A Discrete-time Mathematical Model of Smoking Dynamics with Two Sub-populations of Smokers
Keywords:
Smoking, Standard difference scheme, Boundedness, Jury stability conditions, Sensitivity analysisAbstract
We analyze smoking dynamics with two sub-populations of smokers using a discrete-time mathematical model with a standard difference scheme. We divide the smokers' populations into beginners and heavy smokers. The boundedness of the solution is obtained. The equilibrium stability is assessed through the Jury stability conditions. We additionally present numerical simulations to validate the analytical results by giving several examples to depict the stability of all equilibriums. The sensitivity analysis of the model's parameters is performed to that can offer recommendations for regulators to reduce the number of smokers.
References
U.S. National Cancer Institute and World Health Organization, The Economics of Tobacco and Tobacco Control. National Cancer Institute Tobacco Control Monograph 21, U.S. Department of Health and Human Services, National Institutes of Health, National Cancer Institute; and Geneva, CH: World Health Organization, 2016. NIH Publication No. 16-CA-8029A.
World Health Organization, “Tobacco.” https://www.who.int/news-room/fact-sheets/detail/tobacco, 2021. Accessed: 2025-01-07.
F. Islami, L. A. Torre, and A. Jemal, “Global trends of lung cancer mortality and smoking prevalence,” Translational Lung Cancer Research, vol. 4, no. 4, pp. 327–338, 2015.
M. Eriksen, J. Mackay, N. Schluger, F. Islami, and J. Drope, The Tobacco Atlas. American Cancer Society, 5th ed., 2015.
Y.-H. Chang, C.-H. Fu, M.-H. Hsu, C. Okoli, and S.-E. Guo, “The effectiveness of a transtheoretical model-based smoking cessation intervention for rural smokers: A quasi-experimental longitudinal study,” Patient Education and Counseling, vol. 122, p. 108136, 2024.
Z. Zhang, G. ur Rahman, and R. P. Agarwal, “Harmonic mean type dynamics of a delayed giving up smoking model and optimal control strategy via legislation,” Journal of the Franklin Institute, vol. 357, no. 15, pp. 10669– 10690, 2020.
I. Sofia, S. R. Bandekar, and M. Ghosh, “Mathematical modeling of smoking dynamics in society with impact of media information and awareness,” Results in Control and Optimization, vol. 11, p. 100233, 2023.
R. Herdiana, R. H. Tjahjana, A. H. Permatasari, and N. S. A. Latif, “Optimal control of smoking cessation programs for two subclasses of smoker,” J. Math. Computer Sci., vol. 31, pp. 41–55, 2023.
M. F. Ansori and R. Herdiana, “Dynamic model of smokers and its sensitivity analysis,” Commun. Math. Biol. Neurosci., vol. 2023, no. 39, pp. 1–16, 2023.
S. Zhang, Y. Meng, A. K. Chakraborty, and H. Wang, “Controlling smoking: A smoking epidemic model with different smoking degrees in deterministic and stochastic environments,” Mathematical Biosciences, vol. 368, p. 109132, 2024.
B. Han and D. Jiang, “Global dynamics of a stochastic smoking epidemic model driven by black-karasinski process,” Applied Mathematics Letters, vol. 160, p. 109324, 2025.
V. Padmavathi, K. Alagesan, S. Noeiaghdam, U. Fernandez-Gamiz, M. Angayarkanni, and V. Govindan, “Tobacco smoking model containing snuffing class,” Heliyon, vol. 9, no. 10, 2023.
H. Khan, J. Alzabut, J. G´omez-Aguilar, and A. Alkhazan, “Essential criteria for existence of solution of a modifiedabc fractional order smoking model,” Ain Shams Engineering Journal, vol. 15, no. 5, p. 102646, 2024.
S. Soulaimani, A. Kaddar, and F. A. Rihan, “Stochastic stability and global dynamics of a mathematical model for drug use: Statistical sensitivity analysis via prcc,” Partial Differential Equations in Applied Mathematics, vol. 12, p. 100964, 2024.
B. Buonomo, A. Giacobbe, and G. Mulone, “Analysis of an epidemic model with peer-pressure and informationdependent transmission with high-order distributed delay,” Ricerche di Matematica, vol. 68, pp. 453–468, 2019.
O. R. Isik, N. Tuncer, and M. Martcheva, “A mathematical model for the role of vaccination and treatment in measles transmission in turkey,” Journal of Computational and Applied Mathematics, vol. 457, p. 116308, 2025.
Y. Tan and R. Yao, “Dynamics of an influenza epidemic model incorporating immune boosting and ornstein– uhlenbeck process,” Chaos, Solitons & Fractals, vol. 188, p. 115446, 2024.
M. G¨um¨us¸ and K. T¨urk, “Dynamical behavior of a hepatitis b epidemic model and its nsfd scheme,” Journal of Applied Mathematics and Computing, vol. 70, no. 4, pp. 3767–3788, 2024.
M. G¨um¨us¸ and K. T¨urk, “A note on the dynamics of a covid-19 epidemic model with saturated incidence rate,” The European Physical Journal Special Topics, pp. 1–8, 2024.
M. Ahmed, M. A. B. Masud, and M. M. A. Sarker, “Bifurcation analysis and optimal control of discrete sir model for covid-19,” Chaos, Solitons & Fractals, vol. 174, p. 113899, 2023.
Y. Yan, S. Yu, Z. Yu, H. Jiang, and H. Wang, “Global dynamics of delayed discrete-time seir negative information propagation model with multi-platform and cross-transmission mechanism,” Communications in Nonlinear Science and Numerical Simulation, vol. 143, p. 108591, 2025.
J. Andaluz, A. A. Elsadany, and G. Jarne, “Nonlinear cournot and bertrand-type dynamic triopoly with differentiated products and heterogeneous expectations,” Mathematics and Computers in Simulation, vol. 132, pp. 86–99, 2017.
J. C. Veilleux and J. C. Steggerda, “The dynamics of smoking quit motivation in daily life: Associations with momentary self-regulation and nightly quit intentions,” Addictive behaviors, vol. 140, p. 107605, 2023.
R. E. Mickens, Nonstandard finite difference models of differential equations. world scientific, 1993.
M. S. Khan, M. Samreen, M. Ozair, T. Hussain, E. Elsayed, and J. G´omez-Aguilar, “On the qualitative study of a two-trophic plant–herbivore model,” Journal of Mathematical Biology, vol. 85, no. 4, p. 34, 2022.
M. F. Ansori, H. A. Jasir, A. H. Sihombing, S. M. Putra, D. A. Nurfaizah, and E. Nurulita, “Assessing the impact of deposit benchmark interest rate on banking loan dynamics,” Computer Research and Modeling, vol. 16, no. 4, pp. 1023–1032, 2024.
M. G¨um¨us¸ and S. W. Teklu, “Cost-benefit and dynamical investigation of a fractional-order corruption population dynamical system,” Fractal and Fractional, vol. 9, no. 4, p. 207, 2025.
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