DOI: https://doi.org/10.14710/jfma.v9i1.28574

OPTIMAL CONTROL MODEL OF DIVORCE DYNAMICS BY POST-MARRIAGE EDUCATION AND COUNSELING

*Bunga Noer Intan Permatasari  -  Department of Mathematics, State Islamic University Walisongo, Jl. Prof. Hamka, Nglaiyan, Semarang City, Indonesia 50185, Indonesia
Zulaikha Zulaikha orcid scopus  -  Department of Mathematics, State Islamic University Walisongo, Jl. Prof. Hamka, Nglaiyan, Semarang City, Indonesia 50185, Indonesia

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Abstract

Divorce is a complex social phenomenon with various causes, including in-
compatibility between partners, poor communication, economic issues, and infidelity.
This research was conducted by modifying the SMBD model with the addition of the
Healthy Marriage (H) and Unhealthy Marriage (Uh) subpopulations, adapted from the
MHUCKD model, and considering controls in the form of post-marriage education and
counseling, resulting in the SMHUhD model. The purpose of implementing controls is
to minimize the Unhealthy Marriage (Uh) and Divorce (D) subpopulations, as well as
the intervention costs correlated with post-marriage education and counseling. The op-
timal control condition is obtained by applying the Pontryagin’s Maximum Principle.
Next, a numerical simulation was conducted using the 4th-order Runge-Kutta method
with the Forward-Backward Sweep Method approach, where the state equations were
solved using a forward step and the costate equations were solved using a backward
step. The research results show that educational control and counseling, when given
together, can minimize the occurrence of divorce.

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Keywords: Mathematical Model, Divorce, Optimal Control, Post-marital Education, Counseling.

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Section: FUNDAMENTAL MATHEMATICS AND APPLICATIONS
Language : EN
  1. M. S. Aulana et al., “Perceraian di Indonesia Ditinjau dalam Persfektif Hukum Islam yang
  2. Berlaku,” Jurnal Kajian Agama dan Dakwah, vol. 4, no. 1, pp. 1-8, 2024
  3. Abdurrahman, Kompilasi Hukum Islam di Indonesia. Jakarta: Akademika Press, 2014
  4. Z. Ali, Hukum Perdata Islam di Indonesia. Jakarta: Sinar Grafika, 2006
  5. Indonesia, Kompilasi Hukum Islam. Jakarta: Departemen Agama Republik Indonesia,
  7. Badan Pusat Statistik Jawa Tengah, Provinsi Jawa Tengah dalam Angka (Jawa Tengah
  8. Province in Figures 2023). Jawa Tengah: BPS, 2023
  9. M. Z. Ndii, Pemodelan Matematika Dinamika Populasi dan Penyebaran Penyakit. Yo-
  10. gyakarta: Deepublish, 2018
  11. I. Kurniawati and A. H. Rosyidi, “Profil Pemodelan Matematika Siswa SMP dalam
  12. Menyelesaikan Masalah pada Fungsi Linear,” Jurnal Ilmiah Pendidikan Matematika, vol
  13. , no. 2, pp. 174–180, 2019
  14. P. Saraswati, Mardlijah, and Kamiran, “Analisis dan Kontrol Optimal Sistem Gerak Sateli
  15. Menggunakan Prinsip Minimum Pontryagin,” Jurnal Sains dan Seni ITS, vol. 6, no. 2, pp
  16. -50, 2017
  17. Zulaikha, Trisilowati, and I. Fadhilah, “Kontrol Optimal pada Model Epidemi SEIQR den-
  18. gan Tingkat Kejadian Standar,” Prosiding SI MaNIs (Seminar Nasional Integrasi Matem-
  19. atika dan Nilai Islami), vol. 1, no. 1, pp. 41–51, 2017
  20. Y. Norasia et al., “Optimal Control of HIV-1 Spread in Combination with Nutritional
  21. Status and ARV-Treatment,” International Journal of Computing Science and Applied,
  22. vol. 8, no. 2, pp. 66-70, 2022
  23. D. Mahardika, R. H. Tjahjana, and Sunarsih, “Optimal Control of COVID-19 Outbreak,”
  24. Journal of Fundamental Mathematics and Applications (JFMA), vol. 3, no. 2, pp. 158-
  25. , 2020
  26. A. Nabila, D. Satryo, S. Maida, and S. Nadhira, “Pembinaan Pasca Pernikahan dalam
  27. Meminimalisir Kasus Perceraian di Indonesia,” Indonesian Gender and Society Journal,
  28. vol. 5, no. 1, pp. 8-13, 2024
  29. J. Andriyani, “Konsep Konseling Individual dalam Proses Penyelesaian Perselisihan
  30. Keluarga,” Jurnal At-Taujih, vol. 1, no. 1, pp. 17-29, 2018
  31. A. Hugo and E. M. Lusekelo, “Mathematical Control of Divorce Stress Among Mar-
  32. riages,” International Journal of Statistics and Applied Mathemathics, vol. 6, no. 5, pp
  33. -135, 2021
  34. H. Tessema, I. Haruna, S. Osman, and E. Kassa, “A Mathematical Model Analysis of
  35. Marriage Divorce,” Journal Communications in Mathematical Biology and Neuroscience,
  36. vol. 2022, no. 15, pp. 1–18, 2022
  37. M.A. Hasan, Pedoman Hidup Berumah Tangga dalam Islam. Jakarta: Prenada Media,
  39. A. Murtadho, Konseling Perkawinan (Perspektif Agama-Agama). Semarang: Walisongo
  40. Press, 2009
  41. W. H. Fleming and R. W. Rishel, Deterministic and Stochastic Optimal Control. New York: Springer-Verlag, 1975

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