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All Journal Media Statistika JURNAL MATEMATIKA STATISTIKA DAN KOMPUTASI Edumatsains AKSIOMA BAREKENG: Jurnal Ilmu Matematika dan Terapan Jurnal Pengabdian Masyarakat Bumi Raflesia InPrime: Indonesian Journal Of Pure And Applied Mathematics Journal of Midwifery Jurnal Kesehatan Tambusai Griya Journal of Mathematics Education and Application Bulletin of Applied Mathematics and Mathematics Education Indonesian Journal of Community Empowerment and Service J-KOMA : Jurnal Ilmu Komputer dan Aplikasi Journal of Statistics and Data Science Journal for Quality in Women's Health
Ramya Rachmawati
Jurusan Matematika Fakultas Matematika Dan Ilmu Pengetahuan Alam Universitas Bengkulu
Agriculture, Biological Sciences & Forestry Humanities Chemistry Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Dentistry Economics, Econometrics & Finance Education Energy Engineering Health Professions Languange, Linguistic, Communication & Media Mathematics Mechanical Engineering Medicine & Pharmacology Nursing Physics Public Health Social Sciences Transportation Other

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Mathematical Model of Social Media Addiction: An Optimal Control Approach Ratna Widayati; Intrada Reviladi; Nur Afandi; Ramya Rachmawati
Bulletin of Applied Mathematics and Mathematics Education Vol. 5 No. 2 (2025)
Publisher : Universitas Ahmad Dahlan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12928/bamme.v5i2.14795

Abstract

In this study, we developed a deterministic mathematical model to analyze social media addiction, incorporating an optimal control strategy. The basic model captures the dynamics through which individuals become exposed to and eventually addicted to social media platforms. To enhance the model, we introduced two time-dependent control variables: one representing awareness campaigns through advertising and education, and the other representing treatment interventions for individuals suffering from addiction. An optimal control framework was then formulated based on these interventions. By applying Pontryagin’s Minimum Principle, we derived the necessary conditions for optimality and constructed the corresponding optimality system. Numerical simulations of the optimal control problem were conducted using the forward-backward sweep method to assess the effectiveness of the proposed strategies. The results demonstrate that the integrated control strategy—combining public awareness efforts with treatment interventions— substantially reduces the number of individuals exposed to and addicted to social media. Compared to scenarios without intervention, the number of affected individuals was significantly lower. These findings underscore the importance of implementing combined strategies rather than isolated measures. Therefore, this integrated approach is strongly recommended for policymakers and stakeholders as a practical and effective means to mitigate the adverse effects of social media addiction on public health and societal well-being.. Keywords: Social Media Addiction, Mathematical Model, Pontryagin Minimum Principle, Optimal Control.
Optimal Control Analysis of a Human-Animal Nipah Virus Transmission Model Ratna Widayati; Ramya Rachmawati; Yulian Fauzi; Septri Damayanti; Arlin Marsyanda
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol. 8 No. 1 (2026)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15408/inprime.v8i1.49631

Abstract

This study proposes a novel multi-host SIRS optimal control model for Nipah virus transmission involving bats, pigs, and humans, extending classical SIR/SEIR frameworks by explicitly incorporating cross-species transmission, reinfection, and heterogeneous contact pathways supported by ecological evidence. Unlike uncontrolled epidemic models, the proposed framework integrates three time-dependent interventions: infected-pig culling, human–animal protective measures, and isolation of infected humans, allowing simultaneous evaluation of epidemiological impact and implementation cost. The existence of an optimal control set is established, and Pontryagin’s Maximum Principle is applied to derive the necessary optimality system. Numerical simulations show that coordinated interventions substantially outperform no-control scenarios. The peak number of infected humans decreases from more than 650,000 to approximately 70,000, while the peak number of infected pigs declines from over 68,000 to about 16,000. Control trajectories indicate that strong early implementation of all measures is the most effective strategy, followed by gradual relaxation as prevalence declines, leading to more efficient resource allocation over time. Compared with classical single-host SIR/SEIR models, the proposed model better captures interspecies spillover dynamics and enables evaluation of integrated response policies that cannot be represented in simpler frameworks. These findings demonstrate the importance of coordinated multi-component strategies for mitigating Nipah outbreaks across interacting host populations. A limitation of this study is the use of assumed parameter values in several transmission processes; future work may incorporate data-driven calibration, stochastic effects, spatial mobility, and uncertainty analysis to improve predictive accuracy. AbstrakPenelitian ini mengusulkan model optimal kontrol SIRS multi-host yang baru untuk penularan virus Nipah yang melibatkan kelelawar, babi, dan manusia, sebagai pengembangan dari kerangka klasik SIR/SEIR dengan secara eksplisit memasukkan penularan antarspesies, reinfeksi, serta jalur kontak heterogen yang didukung oleh bukti ekologis. Berbeda dengan model epidemi tanpa kontrol, kerangka yang diusulkan mengintegrasikan tiga intervensi bergantung waktu, yaitu pemusnahan babi terinfeksi, tindakan perlindungan manusia–hewan, dan isolasi manusia terinfeksi, sehingga memungkinkan evaluasi simultan terhadap dampak epidemiologis dan biaya implementasi. Keberadaan himpunan kontrol optimal dibuktikan, dan Prinsip Maksimum Pontryagin diterapkan untuk menurunkan sistem syarat optimalitas yang diperlukan. Simulasi numerik menunjukkan bahwa intervensi terkoordinasi secara signifikan lebih unggul dibandingkan skenario tanpa kontrol. Puncak jumlah manusia terinfeksi menurun dari lebih dari 650.000 menjadi sekitar 70.000, sedangkan puncak babi terinfeksi turun dari lebih dari 68.000 menjadi sekitar 16.000. Profil kontrol menunjukkan bahwa penerapan kuat pada tahap awal untuk seluruh tindakan merupakan strategi paling efektif, kemudian dikurangi secara bertahap seiring menurunnya prevalensi sehingga menghasilkan alokasi sumber daya yang lebih efisien dari waktu ke waktu. Dibandingkan model klasik SIR/SEIR satu-host, model yang diusulkan lebih mampu menggambarkan dinamika spillover antarspesies serta mengevaluasi kebijakan respons terpadu yang tidak dapat direpresentasikan pada model yang lebih sederhana. Temuan ini menegaskan pentingnya strategi multi-komponen yang terkoordinasi dalam mitigasi wabah Nipah pada populasi host yang saling berinteraksi. Keterbatasan penelitian ini adalah penggunaan beberapa nilai parameter asumsi pada proses transmisi tertentu; penelitian selanjutnya dapat memasukkan kalibrasi berbasis data, efek stokastik, mobilitas spasial, dan analisis ketidakpastian untuk meningkatkan akurasi prediksi.Kata Kunci: Penularan antarspesies; Nipah virus; Kontrol optimal; Dinamika populasi; Model SIRS. 2020MSC: 49J15
“Data-Driven Decision Making”: Pengenalan Statistika dan Pemanfaatannya di SMA IT Iqra Kota Bengkulu Firdaus; Ramya Rachmawati; Nurul Hidayati; Septri Damayanti; Siska Yosmar
Jurnal Pengabdian Masyarakat Bumi Rafflesia Vol. 8 No. 1 (2025): APRIL: Jurnal Pengabdian Kepada Masyarakat Bumi Raflesia
Publisher : Universitas Muhammadiyah Bengkulu

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

Kemampuan mengambil keputusan yang baik merupakan kebutuhan esensial bagi siswa. Terdapat banyak metode dalam mengambil keputusan, salah satunya adalah Data-Driven Decision Making, yaitu pengambilan keputusan berdasarkan analisis data. Pentingnya peran data dalam menentukan pengambilan keputusan berdasarkan data belum utuh dipahami oleh siswa SMA IT Iqra Kota Bengkulu karena kurikulum pada jenjang SMA terbatas pada statistika deskriptif yang meliputi pengenalan ukuran pemusatan, ukuran penyebaran, dan visualisasi data. Program Pengabdian Kepada Masyarakat (PkM) dengan judul “Data-Driven Decision Making”: Pengenalan Statistika dan Pemanfaatannya di SMA IT Iqra Kota Bengkulu bertujuan untuk mengenalkan analisis korelasi dan regresi yang dapat digunakan untuk mendukung pengambilan keputusan. Pelaksanaan PkM dilaksanakan secara klasikal dengan penyampaian materi dan pelatihan langsung dengan memanfaatkan Bahasa pemrograman RStudio. Evaluasi program PkM yang dilakukan dengan memberikan pre-test dan post-test menunjukkan bahwa terdapat perbedaan rata-rata hasil pemahaman sebelum dan setelah mengikuti kegiatan. Hal ini dapat diinterpretasikan bahwa kegiatan PkM memberikan pengaruh terhadap pemahaman siswa pengambilan keputusan berdasarkan analisis data.
Co-Authors Abda Abda Agwil, Winalia Ajeng Siti Nurul Kharima Alwansyah, Muhammad Arib APRIANISA, TRI Arlin Marsyanda Asmariyah Deni Maryani Dewiani, Kurnia Dwi Kumala, Siska Faisal, Fahri Fakhry Asad Agusfrianto Firdaus Firdaus Fransiska, Welly Intrada Reviladi Jose Rizal Jumeysi Herlina Irawan Muhammad Arib Alwansyah Muhammad Arib Alwansyah Arib Muhammad Chairul Imam Novianti Novianti Nur Afandi Nurul Hidayati Putriasari, Novi Rafflesia, Ulfa Ratna Widayati Ratna Widayati Ratna Widayati Rewan Jayadi Rina Filia Sari Rina Widyasari Risfa Fadila Saniyyah, Nabilah Sarumpaet, Mey Yanti Septa, Oon Septri Damayanti Septri Damayanti Setiawan, Aisyah Nooravieta Sigit Nugroho Sigit Nugroho Siska Yosmar Sitohang, Yosep O Suci Rahmawati Wijuniamurti, Susi Yulian Fauzi Yusanti, Linda