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BAREKENG: Jurnal Ilmu Matematika dan Terapan
Published by Universitas Pattimura
ISSN : 19787227     EISSN : 26153017     DOI : https://search.crossref.org/?q=barekeng
Core Subject : Economy, Science, Education, Engineering,
Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation
BAREKENG: Jurnal ilmu Matematika dan Terapan is one of the scientific publication media, which publish the article related to the result of research or study in the field of Pure Mathematics and Applied Mathematics. Focus and scope of BAREKENG: Jurnal ilmu Matematika dan Terapan, as follows: - Pure Mathematics (analysis, algebra & number theory), - Applied Mathematics (Fuzzy, Artificial Neural Network, Mathematics Modeling & Simulation, Control & Optimization, Ethno-mathematics, etc.), - Statistics, - Actuarial Science, - Logic, - Geometry & Topology, - Numerical Analysis, - Mathematic Computation and - Mathematics Education. The meaning word of "BAREKENG" is one of the words from Moluccas language which means "Counting" or "Calculating". Counting is one of the main and fundamental activities in the field of Mathematics. Therefore we tried to promote the word "Barekeng" as the name of our scientific journal also to promote the culture of the Maluku Area. BAREKENG: Jurnal ilmu Matematika dan Terapan is published four (4) times a year in March, June, September and December, since 2020 and each issue consists of 15 articles. The first published since 2007 in printed version (p-ISSN: 1978-7227) and then in 2018 BAREKENG journal has published in online version (e-ISSN: 2615-3017) on website: (https://ojs3.unpatti.ac.id/index.php/barekeng/). This journal system is currently using OJS3.1.1.4 from PKP. BAREKENG: Jurnal ilmu Matematika dan Terapan has been nationally accredited at Level 3 (SINTA 3) since December 2018, based on the Direktur Jenderal Penguatan Riset dan Pengembangan, Kementerian Riset, Teknologi, dan Pendidikan Tinggi, Republik Indonesia, with Decree No. : 34 / E / KPT / 2018. In 2019, BAREKENG: Jurnal ilmu Matematika dan Terapan has been re-accredited by Direktur Jenderal Penguatan Riset dan Pengembangan, Kementerian Riset, Teknologi, dan Pendidikan Tinggi, Republik Indonesia and accredited in level 3 (SINTA 3), with Decree No.: 29 / E / KPT / 2019. BAREKENG: Jurnal ilmu Matematika dan Terapan was published by: Mathematics Department Faculty of Mathematics and Natural Sciences University of Pattimura Website: http://matematika.fmipa.unpatti.ac.id
Arjuna Subject : Matematika - Matematika Terapan
Articles 1,309 Documents
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DYNAMIC MODELING OF CARBON DIOXIDE EMISSIONS USING HIGH-ORDER DIFFERENTIAL EQUATIONS AND NONLINEAR ESTIMATION Pasaribu, Udjianna Sekteria; Mahdiyasa, Adilan Widyawan; Irfanullah, Asrul
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 2 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss2pp1215-1228

Abstract

Carbon dioxide (CO₂) is one of the main factors contributing to global warming. As the second largest CO₂ emitter globally, the United States (US) faces increasing political and economic pressure to reduce its emissions. Historical emission data exhibits complex structural patterns characterized by linear growth, quadratic trends, and periodic oscillations. Most existing models fail to capture this multifaceted behavior. In this study, we propose a high-order differential equation to represent the dynamic behavior of CO₂ emissions in the US. The model integrates linear, quadratic, and oscillatory components to reflect both long-term and short-term fluctuations. Nonlinear parameter estimation techniques are employed to fit the model to historical emission data with high accuracy. The proposed model effectively captures historical emission behavior, demonstrating strong goodness of fit and identifying both trend and cyclical components. Model-based projections indicate a likely resurgence in emission growth over the next decade, raising concerns regarding compliance with climate commitments and potential exposure to international carbon pricing instruments. The findings highlight the value of combining differential equation modeling with nonlinear estimation in analyzing environmental systems. The main limitation of this study is that it focuses only on historical emission dynamics, without direct integration of socio-economic drivers. This gap, however, highlights opportunities for future research.
ENHANCED GIANT TREVALLY OPTIMIZER FOR ENGINEERING DESIGN AND EPIDEMIOLOGICAL MODEL As-Shidiq, Ikhsan Rizqi Az-Zukruf; Kurniawan, E. Andry Dwi; Sidarto, Kuntjoro Adji
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 2 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss2pp1229-1250

Abstract

Metaheuristic algorithms are widely used for solving complex optimization problems, but their performance often depends on the initialization strategy. This study proposes an enhanced Giant Trevally Optimizer (GTO) by introducing quasi-random Sobol sequences in the initialization phase, yielding the Sobol-initialized Giant Trevally Optimizer (SGTO). The algorithm was tested on forty benchmark functions, five engineering design problems, and an epidemiological model case study. Experimental results show that SGTO consistently outperforms the original GTO in terms of achieving optimal solutions, convergence, and its ability to maintain a consistent solution across multiple independent runs. Furthermore, the epidemiological case study demonstrates the adaptability of SGTO for tackling more complex real-world problems. This work is the first to adapt Sobol sequences for the GTO and apply it to an epidemiological model. These findings confirm that quasi-random initialization substantially improves exploration and exploitation, establishing SGTO as a versatile and reliable optimization tool.
USE OF GLUE VALUE AT RISK FOR OPTIMAL PORTFOLIO RISK MEASUREMENT WITH THE SINGLE INDEX MODEL METHOD Rafni, Turnika Afdatul; Agustina, Dina
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 2 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss2pp1251-1262

Abstract

Creating an optimal portfolio and measuring risk are ways that can be used to reduce losses and maximize returns in an investment. In this study, the optimal portfolio is formed using the Single Index Model method, which assumes stock returns are influenced only by market returns. The stocks used are stocks that are consistently included in the IDX30 index during the period October 24, 2022-October 25, 2024 and provide positive expected returns, so that based on the Single Index Model method, 5 stocks are included in the optimal portfolio with the proportion of each stock as follows, PT Indofood Sukses Makmur Tbk (INDF) 30%, PT Barito Pacific Tbk (BRPT) 8%, PT Bank Mandiri Tbk (BMRI) 35%, PT Bank Central Asia Tbk (BBCA)17%, and PT Bank Negara Indonesia Tbk (BBNI) 10%. The risk of the optimal portfolio can be calculated using the Glue Value at Risk method, which provides a more accurate and coherent measure of risk. In this study with a confidence level of and and used a high distortion function and , the Glue Value at Risk amount for the optimal portfolio was obtained at Rp1,996,926. The backtesting results show that Glue Value at Risk provides valid and accurate results for measuring risk at this level of confidence.
A NOVEL APPROACH TO SYMBOLIC DATA CLUSTERING USING ENHANCED K-MEANS ALGORITHM Serviana Husain, Husty; Wahyu Indratno, Sapto; Vantika, Sandy
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 2 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss2pp1263-1282

Abstract

Clustering is a crucial technique in image analysis, yet traditional methods such as K-Means often struggle when dealing with complex, high-dimensional, or uncertain data. This limitation reduces their effectiveness in accurately grouping images, particularly when variability and overlapping features exist across categories. To address this problem, this paper introduces a novel approach that integrates symbolic data with the K-Means algorithm to cluster image data more effectively. By symbolically representing both color intensity and spatial features, we enhance the algorithm’s ability to handle variability and uncertainty. We test our method on the CIFAR-10 dataset, where it achieves a clustering accuracy of 94.0% with an Adjusted Rand Index of 0.7, outperforming traditional methods such as K-Means (82.5%), DBSCAN (78.1%), and Hierarchical clustering (81.3%). Our results demonstrate that symbolic data analysis offers a more flexible and accurate solution for image clustering, with potential applications in fields such as medical image processing and environmental monitoring. Limitations and directions for future research are also discussed.
PRELIMINARY MATHEMATICAL MODEL FOR CANCER TREATMENT USING BORON NEUTRON CANCER THERAPY (BNCT) Trihandaru, Suryasatriya; Parhusip, Hanna Arini; Sardjono, Yohannes; Triatmoko, Isman Mulyadi; Wijaya, Gede Sutresna; Labadin, Jane
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 2 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss2pp1283-1300

Abstract

This article outlines a revolutionary approach to immunotherapy and stem-cell cancer treatments that leverages Boron Neutron Cancer Therapy (BNCT). We formulated two models, one being the immunotherapy-BNCT model and the other featuring a stem-cell model and BNCT therapy. The former simulates the dynamics of the concentration of BNCT with anticancer properties present at the cancer site, the number of cancer cells, and the blood drug concentration, while considering periodicity. Similarly, using boronophenylalanine in the simulation, our stem-cell BNCT model evaluates the drug’s impact on the dynamics of cancer cells, stem cells, effector cells, and BNCT involvement. Using the eigenvalues of the Jacobian matrix calculated from those solutions, each model is examined for the stability of equilibrium solutions. Next, the equilibrium solution is generated and found to be unstable using the simulation parameters given in the literature. Furthermore, one of the equilibrium solutions has a zero-value variable, rendering it practically meaningless. The models have impacted the new approach to utilizing BNCT in immunotherapy and stem-cell therapy, underscoring the need for follow-up in developing stable and balanced model parameters. Such efforts will improve the existing model while also yielding positive results from the BNCT approach.
OPTIMAL STRATEGIES FOR DENGUE CONTROL: WOLBACHIA-INFECTED MOSQUITOES DEPLOYMENT, PUBLIC HEALTH EDUCATION, AND VACCINATION Bakhtiar, Toni; Jaharuddin, Jaharuddin; Hanum, Farida
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 2 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss2pp1301-1316

Abstract

Wolbachia-infected mosquitoes present a promising method for dengue control by inhibiting viral replication, reducing mosquito reproductive capacity, and shortening the lifespan of Aedes aegypti mosquitoes. This study introduces a novel optimal control model that uniquely integrates two distinct release strategies for Wolbachia-infected mosquitoes—constant and proportional rates. While prior research has explored Wolbachia deployment, our model is the first to directly compare and contrast these two rate types within the same framework to assess their differential impact on dengue transmission dynamics. This provides a more comprehensive understanding of effective release protocols, addressing a critical gap in the literature regarding optimal and adaptive Wolbachia deployment. Based on model simulations for North Kembangan Village, Jakarta, we find that a single-control strategy using Wolbachia mosquito release alone can reduce dengue cases by up to 15%. However, a multiple-control strategy that combines Wolbachia releases with public health education and vaccination is the most effective approach, achieving a substantial reduction of up to 58%. In a cost-effectiveness analysis, the study reveals that the Wolbachia-only strategy (proportional release) is the most cost-effective in terms of cost per infection averted. In terms of release dynamics, the study reveals that a constant release rate provides long-term benefits by establishing a stable Wolbachia-infected mosquito population, whereas a proportional release rate is more effective for achieving a rapid, short-term reduction in dengue cases.
DESIGN AND IMPLEMENTATION OF ANFIS CONTROLLERS FOR STABILIZING FINANCIAL SYSTEMS: A COMPARATIVE STUDY WITH NONLINEAR FEEDBACK CONTROL Patria, Lintang; Hamidzadeh, Seyed Mohamad; Mohamed, Mohamad Afendee
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 2 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss2pp1317-1330

Abstract

The study revisits the well-known Bouali chaotic financial model, which is characterized by nonlinear dynamics. As a benchmark, the nonlinear feedback control method is implemented and compared with an Adaptive Neuro-Fuzzy Inference System (ANFIS) controller. The ANFIS model is trained using 250 data samples derived from the nonlinear feedback controller and divided into training, validation, and testing subsets. The proposed ANFIS controller demonstrates superior stabilization performance by effectively eliminating chaotic behavior, ensuring stability, and achieving faster convergence than the traditional nonlinear feedback method. Quantitative results confirm this improvement: the ANFIS controller achieved very low Root Mean Square Error (RMSE) values, such as 8.78×10−5 for training and 1.37×10−4 for validation in the profit control input, highlighting its learning accuracy. Additionally, the ANFIS maintained stability even with a reduced number of controllers, demonstrating robustness and adaptability. These findings emphasize the potential of ANFIS controllers to provide efficient and reliable chaos control in complex financial systems.
A SARIMA APPROACH WITH PARAMETER OPTIMIZATION FOR ENHANCING FORECAST ACCURACY FOR NATIVE CHICKEN EGG PRODUCTION Gustriansyah, Rendra; Dewi, Deshinta Arrova; Puspasari, Shinta; Sanmorino, Ahmad
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 2 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss2pp1331-1344

Abstract

This study aims to accurately forecast monthly native chicken egg production using the Seasonal Autoregressive Integrated Moving Average (SARIMA) model with parameter optimization. The optimization process was conducted through a combination of auto.arima() initialization and an exhaustive grid search across the parameter space, evaluated using multiple performance metrics. The dataset comprised monthly production data from Magelang City, Indonesia, spanning the period from 2016 to 2022. The best-performing model, SARIMA (2,1,2)(1,0,1,12), achieved an R² of 0.89, MAE of 82.13, RMSE of 92.92, MAPE of 7.21%, and MASE of 0.67 on the testing set, indicating satisfactory forecasting performance. Compared with the non-optimized SARIMA baseline, the optimized model showed improved predictive accuracy. However, the residuals did not follow a normal distribution, suggesting potential limitations in model assumptions. Moreover, the study is limited by its focus on a single geographic location and native chicken production data, which may restrict its generalizability. Despite these limitations, the findings demonstrate that parameter optimization in SARIMA enhances forecast accuracy and can support better planning for food security initiatives.
COMPARISON OF FRUIT FLY OPTIMIZATION ALGORITHM (FOA) AND PARTICLE SWARM OPTIMIZATION (PSO) FOR SUPPORT VECTOR REGRESSION (SVR) IN UNITED TRACTORS STOCK PRICES FORECASTING Wibowo, Belva Hadaya; Utami, Iut Tri; Rochayani, Masithoh Yessi
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 2 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss2pp1345-1358

Abstract

Stock price forecasting is one of the analytical approaches used by capital market participants to identify future price movement patterns. This study evaluates the performance of the Support Vector Regression (SVR) model in predicting the stock price of United Tractors (UNTR) by optimizing the model’s parameters using two metaheuristic algorithms. The selection of SVR is based on its ability to handle nonlinear regression problems through the use of the Radial Basis Function (RBF) kernel. The parameter optimization of SVR is carried out using the Fruit Fly Optimization Algorithm (FOA), an algorithm inspired by the olfactory and visual system of fruit flies in locating food sources. The advantage of FOA lies in its computational simplicity and fast convergence speed. This study also implements Particle Swarm Optimization (PSO) for comparison purposes. This algorithm adopts a collaborative mechanism among particles in the search space, inspired by the flocking behavior of birds. The stock price data used in this study, covering the period from January 2020 to December 2023, was obtained from Yahoo Finance (https://finance.yahoo.com). The results show that SVR-FOA yields a parameter combination of C = 1000, gamma = 0.9182, and epsilon = 0.9997, while SVR-PSO produces a different configuration, namely C = 1000, gamma = 0.0001, and epsilon = 1. Accuracy evaluation using Mean Absolute Percentage Error (MAPE) indicates that the SVR-PSO model achieves a MAPE of 2.3164%, suggesting a relatively low prediction error. SVR-FOA yields a MAPE of 5.8727%, which is still within the acceptable tolerance range for financial data. While this study focuses on a single stock and uses only historical closing prices, its results provide a strong baseline for applying SVR with metaheuristic optimization in financial forecasting. This research contributes by presenting a direct comparative analysis of FOA and PSO for SVR parameter tuning in an emerging market context, offering practical insights for investors and researchers seeking robust forecasting models.
DEVELOPMENT OF A MATHEMATICAL MODEL FOR SMARTPHONE ADDICTION USING A DETERMINISTIC COMPARTMENTAL APPROACH Amalina, Amalina; Samat, Nor Azah; Sabri, Ahmad
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 2 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss2pp1359-1372

Abstract

Smartphone usage is increasing with technological advancements. However, excessive use can lead to addiction, negatively impacting an individual’s physical health, mental well-being, communication skills, and cognitive development. While previous studies have discussed the psychological and social aspects of smartphone addiction, there is still a lack of mathematical models that capture its spread at the population level. To address this gap, this study develops a deterministic compartmental model to describe the dynamics of smartphone addiction, representing real-world addiction scenarios through mathematical analysis. The novelty of this study lies in formulating a theoretical framework that identifies equilibrium points, conducts sensitivity analysis for each parameter, and employs numerical simulations to demonstrate the role of transmission rate and initial conditions in shaping addiction dynamics. The findings highlight that both transmission rate and initial conditions significantly influence the persistence of addiction, underscoring the importance of early interventions to reduce its long-term impact on the population.

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