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All Journal Pythagoras: Jurnal Matematika dan Pendidikan Matematika JURNAL MATEMATIKA STATISTIKA DAN KOMPUTASI Edumatsains Saintifik : Jurnal Matematika, Sains, dan Pembelajarannya InPrime: Indonesian Journal Of Pure And Applied Mathematics Journal of Mathematics Education and Science Jurnal Pengabdian dan Peningkatan Mutu Masyarakat (JANAYU) Griya Journal of Mathematics Education and Application Bulletin of Applied Mathematics and Mathematics Education Indonesian Journal of Community Empowerment and Service Journal of Mathematics, Computation and Statistics (JMATHCOS) Diophantine Journal of Mathematics and Its Applications Journal of Innovation in Applied Natural Science
Ratna Widayati
Universitas Nahdlatul Ulama Al Ghazali Cilacap
Religion Aerospace Engineering Agriculture, Biological Sciences & Forestry Humanities Astronomy Biochemistry, Genetics & Molecular Biology Chemical Engineering, Chemistry & Bioengineering Chemistry Computer Science & IT Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Energy Engineering Environmental Science Immunology & microbiology Industrial & Manufacturing Engineering Languange, Linguistic, Communication & Media Law, Crime, Criminology & Criminal Justice Library & Information Science Materials Science & Nanotechnology Mathematics Physics Social Sciences 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
Penanganan Multikolinieritas dalam Regresi Saham GOTO Menggunakan PCA, Ridge, LASSO, dan PLS Fachri Faisal; Ratna Widayati; Zulfia Memi Mayasari; Siska Dwi Kumala; Aisyah Nooravieta Setiawan; Nur El Hasanah; Revika Putri Asharia
Griya Journal of Mathematics Education and Application Vol. 6 No. 1 (2026): Maret 2026
Publisher : Pendidikan Matematika FKIP Universitas Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/griya.v6i1.1047

Abstract

This study aims to address the problem of multicollinearity in a multiple regression model of the daily closing stock price of PT GoTo Gojek Tokopedia Tbk (GOTO) during the period from 2022 to early 2025. Multicollinearity occurs when independent variables are highly correlated, which can lead to inefficient and unreliable parameter estimates. GOTO’s stock price experienced high volatility following its Initial Public Offering (IPO) in April 2022, making it necessary to apply appropriate analytical approaches to identify factors influencing its price movements. The study uses the closing price as the dependent variable, with opening price, high price, low price, and trading volume as independent variables. The methods employed include multiple regression and several approaches to handle multicollinearity, namely variable elimination, Principal Component Analysis (PCA), Ridge Regression, LASSO Regression, and Partial Least Squares (PLS) Regression. The initial multiple regression model achieved an R² of 0.9990 and an RMSE of 2.88, but Variance Inflation Factor (VIF) analysis indicated severe multicollinearity. After applying the alternative methods, PLS Regression demonstrated the best performance, with an R² of 0.9990 and an RMSE of 0.0318. Therefore, it can be concluded that PLS Regression is a more stable and accurate method for addressing multicollinearity and improving the prediction of GOTO’s stock prices. Abstrak Penelitian ini bertujuan menangani masalah multikolinearitas dalam model regresi berganda terhadap harga saham penutupan harian PT GoTo Gojek Tokopedia Tbk (GOTO) selama periode 2022 hingga awal 2025. Multikolinearitas terjadi ketika variabel bebas saling berkorelasi kuat sehingga menyebabkan estimasi parameter menjadi tidak efisien dan kurang akurat. Harga saham GOTO mengalami volatilitas tinggi sejak IPO April 2022, sehingga diperlukan pendekatan analisis yang tepat untuk mengidentifikasi faktor-faktor yang memengaruhi pergerakan harga. Data penelitian menggunakan variabel Terakhir sebagai variabel dependen, serta Pembukaan, Tertinggi, Terendah, dan Volume sebagai variabel independen. Metode yang digunakan meliputi regresi berganda dan beberapa pendekatan penanganan multikolinearitas, yaitu penghapusan variabel, Principal Component Analysis (PCA), Ridge Regression, LASSO Regression, dan Partial Least Squares (PLS) Regression. Model awal menghasilkan R² sebesar 0,9990 dan RMSE 2,88, namun terindikasi multikolinearitas tinggi berdasarkan nilai VIF. Setelah penerapan metode alternatif, PLS Regression memberikan performa terbaik dengan R² = 0,9990 dan RMSE = 0,0318. Dengan demikian, PLS Regression dinilai paling stabil dan akurat dalam mengatasi multikolinearitas serta meningkatkan ketepatan prediksi harga saham GOTO.
Comparative Analysis of K-Nearest Neighbor and Fuzzy K-Nearest Neighbor for Diabetes Classification Using the Pima Indians Diabetes Dataset Ulfasari Rafflesia; Siska Dwi Kumala; Ratna Widayati; Aisyah Nooravieta S.; Oon Septa
Journal of Innovation in Applied Natural Science Vol. 2 No. 2 (2026): Journal of Innovation in Applied Natural Science
Publisher : CV Media Inti Teknologi

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58723/jinas.v2i2.223

Abstract

Background of study: Diabetes mellitus remains one of the most common chronic diseases worldwide; thus, early and accurate prediction is critical for appropriate intervention. Aims: This study examines the performance of the standard K-Nearest Neighbor (KNN) method and its fuzzy counterpart, Fuzzy K-Nearest Neighbor (Fuzzy KNN), in classifying diabetes status and compares their behavior across different neighborhood sizes (k). Methods: The Pima Indians Diabetes Dataset (768 cases, 8 clinical variables) was used. Zero values in physiologically implausible attributes (glucose, blood pressure, skin thickness, insulin, and BMI) were treated as missing values based on the physiological interpretation of these variables and imputed using class-wise medians. The dataset was then split into 80% training and 20% testing subsets using stratified sampling to preserve class proportions. Five-fold cross-validation on the training set was used to determine the optimal number of neighbors (k), after which both models were evaluated on the held-out test set using accuracy, precision, recall, and F1-score. Result: The optimal k varied between models: k=15 for KNN and k=3 for Fuzzy KNN. Cross-validation accuracy across the tested k range (3–21) remained relatively stable for both methods (approximately 0.80–0.83), indicating that performance was not highly sensitive to k selection. On the test set, Fuzzy KNN outperformed conventional KNN across all evaluation metrics (accuracy: 0.779 vs. 0.773; precision: 0.679 vs. 0.673; recall: 0.704 vs. 0.685; F1-score: 0.691 vs. 0.679). Conclusion: For the Pima Indians Diabetes Dataset, Fuzzy KNN achieved slightly better performance than conventional KNN across all evaluated metrics on the held-out test set. These findings indicate that distance-based membership weighting may provide a modest advantage over crisp majority voting for diabetes classification in this dataset.
Social Engineering Vulnerability Index pada Provinsi di Indonesia Tahun 2025 dengan Principal Component Analysis dan K-Medoids Clustering Hafizh Nursalim; Ratna Widayati; Zulfia Memi Mayasari; Oon Septa
Griya Journal of Mathematics Education and Application Vol. 6 No. 3 (2026): September 2026
Publisher : Pendidikan Matematika FKIP Universitas Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/griya.v6i3.1353

Abstract

Indonesia generates a wide range of data, including both public data and sensitive personal data. Generally, cyber attacks can occur through software vulnerabilities, human intermediaries using social engineering techniques, or combination of both. If social engineering involves software vulnerabilities, the CVSS can be used to assess software vulnerabilities and the EPSS to estimate the probability of the exploitation. However, CVSS and EPSS cannot be applied to social engineering techniques that do not involve software or merely use it as a medium without exploiting its vulnerabilities. Based on a literature review, no study has been found that develops social engineering vulnerability index at the subnational level. Therefore, this research aims to fill this gap by constructing Social Engineering Vulnerability Index for 38 Indonesian provinces in 2025 using Principal Component Analysis (PCA), preserving 79.33% of the original data's information. Subsequently, the vulnerability levels were analyzed using K-Medoids clustering, where the optimal number of clusters was based on the interpretation of Silhouette Coefficient (SC) and average Silhouette Coefficient. The index ranges from 0 to 1, representing 5 vulnerability levels. This research indicates that there are variations in social engineering vulnerability due to socioeconomic and digital ecosystem disparities
Kendali Optimal pada Penyebaran Penyakit Covid-19 berdasarkan model SIVRS Ratna Widayati; Mizan Ahmad; Noor Sofiyati
Journal of Mathematics, Computations and Statistics Vol. 6 No. 2 (2023): Volume 06 Nomor 02 (Oktober 2023)
Publisher : Jurusan Matematika FMIPA UNM

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

Abstract

This study discusses about optimal control for spread of Covid-19 disease with the assumptionthat there is a subpopulation of individuals infected with the new variant of Covid-19. Transmission canoccur between individuals in susceptible subpopulations and individuals in subpopulations infected withCovid-19. SIVRS model is used by assumes that there is control variable in the form of the vaccinationstrategy given to susceptible individuals. This study aims to minimize the number of individuals in thesubpopulation infected and infected with the new variant. An analysis of the optimal control solution wascarried out using the Hamiltonian function and then solving it using the Sweep Forward and Back methodin Matlab. The results show that the vaccination strategy implemented can minimize the number ofindividuals in the subpopulation infected and infected with the new variant.
Co-Authors Aisyah Nooravieta S. Ajeng Siti Nurul Kharima Arlin Marsyanda Dwi Kumala, Siska Eka Susilowati, Eka Endah Purda Listya Evelyne Riandini Fachri Faisal Faisal, Fahri Firdaus Hafizh Nursalim Hamim Muntoha, Renal Hasrita Octaliana Intrada Reviladi ISNAENI, NUR Jose Rizal Ma'rifah, Umi Mizan Ahmad Nita Yulianti, Nita Noor Sofiyanti noor Sofiyati Nur Afandi Nur El Hasanah Nurul Fatimah  Susanti Oon Septa Oon Septa Rafflesia, Ulfa Ramya Rachmawati Revika Putri Asharia Reviladi, Intrada Risfa Fadila Septa, Oon Septri Damayanti Septri Damayanti Setiawan, Aisyah Nooravieta Siska Dwi Kumala Siska Dwi Kumala Siska Yosmar Ulfasari Rafflesia Yulian Fauzi Zulfia Memi Mayasari Zulfia Memi Mayasari