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G, Keerthana, THIRUMALAI, SAGITHYA. (1405). Numerical investigation of smoking behavior dynamics using the spectral collocation method. سامانه مدیریت نشریات علمی, 14(3), 1387-1407. doi: 10.22034/cmde.2025.63796.2861
Keerthana G; SAGITHYA THIRUMALAI. "Numerical investigation of smoking behavior dynamics using the spectral collocation method". سامانه مدیریت نشریات علمی, 14, 3, 1405, 1387-1407. doi: 10.22034/cmde.2025.63796.2861
G, Keerthana, THIRUMALAI, SAGITHYA. (1405). 'Numerical investigation of smoking behavior dynamics using the spectral collocation method', سامانه مدیریت نشریات علمی, 14(3), pp. 1387-1407. doi: 10.22034/cmde.2025.63796.2861
G, Keerthana, THIRUMALAI, SAGITHYA. Numerical investigation of smoking behavior dynamics using the spectral collocation method. سامانه مدیریت نشریات علمی, 1405; 14(3): 1387-1407. doi: 10.22034/cmde.2025.63796.2861

Numerical investigation of smoking behavior dynamics using the spectral collocation method

Computational Methods for Differential Equations
مقاله 24، دوره 14، شماره 3، مهر 2026، صفحه 1387-1407    اصل مقاله (1.93 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2025.63796.2861
نویسندگان
Keerthana G؛ SAGITHYA THIRUMALAI*
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai Campus, India.
چکیده
Smoking poses a significant threat to global public health and remains one of the leading causes of health problems. To examine these smoking-related issues, this paper aims to study the modified smoking model, which represents a five-compartment system consisting of potential smokers, snuffing class, irregular smokers, regular smokers, and quitters. The model is evaluated computationally using the spectral collocation method. The core idea of the spectral collocation technique is to approximate the solution as a truncated series of basis functions using Chebyshev polynomials. By incorporating collocation points, the truncated series is transformed into an operational matrix form, which in turn converts the governing differential equations into a system of non-linear algebraic equations. Furthermore, the residual and absolute error for different collocation points are established. Additionally, the effects of various parameters such as transmission rate, recovery rate, quit rate, and death rate on the smoking model have been analyzed. All these computational investigations on the model are displayed in the form of figures. Finally, the effect of different combinations of parameters on the smoking dynamics and its impact is represented using contour plots.
کلیدواژه‌ها
Spectral collocation method؛ Smoking model؛ Chebyshev polynomial
مراجع
  • [1] R. M. Anderson and R. M. May, Population biology of infectious diseases: Part I. Nature, 280(5721) (1979), 361-7.
  • [2] R. M. Anderson and R. M. May, Infectious diseases of humans: dynamics and control, Oxford University Press, (1991).
  • [3] R. M. Anderson, Discussion: the Kermack-McKendrick epidemic threshold theorem, Bulletin of Mathematical Biology, 53 (1991), 1-32.
  • [4] Z. Alkhudhari, S. Al-Sheikh, and S. Al-Tuwairqi, Global dynamics of a mathematical model on smoking, International Scholarly Research Notices, 1 (2014), 847075.
  • [5] E. Alzahrani and A. Zeb, Stability analysis and prevention strategies of tobacco smoking model, Boundary Value Problems, (2020), 1-3.
  • [6] A. A. Alshareef and H. A. Batar, Stability analysis of chain, mild and passive smoking model, American Journal of Computational Mathematics, 10(1) (2020), 31.
  • [7] A. U. Awan, A. Sharif, K. A. Abro, M. Ozair, and T. Hussain, Dynamical aspects of smoking model with cravings to smoke, Nonlinear Engineering, 10(1) (2021), 91-108.
  • [8] L. Bednarova, Z. Simkova, A. Behunova, and A. Wozny, How does the Excise Tax Affect Secondhand Smokers and the Health Consequences of such Addiction?, Addictology/Adiktologie, 2 (2023).
  • [9] C. Cesarano, Generalized Chebyshev polynomials, Hacettepe Journal of Mathematics and Statistics, 43(5) (2014), 731-740.
  • [10] H. Choi, I. Jung, and Y. Kang, Giving up smoking dynamic on adolescent nicotine dependence: a mathematical modeling approach, In: KSIAM 2011 Spring Conference, Daejeon, Korea (2011).
  • [11] Y. Chakir, Semi-analytical method for solving a model of the evolution of smoking habit using global rational approximants, International Journal of Dynamics and Control, 12(6) (2024), 1717-1727.
  • [12] G. Dattoli and C. Cesarano, On a new family of Hermite polynomials associated to parabolic cylinder functions, Applied Mathematics and Computation, 141(1) (2003), 143-149.
  • [13] Q. Din, M. Ozair, T. Hussain, and U. Saeed, Qualitative behavior of a smoking model, Advances in Difference Equations, (2016), 1-2.
  • [14] D. Gottlieb and S. A. Orszag, Numerical analysis of spectral methods: theory and applications, Society for Industrial and Applied Mathematics, (1977).
  • [15] C. C. Garsow, G. J. Salivia, and A. R. Herrera, Mathematical Models for the Dynamics of Tobacco use, recovery and relapse, Technical Report Series BU-1505-M. UK: Cornell University, (1997).
  • [16] I. Goldenberg, M. Jonas, A. Tenenbaum, V. Boyko, S. Matetzky, A. Shotan, S. Behar, and H. Reicher-Reiss, Bezafibrate Infarction Prevention Study Group, Current smoking, smoking cessation, and the risk of sudden cardiac death in patients with coronary artery disease, Archives of internal medicine, 163(19) (2003), 2301-2305.
  • [17] O. K. Ham, Stages and processes of smoking cessation among adolescents, Western Journal of Nursing Research, 29(3) (2007), 301-315.
  • [18] T. Hussain, A. U. Awan, K. A. Abro, M. Ozair, and M. Manzoor, A mathematical and parametric study of epidemiological smoking model: a deterministic stability and optimality for solutions, European Physical Journal Plus, 136 (2021), 1-23.
  • [19] M. M. Khader and A. H. Tedjani, Numerical simulation for the fractional-order smoking model using a spectral collocation method based on the Gegenbauer wavelet polynomials, Journal of Applied Analysis and Computation, 14(2) (2024), 847-863.
  • [20] S. Kumbinarasaiah and R. Yeshwanth, A numerical study of the evolution of smoking habit model through Haar wavelet technique, International Journal of Dynamics and Control, (2024), 1-19.
  • [21] A. L. Mojeeb and I. K. Adu, Modelling the dynamics of smoking epidemic, Journal of Advances in Mathematics and Computer Science, 25(5) (2017), 1-19.
  • [22] O. Sharomi and A. B. Gumel, Curtailing smoking dynamics a mathematical modeling approach, Applied Mathematics and Computation, 195(2) (2008), 475-499.
  • [23] J. M. Samet, Tobacco smoking: the leading cause of preventable disease worldwide, Thoracic Surgery Clinics, 23(2) (2013), 103-12.
  • [24] N. H. Shah, F. A. Thakkar, and B. M. Yeolekar, Stability analysis of tuberculosis due to smoking, Int J Innov Sci Res Technol, 3(1) (2018), 230-7.
  • [25] L. N. Trefethen, Spectral methods in MATLAB, Society for industrial and applied mathematics, (2000).
  • [26] S. Thirumalai, R. Seshadri, and S. Yuzbasi, Population dynamics between a prey and a predator using spectral collocation method, International Journal of Biomathematics, 12(05) (2019), 1950049.
  • [27] S. Thirumalai, R. Seshadri, and S. Yuzbasi, On the solution of the human immunodeficiency virus (HIV) infection model using spectral collocation method, International Journal of Biomathematics, 14(02) (2021), 2050074.
  • [28] S. Thirumalai, R. Seshadri, and S. Yuzbasi, Spectral collocation method based on special functins for solving nonlinear high-order pantograph equations, Computational Methods for Differential Equations, 11(3) (2023), 589- 604.
  • [29] G. Ur Rahman, R. P. Agarwal, and Q. Din, Mathematical analysis of giving up smoking model via harmonic mean type incidence rate, Applied Mathematics and Computation, 354 (2019), 128-48.
  • [30] World Health Organization. Tobacco control for sustainable development, World Health Organization, Regional Office for South-East Asia, (2017).
  • [31] R. West, Tobacco smoking: Health impact, prevalence, correlates and interventions, Psychology and health, 32(8) (2017), 1018-1036.
  • [32] G. Zaman, Qualitative behavior of giving up smoking models, Bulletin of the Malaysian Mathematical Sciences Society, Second Series 34(2) (2011), 403-415.
  • [33] G. Zaman, Optimal campaign in the smoking dynamics, Computational and Mathematical Methods in Medicine, 1 (2011), 163834.
  • [34] A. Zeb, G. Zaman, and S. Momani, Square-root dynamics of a giving up smoking model, Applied Mathematical Modelling, 37(7) (2013), 5326-34.
  • [35] Z. Zhang, J. Zou, R. K. Upadhyay, and A. Pratap, Stability and Hopf bifurcation analysis of a delayed tobacco smoking model containing snuffing class, Advances in Difference Equations, 349 (2020), 1-19.
  • [36] A. Zeb and A. Alzahrani, Non-standard finite difference scheme and analysis of smoking model with reversion class, Results in Physics, 21 (2021), 103785.
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