: https://doi.org/10.18860/cauchy.v11i1.40109

Refbacks

  • There are currently no refbacks.


Copyright (c) 2026 Budi Priyo Prawoto, Binti Mu'alafi Suryantini

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Editorial Office
Mathematics Department,
Universitas Islam Negeri Maulana Malik Ibrahim Malang
Gajayana Street 50 Malang, East Java, Indonesia 65144
Faximile (+62) 341 558933
e-mail: cauchy@uin-malang.ac.id

Creative Commons License
CAUCHY: Jurnal Matematika Murni dan Aplikasi is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.