Model Epidemi SIR Pengguna/Pemain Mobile Games Pada Mahasiswa Fakultas Matematika dan Ilmu Pengetahuan Alam Universitas Sulawesi Barat
DOI:
https://doi.org/10.31605/jomta.v2i2.1185Keywords:
ekuilibrium, mobile games, model epidemiAbstract
Game saat ini berkembang sangat pesat, tidak hanya sebagai hiburan bahkan game kini banyak yang diperlombakan. Game semakin mudah untuk diakses oleh berbagai kalangan umur sejak munculnya mobile games pada era mobile phone seperti sekarang. Oleh karena itu, pada skripsi ini penulis menganalisis model matematika epidemi untuk pemain/pengguna mobile games. Model epidemi umumnya digunakan untuk melihat fenomena penyebaran suatu penyakit. Pada penelitian ini, penulis membangun model epidemi SIR untuk pengguna/pemain mobile games Mahasiswa FMIPA Unsulbar, kemudian titik kesetimbangan model tersebut yaitu E(192,0) dan bersifat stabil, serta bilangan reproduksi dasar sebesar 0,51 yang menunjukkan bahwa tidak akan terjadi endemik dan penyakit akan menghilang secara perlahan seiring berjalannya waktu. Untuk simulasi model, penulis menggunakan program maple
References
[1] Ariesy, D.E., 2018, Pemodelan penyebaran pengguna narkoba, Jurnal Matematika UNAND, No.3, Vol.7, 21-26, :http://jmua.fmipa.unand.ac.id/index.php/jmua/article/download/365/350.
[2] Asyabah, Z., Waluya, S.B., Kharis, M., 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.
[3] Campbell, S. L., and Haberman, R., 2008, Introduction to Differential Equations with Dynamical System, Princeton University Press, New Jersey.
[4] Driessche and Watmough, 2002, Reproduction numbers and sub thresholdendemic equilibria for compartmental models of disease transmission, Mathematical Biosciences, Vol. 180, 29–48
[5] Farlow, S. J., 1994. An Introduction to Differential Equations and Their Applications, Mc. Graw-Hill, Inc.
[6] Haberman, R., 1997, Mathematical Models An Introduction to Applied Mathematics, Prentice-Hall, New Jersey.
[7] Hahn, 1967, Stability of Motion, Springer-Verlag, New York.
[8] Harko, T., Lobo, F.S.N., Mak, M.K., 2014, Exact analytical solutions of the Susceptible-Infected-Recovered (SIR) epidemic model and of the SIR model with equal death and birth rates, Applied Mathematics and Computation, https://www.researchgate.net/publication/260679051_Exact_analytical_solutions_of_the_Susceptible-Infected-Recovered_SIR_epidemic_model_and_of_the_SIR_model_with_equal_death_and_birth_rates/link/5b8cc2c54585151fd14479a9/download
[9] Jaya, E.S., 2018, WHO Tetapkan Kecanduan Game sebagai Gangguan Mental, Bagaimana Gamer Indonesia Bisa Sembuh?, http://theconversation.com/who-tetapkan-kecanduan-game-sebagai-gangguan-mental-bagaimana-gamer-indonesia-bisa-sembuh-99029, diakses tgl 20 Februari 2020
[10] Kocak, H. & J.K. Hole, 1991, Dynamic and Bifurcation, Springer – Verlag, New York.
[11] Murray, J. D., 2002, Mathematical Biologi An Introduction. Third edition, Springer-Verlag, New York Berlin Heidelberg.
[12] Olsder, G. J. & Woude, J.W. van der, 2004, Mathematical Systems Theory, Netherland: VVSD.
[13] Pratama, W., 2014, Game adventure misteri kotak Pandora, Jurnal Telematika, No.2, Vol.7, 13-31, :
http://ejournal.amikompurwokerto.ac.id/index.php/telematika/article/view/247.
[14] Ross, L., 1984, Differential Equations, Ed.3, Springer, New York.
[15] Tjolleng, A., Komalig, H.A.H., Prang, J.D., 2016, Dinamika perkembangan HIVV/AIDS di Sulawesi Utara menggunakan model persamaan diferensial onlinear SIR, Jurnal Ilmiah Sains, No.1, Vol.13, 9-14, : https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=9&cad=rja&uact=8&ved=2ahUKEwifyf7c4q7mAhWQ6nMBHQITDSsQFjAIegQIChAB&url=https%3A%2F%2Fwww.researchgate.net%2Fpublication%2F303008134_Dinamika_Perkembangan_HIVAIDS_di_Sulawesi_Utara_Menggunakan_Model_Persamaan_Diferensial_Nonlinear_SIR_Susceptible_Infectious_Recovered&usg=AOvVaw1_k6O8Xdmm03YrBKh1jzUP
[17] Tridhonanto, A., 2011, Optimalkan Potensi Anak Dengan Game, Elex Media Komputindo, Jakarta.
[18] Wibowo, A. 2017, Ada 4 Jenis dan 11 Genre Game, yang Mana Favorit Kamu?, https://www.google.com/amp/s/www.pricebook.co.id/article/review/2016/01/26/3593/amp/ada-4-jenis-dan-11-genre-game-yang-mana-favorit-kamu, diakses tgl 20 Februari 2020.
[19] Widowati & Sutimin, 2007, Buku ajar pemodelan matematika, Semarang: Universitas Diponegoro
[2] Asyabah, Z., Waluya, S.B., Kharis, M., 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.
[3] Campbell, S. L., and Haberman, R., 2008, Introduction to Differential Equations with Dynamical System, Princeton University Press, New Jersey.
[4] Driessche and Watmough, 2002, Reproduction numbers and sub thresholdendemic equilibria for compartmental models of disease transmission, Mathematical Biosciences, Vol. 180, 29–48
[5] Farlow, S. J., 1994. An Introduction to Differential Equations and Their Applications, Mc. Graw-Hill, Inc.
[6] Haberman, R., 1997, Mathematical Models An Introduction to Applied Mathematics, Prentice-Hall, New Jersey.
[7] Hahn, 1967, Stability of Motion, Springer-Verlag, New York.
[8] Harko, T., Lobo, F.S.N., Mak, M.K., 2014, Exact analytical solutions of the Susceptible-Infected-Recovered (SIR) epidemic model and of the SIR model with equal death and birth rates, Applied Mathematics and Computation, https://www.researchgate.net/publication/260679051_Exact_analytical_solutions_of_the_Susceptible-Infected-Recovered_SIR_epidemic_model_and_of_the_SIR_model_with_equal_death_and_birth_rates/link/5b8cc2c54585151fd14479a9/download
[9] Jaya, E.S., 2018, WHO Tetapkan Kecanduan Game sebagai Gangguan Mental, Bagaimana Gamer Indonesia Bisa Sembuh?, http://theconversation.com/who-tetapkan-kecanduan-game-sebagai-gangguan-mental-bagaimana-gamer-indonesia-bisa-sembuh-99029, diakses tgl 20 Februari 2020
[10] Kocak, H. & J.K. Hole, 1991, Dynamic and Bifurcation, Springer – Verlag, New York.
[11] Murray, J. D., 2002, Mathematical Biologi An Introduction. Third edition, Springer-Verlag, New York Berlin Heidelberg.
[12] Olsder, G. J. & Woude, J.W. van der, 2004, Mathematical Systems Theory, Netherland: VVSD.
[13] Pratama, W., 2014, Game adventure misteri kotak Pandora, Jurnal Telematika, No.2, Vol.7, 13-31, :
http://ejournal.amikompurwokerto.ac.id/index.php/telematika/article/view/247.
[14] Ross, L., 1984, Differential Equations, Ed.3, Springer, New York.
[15] Tjolleng, A., Komalig, H.A.H., Prang, J.D., 2016, Dinamika perkembangan HIVV/AIDS di Sulawesi Utara menggunakan model persamaan diferensial onlinear SIR, Jurnal Ilmiah Sains, No.1, Vol.13, 9-14, : https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=9&cad=rja&uact=8&ved=2ahUKEwifyf7c4q7mAhWQ6nMBHQITDSsQFjAIegQIChAB&url=https%3A%2F%2Fwww.researchgate.net%2Fpublication%2F303008134_Dinamika_Perkembangan_HIVAIDS_di_Sulawesi_Utara_Menggunakan_Model_Persamaan_Diferensial_Nonlinear_SIR_Susceptible_Infectious_Recovered&usg=AOvVaw1_k6O8Xdmm03YrBKh1jzUP
[17] Tridhonanto, A., 2011, Optimalkan Potensi Anak Dengan Game, Elex Media Komputindo, Jakarta.
[18] Wibowo, A. 2017, Ada 4 Jenis dan 11 Genre Game, yang Mana Favorit Kamu?, https://www.google.com/amp/s/www.pricebook.co.id/article/review/2016/01/26/3593/amp/ada-4-jenis-dan-11-genre-game-yang-mana-favorit-kamu, diakses tgl 20 Februari 2020.
[19] Widowati & Sutimin, 2007, Buku ajar pemodelan matematika, Semarang: Universitas Diponegoro
Published
2021-09-20
Issue
Section
Articles
