ANALISIS KESTABILAN MODEL DINAMIKA PERCERAIAN MVQEDR
DOI:
https://doi.org/10.25077/jmua.13.4.358-372.2024Keywords:
cerai, model matematika, simulasi numerikAbstract
Tiga faktor penyebab perceraian, yaitu masalah ekonomi rumah tangga, perselisihan dan pertengkaran terus- menerus, dan kekerasan dalam rumah tangga, masih memberikan kontribusi besar terhadap angka perceraian di Indonesia. Meskipun pemerintah telah melakukan upaya penyuluhan bagi ketiga kelompok rumah tangga tersebut, namun pada kenyataannya kasus perceraian tidak kunjung berkurang. Oleh karena itu, perlu diketahui secara pasti seberapa besar pengaruh penyuluhan yang telah dilaksanakan oleh pemerintah terhadap kelompok ini. Pada penelitian ini, model matematika MVQEDR terlebih dahulu dibangun. Analisis kestabilan titik ekuilibrium model dilakukan dengan menentukan nilai eigen dan matriks Jacobian dan diperoleh bahwa titik ekuilibrium bebas perceraian stabil asimtotik jika R0 = 0, 003111368984 < 1 dan titik ekuilibrium endemik tidak stabil asimtotik jika R0 = 1, 065035325 > 1. Simulasi numerik dilakukan dengan menggunakan perangkat lunak MAPLE.References
Gweryina, R. I., Kaduna, F. S., dan Kura, M. Y, 2021, Qualitative Analysis of A Mathematical Model of Divorce Epidemic with Anti-Divorce Therapy, Engineering and Applied Science Letters, Volume : 4(2).
Badan Pusat Statistik (2024), â€Statistik Indonesia 2024â€,Tersedia:
https://www.bps.go.id/id/publication/2024/02/28/c1bacde03256343b2bf769b0/statistik-indonesia-2024.html, Diakses pada tanggal 23 Mei 2024.
Purnamasari, I. A, 2019, Layanan Bimbingan Konseling Keluarga untuk Meminimalisasi Angka Perceraian, Irsyad: Jurnal Bimbingan, Penyuluhan, Konseling, dan Psikoterapi Islam, Volume : 7(1).
Gambrah, P. P., Abdul-Rahaman, A. S., dan Adu, A, 2018, Mathematical Model for Minimizing Divorce Through Counseling, International Journal of Statistics and Applied Mathematics, Volume : 3(3).
Tessema, H., Haruna, I., Osman, S., dan Kassa, E,2022, A Mathematical Model Analysis of Marriage Divorce, Commun. Math. Biol. Neurosci, Volume : 2022.
O. Diekmann, J. Heesterbeek, dan M. G. Roberts, 2010, The Construction of Next-Generation Matrices for Compartmental Epidemic Models, Journal of The Royal Society Interface, Volume : 7.
E. Hendricks, O. Jannerup, dan P. H. Sørensen, 2008, Linear Systems Control: Deterministic and Stochastic Methods, Springer.
Lynch, S, 2007, Dynamical Systems with Applications using Mathematica, Boston, Birkhauser.
Bahri S, Pratama EA., 2023, Pemodelan Dinamika Pejudi Muda. MES:
Journal of Mathematics Education and Science, Volume : 9(1).
Diekmann, O., Heesterbeek, J. A. P., dan Metz, J. A. J, 1990, On the
Definition and The Computation of The Basic Reproduction Ratio R0 in
Models for Infectious Diseases in Heterogeneous Populations, Journal of Mathematical Biology, Volume : 28.
Bahri, S., Ningsih, S. A., dan Narwen, N, 2023, Kestabilan Model Penularan Penyakit Malaria di Indonesia, Delta-Pi: Jurnal Matematika dan Pendidikan Matematika, Volume : 12(2).
Diekmann, O., Heesterbeek, J. A. P., dan Roberts, M. G, 2010, The Construction of Next-Generation Matrices for Compartmental Epidemic Models, Journal of The Royal Society Interface, Volume : 7(47)
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- Grafik Subpopulasi V (R0>1)
- Grafik Perbandingan dengan Konseling dan Tanpa Konseling Subpopulasi R
- Grafik Perbandingan dengan Konseling dan Tanpa Konseling Subpopulasi D
- Grafik Perbandingan dengan Konseling dan Tanpa Konseling Subpopulasi E
- Grafik Perbandingan dengan Konseling dan Tanpa Konseling Subpopulasi Q
- Grafik Perbandingan dengan Konseling dan Tanpa Konseling Subpopulasi V
- Grafik Perbandingan dengan Konseling dan Tanpa Konseling Subpopulasi M
- Grafik Subpopulasi R (R0>1)
- Grafik Subpopulasi D (R0>1)
- Grafik Subpopulasi E (R0>1)
- Grafik Subpopulasi Q (R0>1)
- Grafik Subpopulasi M (R0>1)
- Grafik Subpopulasi R (R0<1)
- Grafik Subpopulasi D (R0<1)
- Grafik Subpopulasi E (R0<1)
- Grafik Subpopulasi Q (R0<1)
- Grafik Subpopulasi V (R0<1)
- Grafik Subpopulasi M (R0<1)
- Bagan Model MVQEDR
- ANALISIS KESTABILAN MODEL DINAMIKA PERCERAIAN MVQEDR
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