Application of the 4th Order Runge Kutta Method in Smoking Dynamics Modelling
DOI:
https://doi.org/10.64570/jamm.v1i1.7Keywords:
Equilibrium point, mathematical model, numerical method, runge kutta, smoking dynamicsAbstract
The dynamics of smoking is a problem that has captured the world's attention both in health and social life issues. In modeling, the rate of change in smoking dynamics, there are four populations that affect each other, namely potential smokers (P), light smokers (S), heavy smokers (T) and smokers who have quit smoking (Q). Two equilibrium points were obtained, namely which describes the smoking point, and which describes the non-smoking point. The results of numerical simulations on the model show that the absence of interaction between the potential population of smokers (P) and the population of light smokers (S) results in a decrease in the rate of change in the population of light smokers (S). Meanwhile, the interaction between the potential smoker population (P) and the light smoker population (S) resulted in an increase in the rate of change in the light smoker population (S). So, to limit the growth of the number of light smokers, it is necessary to limit the interaction between the potential population of smokers (P) and the population of light smokers (S).
References
Anita, D. C., Afiati, E., Wibowi, B. Y., 2022. Profile of Student Smoking Behavior and Its Implications for Guidance and Counseling Services.Proffesional, Empty, Islamic Counselling Journal- Vol.5, No.1
Krispiani, Zora. 2015. The Relationship of Self-Concept of Smoking Behavior in Late Adolescence. Syarif Hidayatullah State Islamic University.
Kumboyono. 2011. Analysis of Inhibiting Factors of Motivation to Quit Smoking Based on Health Belief Model in Students of F.T. UNIBRAW Malang. Soedirman Nursing Journal, Vol 6, No 1.
Lestari, S. M., Yulida, Y., Lestia, A. S., & Karim, M. A. (2021, November). Stability analysis of a smoking behavior model. In Journal of Physics: Conference Series (Vol. 2106, No. 1, p. 012025). IOP Publishing.
Marwan and Said Munzir. 2011. Differential Equations, Yogyakarta: Graha Ilmu. Pamuntjak, R.J. and Santoso Widiarti. 1990. Ordinary Differential Equations. ITB : Bandung
Perco, L. 1991. Differenstial Equation and Dynamical System. New York: Springer-Verlag Berlin Heidelberg.
Purcell, J Edwin and Varberg Dale. 1999. Calculus and Analytical Geometry. Jakarta: Erlangga. Son, B. 2013. The relationship between smoking intensity and isomnia levels. Journal of the Department Physics of the University of Semarang.
Riadi, Riyo, Evi Noviani and Meliana Pasaribu. 2022.Square Root Dynamics in Mathematical Modeling Population Smokers. FMIPA Tanjungpura University. https://jurnal.untan.ac.id/index.php/jbmstr/article/download/53267/75676592494
Samsir, Andi Utari, Syamsudin Toaha and Kasbawati. 2021. Optimal control of the mathematical model of smoking with smokers quitting and smokers quitting permanently. Mathematics journal, statistics and komputasi FMIPA-UNHAS. https://journal.lppmunindra.ac.id/index.php/STRING/article/download/1734/1348
Singh, H., Baleanu, D., Singh, J., & Dutta, H. (2021). Computational study of fractional order smoking model. Chaos, Solitons & Fractals, 142, 110440.
Toaha, Syamsudin. 2013. Mathematical Modeling in Population Dynamics. Two Press: Makasar Pagay, Usman. 2009. Mathematical modelling. Uin-Malang Press
WHO. 2009. State of The World Vaccines and Immunization. Third Edition. Switzerland.
Wijayanti, H.Sri setyaningsih. Mahardika Wati. 2011. The runge kutta method in the completion of the transport network. Scientific journal of basic and environmental sciences. Vol. 11, No. 2
Yuliani, S.R. 2016. Analysis of the spread of diarrheal disease as one of the causes of death in toddlers using the sis mathematical model. Journal of applied mathematical studies. Vol. 5, No. 6
Zeb, A., Kumar, S., & Saeed, T. (2022). A robust computational dynamics of fractional-order smoking model with relapse habit. Fractals, 30(01), 2240034.
