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Redaksi BAREKENG: Jurnal ilmu matematika dan terapan, Ex. UT Building, 2nd Floor, Mathematic Department, Faculty of Mathematics and Natural Sciences, University of Pattimura Jln. Ir. M. Putuhena, Kampus Unpatti, Poka - Ambon 97233, Provinsi Maluku, Indonesia Website: https://ojs3.unpatti.ac.id/index.php/barekeng/ Contact us : +62 85243358669 (Yopi) e-mail: barekeng.math@yahoo.com
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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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SURVIVAL ANALYSIS OF CHRONIC KIDNEY FAILURE PATIENTS USING THE COX STRATIFIED MODEL AND RANDOM SURVIVAL FOREST Hamid, Assyifa Lala Pratiwi; Susetyo, Budi; Kurnia, Anang
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/barekengvol20iss2pp1527-1540

Abstract

This study aims to analyze the factors influencing the survival of chronic kidney failure patients undergoing hemodialysis and to compare the performance of the Cox Stratified Model with the Random Survival Forest (RSF) using retrospective data from 741 patients at Asy-Syifa General Hospital, Indonesia. Data were analyzed using the Cox Stratified Model to address violations of the proportional hazards assumption and RSF to capture non-linear patterns and complex interactions among variables. The results showed that age, hypertension, diabetes, anemia, and hemodialysis frequency significantly affected survival, with a C-Index of 0.66 for the Cox Stratified Model and 0.6558 for RSF. The limitations of this study include its single-center retrospective design, which may limit generalizability, potential residual confounding from unmeasured variables, as well as the interpretability limitations and higher computational demands of RSF. The originality of this research lies in the direct comparison between advanced statistical models and machine learning methods in a cohort of chronic kidney failure patients in Indonesia, providing new insights for improving risk stratification and clinical prediction.
COMPARISON OF MARS AND BINARY LOGISTIC REGRESSION MODELS FOR IDENTIFYING STUNTING RISK FACTORS IN TODDLERS IN TELUK WARU, EAST SERAM REGENCY Bension, Johan Bruiyf; Kondo Lembang, Ferry; Idris, Nurul Fadillah; Lewaherilla, Norisca
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/barekengvol20iss2pp1541-1556

Abstract

In 2022, the prevalence of chronic stunting in Indonesia reached 21.6%, surpassing the World Health Organization (WHO) threshold of 20%. East Seram Regency reported an even higher prevalence of 24.1%, with Teluk Waru District identified as one of the areas most affected due to low compliance with healthy lifestyle practices. This study aimed to compare the performance of Multivariate Adaptive Regression Splines (MARS) and Binary Logistic Regression in analyzing risk factors for toddler stunting in Teluk Waru District, East Seram Regency. Data were collected through direct anthropometric measurements at the Integrated Health Post (Posyandu) of Teluk Waru Health Center with 60 respondents. The findings revealed that Binary Logistic Regression outperformed MARS, achieving R2 = 72.7% accuracy in predicting stunting. Significant determinants of toddler stunting included a history of illness, provision of supplementary food for pregnant women, and iron tablet consumption during pregnancy. The novelty of this study lies in the application of a comparative modeling approach—MARS versus Binary Logistic Regression—in identifying stunting risk factors at a district level with high prevalence. Practically, the results can assist local health authorities in prioritizing maternal nutrition and disease prevention programs to reduce stunting.
WAVELET-BASED COMPUTATIONAL FRAMEWORK FOR THE SOLOW-SWAN ECONOMIC MODEL Sahani, Jay Kishore; Sharma, Pankaj; Khanna, Nikhil; Kumar, Ajay
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/barekengvol20iss2pp1557-1568

Abstract

In this paper, we introduce an innovative numerical technique for addressing the classical Solow-Swan economic growth model through the application of the Haar wavelet approach. The Solow-Swan model, a cornerstone of neoclassical economics, elucidates long-run economic growth influenced by capital accumulation, labor, and technological advancements. Although various computational methods have been utilized to study its behavior, the use of wavelet-based techniques, specifically Haar wavelets, has been largely overlooked. The Haar wavelet method provides distinct benefits, such as computational simplicity and adaptability to piecewise continuous functions. By transforming the Solow-Swan model into a set of algebraic equations using Haar wavelet expansion, we showcase the method’s ability to accurately capture growth dynamics. We present numerical results to substantiate the efficacy of this approach and compare it with conventional numerical techniques, underscoring the advantages of wavelet-based solutions. This study offers a fresh perspective on economic modeling, emphasizing the potential of wavelet theory in the numerical analysis of growth equations.
MATHEMATICAL MODEL FOR DETECTING DIABETES IN BLOOD CELLS WITH THE INFLUENCE OF CORTISOL Sujarwo, Imam; Juhari, Juhari; Feby Ariyanti, Adelia Irma; Sutrisno, Sutrisno
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/barekengvol20iss2pp1569-1582

Abstract

Diabetes is a disease that occurs when the body is unable to produce enough insulin or cannot effectively use the insulin it produces, resulting in an increase in blood glucose levels. One of the factors that affects the stability of glucose and insulin is the hormone cortisol, which is produced in response to stress. The purpose of this study is to develop a mathematical model of diabetes detection in blood cells by considering the influence of cortisol. The model is formulated as a system of linear differential equations and analyzed through equilibrium points and eigenvalue analysis. The results show that two eigenvalues form asymptotically stable spirals, while the other two are asymptotically stable nodes, indicating system stability. The novelty of this study lies in the inclusion of cortisol, which delays stabilization of glucose–insulin dynamics and provides a more realistic representation of physiological conditions under stress. A limitation of this study is that the model relies on simplifying assumptions without clinical validation. This research is expected to serve as a foundation for further model development by considering other regulatory factors, with implications for improving diabetes prevention and intervention strategies in stress-related conditions.
FUZZY LOGIC APPROACH TO FOREST FIRE RISK ASSESSMENT IN TANJUNG PUTTING NATIONAL PARK Purba, Rani Natalia; Nababan, Esther Sorta Mauli; Gio, Prana Ugiana; Zahedi, Zahedi; Syahputra, Muhammad Romi
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/barekengvol20iss2pp1583-1598

Abstract

In implementing fuzzy logic, the Sugeno fuzzy method faces several challenges, such as issues in determining the fuzzy rule base and the occurrence of undefined outputs (defuzzification) with values of 0/0. This study examines the application of the Sugeno fuzzy method in identifying the level of forest fire risk by considering various variables. The variables are temperature, humidity, and wind speed. The model is developed using fuzzy rules constructed based on the relationships among the variables. The test results show that after modifying the membership function boundaries to decimal values approaching the original lower bounds, the Zero-Order Sugeno fuzzy method can produce an average forest fire risk level of 68.83 (high category) in Tanjung Puting National Park. In addition, applying the First-Order Sugeno fuzzy method produces a multiple linear regression model that can be applied within the rule base, resulting in an average forest fire risk level of 68.89 (high category) at the same location. During the evaluation phase, the First-Order Sugeno model achieved a lower RMSE value (15.47) than the Zero-Order model (16.03), indicating that it is more suitable for handling extreme conditions such as dangerous spikes in risk. Therefore, this approach has the potential to serve as an effective early warning system for forest fire mitigation, supporting decision-making processes.
ENHANCING FUZZY TIME SERIES FORECASTING WITH REVISED HEURISTIC KNOWLEDGE: A CASE STUDY ON TUBERCULOSIS IN SABAH Lasaraiya, Suriana; Zenian, Suzelawati; Hasim, Risman Mat; Ashaari, Azmirul
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/barekengvol20iss2pp1599-1612

Abstract

Accurate forecasting of tuberculosis (TB) cases is essential for effective public health planning, particularly in regions such as Sabah, Malaysia, where TB remains a significant and persistent health concern. This study aims to improve the accuracy of fuzzy time series models by refining the construction of Fuzzy Logical Relationship Groups using a revised heuristic framework. The proposed approach embeds domain-informed rules to dynamically adjust the formulation of fuzzy relationships. It was applied to monthly tuberculosis case data from 2012 to 2019 and evaluated against both the original fuzzy time series model and a heuristic-based variant. The revised heuristic model achieved the best forecasting accuracy, recording a Mean Squared Error of 1315.0160, a Root Mean Square Error of 36.2631, a Mean Absolute Error of 0.0566, and a Mean Absolute Percentage Error of 0.0138 percent. These consistently lower error values confirm the superiority of the revised model compared to the benchmarks. The study demonstrates that incorporating refined heuristic strategies enables fuzzy time series models to capture the dynamic nature of disease data more effectively. However, the analysis is limited to univariate data (monthly tuberculosis cases), and future work should consider multivariate and hybrid approaches. This research contributes to the understanding by demonstrating that revised heuristic knowledge significantly enhances the predictive capability of fuzzy time series models. The findings provide more reliable forecasts for tuberculosis trends and establish a foundation for broader applications in infectious disease forecasting and healthcare analytics.
MATHEMATICAL MODELING OF VARICELLA TRANSMISSION USING SVEITR MODEL Naqiya, Sadiyana Yaqutna; Lusiana, Vina; Abdurrazzaq, Achmad
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/barekengvol20iss2pp1613-1626

Abstract

Varicella is a highly contagious disease with strong potential to persist endemically if not adequately controlled. This study develops an SVEITR (Susceptible–Vaccinated–Exposed–Infected–Treated–Recovered) model by extending the SVEIR and SEITR frameworks with a treatment compartment to represent individuals receiving medical care. A mathematical modeling approach was applied through differential equation formulation, equilibrium stability analysis, and computation of the basic reproduction number using the Next Generation Matrix method. The results show that , confirming a high transmission potential. Numerical simulations indicate that vaccination and treatment reduce disease spread, yet waning immunity sustains a pool of susceptible individuals. These findings highlight the importance of continuous control strategies. The inclusion of a treatment compartment represents a methodological advancement, providing a more comprehensive framework for evaluating the effects of interventions on varicella transmission.
MODELLING THE NUMBER OF CRIMES IN EAST JAVA USING A TRUNCATED SPLINE SEMIPARAMETRIC REGRESSION APPROACH Saputra, Yahya Vigo Tri; Hafiyusholeh, Moh.; Khaulasari, Hani; Farida, Yuniar; Intan, Putroue Keumala
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/barekengvol20iss2pp1627-1642

Abstract

High crime rates can lead to unrest and financial losses for the community. East Java is one of the provinces with high crime rates, with a total of 21,046 reported crimes in 2023. This study aims to identify the factors that influence crime rates in East Java and evaluate the goodness of the model through truncated spline semiparametric regression. Truncated spline semiparametric regression is a combination of parametric and nonparametric methods that can adjust changes in data patterns through the presence of knot points. The data used in this study were sourced from the Central Statistics Agency, including variables such as the number of people living in poverty, average years of schooling, gross regional domestic product, population, Gini ratio, per capita expenditure, and open unemployment rate. The results of the analysis indicate that the predictor variables have a significant influence on the number of crimes simultaneously. Partially, the variables that influence the number of crimes in East Java Province are average years of schooling, population, Gini ratio, per capita expenditure, and open unemployment rate. The best regression model is obtained using the combination knot point (4,2,4,3) with a minimum GCV value of 49636.60. The coefficient of determination obtained is 93.60%, indicating that the predictor variables can explain 93.60% of the variation in the crime rate, while the remaining 6.40% is attributed to variables outside the scope of the study.
STATISTICAL MODELING FOR DOWNSCALING USING PRINCIPAL COMPONENT REGRESSION AND DUMMY VARIABLES: A CASE OF SIAK DISTRICT Adnan, Arisman; Alika, Elsa Riesta; Silalahi, Divo Dharma; Aulia, Felia Rizki; Erda, Gustriza
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/barekengvol20iss2pp1643-1658

Abstract

Indonesia, as a tropical country, is characterized by two primary seasons: the rainy season and the dry season. It is evident that meteorological shifts can exert considerable influence on the agricultural sector, a notable example being the cultivation of palm oil. Consequently, the ability to predict rainfall has emerged as a pivotal element in the broader endeavor to mitigate the adverse effects of climate change. This study employs statistical downscaling using the Principal Component Regression (PCR) approach to model rainfall predictions. The issue of multicollinearity, a common occurrence in Global Circulation Model (GCM) data, is addressed through the use of Principal Component Regression (PCR). This method has been demonstrated to stabilize the model structure and reduce variance in the regression coefficients. The data utilized encompass observed rainfall from LIBO Estate, which is owned by PT SMART Tbk (SMART Research Institute), for the period from 2013 to 2022. This data serves as the response variable, while the CMIP6 GCM simulation output data functions as the predictor variable. The findings indicated that the initial PCR model exhibited an RMSE value ranging from 97.06 to 131.69, along with an R² value ranging from 14.25% to 20.49%. The incorporation of dummy variables into the model resulted in a substantial enhancement in its performance, as evidenced by a decline in RMSE to 24.46–35.83 and an increase in R² to 89.02%–90.24%. The findings indicate that the use of PCR with dummy variables is an effective approach for enhancing the accuracy of rainfall modeling through statistical downscaling.
SOIL MOISTURE PREDICTION USING LSTM AND GRU: UNIVARIATE AND MULTIVARIATE DEEP LEARNING APPROACHES Batlajery, Jemsri Stenli; Buono, Agus; -Mushthofa, Mushthofa
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/barekengvol20iss2pp1659–1674

Abstract

Soil moisture is an important indicator in the management of water resources, precision agriculture, and disaster mitigation, such as drought and land fires. Fluctuations in soil moisture are influenced by various climate variables, requiring a reliable predictive approach essential. This research develops a daily soil moisture prediction model using Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU) algorithms with univariate and multivariate approaches. Soil moisture data were obtained from Google Earth Engine, while climate data were collected from 10 BMKG stations in East Java for the period 2019–2024. Data preprocessing includes cubic spline interpolation to handle missing values and Min-Max normalization to achieve uniform feature scaling. Models were built using a direct forecasting approach for horizons to and five evaluation metrics: MAE, MSE, RMSE, MAPE, and R². The results show that the multivariate GRU model performs best at horizon with MAE = 0.05455, MSE = 0.00604, RMSE = 0.07539, MAPE = 0.19280, and R² = starting from 0.9626 on day 1 (t), then decreasing to 0.8075 on day 10 The univariate LSTM model excelled in training time efficiency (<400 seconds) at most stations. The multivariate GRU model demonstrates the highest accuracy and stability, making it suitable for medium- to long-term forecasting, while the univariate LSTM excels in training speed, making it effective for daily predictions. The model’s performance remains limited to the dataset's spatial and temporal scope. Therefore, future research should test the model in other regions and under extreme climate conditions, as well as apply transfer learning in data-scarce areas. The novelty of this study lies in comparing LSTM and GRU performance for daily soil moisture prediction in both univariate and multivariate scenarios, using complete climate variables from multiple stations.

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