Article Sidebar

Submitted
Dec 28, 2021
Published
Dec 30, 2021
Download
PDF
Statistic
Read Counter : 0 Download : 0

Main Article Content

Abstract

Smoking is a habit that is favored by some people, but smoking causes health, economic, social and environmental burdens not only for smokers but also for others. This study aims to determine the mathematical model of the number of smokers, analysis of the equilibrium point of the PLSQ mathematical model of the number of smokers and a simulation of the mathematical model of the PLSQ of the number of smokers. In this study, the researcher assumed that the current smoker had a death rate caused by smoking and that the former smoker after he recovered, would not return to smoking. The results obtained are the PLSQ mathematical model of the number of smokers which produces 1 (one) smoke-free equilibrium point and 1 (one) smoker endemic point from the model. The stability analysis of the model was carried out using the Routh-Hurwitz Criteria to identify the characteristics of the eigenvalues. From the results of the stability analysis, it was found that the smoker-free equilibrium point E0 and the smokers endemic equilibrium point E1 were stable if the condition for the relationship between parameters were met. At the end of the study, a simulation model was given using the Maple application

Keywords

Routh- Hurwitz criteria, mathematical model, equilibrium point

Article Details

References

  1. Aditama. 2015. Masalah Merokok dan Penanggulangannya, Ikatan Dokter Indonesia, Jakarta.
  2. Akbar, A, H. 2018. Hubungan Antara Kebiasaan Merokok Dengan Daya Tahan Kardiorespirasi Pada Mahasiswa Perokok Di Program Studi Ilmi Keperawatan Universitas Muhammadiyah Malang. skripsi. Malang: Universitas Muhammadiyah Malang.
  3. Alkhudhari, Z, dkk. 2014. Global Dynamics of a Mathematical Model on Smoking. ISRN Applied Mathematics. 1-7.
  4. Ani, A & Embay, R. 2019. Pengembangan Model Matematika Dinamika Perokok Di Kota Bogor, Kubik, Vol. No. 1 Edisi Mei 2019.
  5. Anton, H. 1997. Alajabar Linear Elementer, Edisi Kelima, terjemahan, Jakarta, Erlangga
  6. Aswan. 2018. perbatasan dinamika merokok dengan menggunakan pendekatan model matematika, skripsi. Makassar: Universitas Islam Negeri.
  7. Asyabah, Z, dkk. 2018. Pemodelan SIR untuk penyebaran penyakit pertusis dengan vaksinasi pada populasi manusia konstan, UNNES Journal of Mathematics, No.1, Vol.7, 96-107. https://journal.unnes.ac.id/sju/index.php/ujm/article/view/11878.
  8. Budiman. 2016. Efektivitas Hypnoterapi Teknik Anctor Terhadap Perubahan Perilaku Merokok Remaja, Palembang, PSIKIS Jurnal Psikologi Islam Vol. 2 No. 2135-148.
  9. Driesche, P.v.d & Watmough, J. 2002. Reproduction Number and Sub Threshold Endemic Equilibria for Compartmental Models of Diseases Transmission, Mathematical Bioscience, 180:29-48.
  10. Fidelis, N, Z, dkk. 2020. Analisis Kestabilan Model Matematika Jumlah Perokok Pengaruh Kenaikan Harga Rokok Dengan Dianamika Akar Kuadrat, E-Jurnal Matematika Vol. 9(4), November, pp 283-287.
  11. Fitri, S, N, dkk, 2017. Terapi Pengganti Nikotin Sebagai Upaya Menghentikan Kebiasaan Merokok, Lampung, Majority, Vol. 6 No. 3, juli, 158.
  12. Indrawati, I. 2012. Analisis Dinamik Kestabilan Dari Model SIR Dengan Perlambatan Waktu. Skripi. Malang: Universitas Islam Negeri Maulana Malik Ibrahim.
  13. Juliah, I. 2015. Analisis kestabilan Titik Kesetimbangan Model Matematika Proses Transmisi Virus Dengue di dalam Tubuh Manusia dengan Terapi Obat Herbal. Skripsi. Semarang: Universitas Negeri Semarang.
  14. Kocak, H. & J. H. Hole. 1991, Dynamic and Bifurcation, spiringer – Verlag, New York.
  15. Mindo, T, R. 2020. Kegiatan Promosi Kesehatan Bahaya Merokok Di SMK SWK Swasta Mandiri Percut Sei Tuan. jurnal abdimas Mutiara. Vol. 1, No, 1, Maret.
  16. Olsder, G. J dkk. 2004. Mathematical Systems Theory, Netherland, VVSD.
  17. Perko, L, 1991, Diferential Equation and Dynamikal system. Spinger-Verlag Berlin Heidelberg, New York.
  18. Rsyka, A, N, A, 2018, Hubungan Antara Kebiasaan Merokok dan Tingkat Keparahan Penyakit Paru Obstruktif Kronik. Skripsi. Makassar: Universitas Muhammadiyah Makassar.
  19. Ross, L, 1984, Diferensial Equations, Ed.3, springer, New York.
  20. Sharomi, O. & Gumel, A, B. 2008. Curtailing Smoking Dynamics A Mathematical Modeling Approach. Applied Mathematics and coputation. Hal 475-499.
  21. Side. S, dkk. 2016. Analisis Dan Simulasi Model SITR Pada Penyebaran Penyakit Tuberkolosis di Kota Makassar. Jurnal Sainsmat. No. 2, Vol. 5, 191-204.
  22. Soleh, M. Sazmita, D. 2017. Model matematika jumlah perokok dengan dinamika akar kuadrat dan faktor migrasi, Seminar Nasional Teknologi Informasi, Komunikasi dan Industri (SNTIK) 9, pekanbaru, 18–19 Mei.
  23. Wahab, W & Subiantoro, A. 2017, Fundamental of Control System Stability Criterion-Routh Hurwitz,
  24. Widowati, s. 2007. Buku ajar pemodelan matematika. Semarang: Universitas Diponegoro.
  25. Yuliani, S, R, B, N. 2016. Analisis Penyebaran Penyakit Diare Sebagai Salah Satu Penyebab Kematian Balita Menggunakan Model Matematika SIS. Jurnal Matematika-SI. 5 (6), 2016