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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 1,248 Documents
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MAPPING DISASTER-PRONE AREAS ON JAVA ISLAND USING THE K-PROTOTYPES ALGORITHM Tauryawati, Mey Lista; Zainuddin, Ahmad Fuad
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss1pp0179-0196

Abstract

Clustering in disaster areas is often implemented as a disaster mitigation effort with the aim of minimizing risk. Determining the appropriate clustering method based on the data set will influence the clustering results. K-Prototypes is a clustering method that is capable of handling mixed data, numerical and categorical data, so this method is suitable to clustering disaster prone area with mixed data of disaster factors such as incident intensity, type of disaster, population density, and level of infrastructure vulnerability. This research focuses on disaster prone areas on Java Island and clustering using K-Prototypes to group and map areas that have the highest to lowest levels of disaster vulnerability based on the number of incidents, number of victims, and the amount of damage to facilities and the type of disaster. The clustering results obtained mapping of cities in the province into cluster groups based on the level of vulnerability and calculated potential losses based on disasters in each province. Afterward, the clustering results are used to determine priority areas for disaster mitigation to minimize losses.
IMPLEMENTATION OF RESPONSE-BASED UNIT SEGMENTATION IN PARTIAL LEAST SQUARE (REBUS-PLS) FOR ANALYSIS AND REGIONAL GROUPING Al-Ham, Hairil; Satyahadewi, Neva; Preatin, Preatin
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss1pp0197-0210

Abstract

Housing environmental health is a key indicator of community quality of life. In West Kalimantan Province, variations in geographical and socioeconomic conditions contribute to disparities in housing conditions. This study analyzes and classifies regions based on factors influencing housing environmental health using the Response-Based Unit Segmentation in Partial Least Squares (REBUS-PLS) method. REBUS-PLS helps detect unobserved heterogeneity by identifying subgroups with different structural relationships. The exogenous latent variables include household economics, education, and housing facilities, while the endogenous variable is housing environmental health, measured through 15 indicators. The results of the SEM-PLS analysis obtained 3 paths that had a significant effect: household economics on housing facilities, household economics on education, and housing facilities on the health of the Housing environment. SEM-PLS assumes homogeneity across data, meaning all observations follow the same structural pattern. However, this assumption may not hold, especially with data representing diverse regions. To address potential heterogeneity, REBUS-PLS was applied. The analysis revealed two distinct segments, each with stronger explanatory power than the global model, as indicated by higher R² values (Segment 1 = 95.6%, Segment 2 = 91.4%, compared to 87.7% in the global model). Segment 1 consists of Landak, Sanggau, Sekadau, Kayong Utara, and Singkawang City. Segment 2 includes Bengkayang, Melawi, Ketapang, Kapuas Hulu, Sanggau, Sekadau, Sintang, and Pontianak City. These findings confirm the presence of structural heterogeneity and demonstrate that REBUS-PLS provides a more accurate understanding of the factors affecting housing environmental health across regions.
MATHEMATICAL MODEL OF THE SPREAD OF HIV/AIDS CONSIDERING THE LEVEL OF IMMUNITY Linarta, Anisa Sukma; Adi, Yudi Ari
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss1pp0211-0226

Abstract

The immune system, crucial for defending the body against infections, is a primary target of HIV, compromising its ability to resist illnesses that may progress to AIDS. This study develops a mathematical model incorporating the immune response to simulate HIV/AIDS transmission dynamics. The model analysis includes the determination of equilibrium points, the basic reproduction number , and bifurcation behavior. Two equilibrium points are identified: the disease-free and endemic equilibria. The disease-free equilibrium is asymptotically stable when , while the endemic equilibrium is stable when , indicating persistent transmission. A forward bifurcation occurs at , which biologically implies that reducing below one is critical for eliminating the disease. Numerical simulations using actual data yield an estimated with a Mean Absolute Percentage Error (MAPE) of 4.5583%, indicating good agreement between the model and data. Although the model assumes homogeneous mixing and constant parameters, it provides meaningful insights into HIV/AIDS transmission and offers a quantitative basis for evaluating control strategies.
ENHANCING STOCK PORTFOLIO PERFORMANCE USING MARKOV-SWITCHING MODELS AND CANDLESTICK PATTERNS FOR LONG-TERM INVESTMENT Nurdiansyah, Denny; Sulistiawan, Agus
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss1pp0227-0238

Abstract

Islamic stocks in Indonesia face challenges in portfolio management due to the limited number of issuers and low diversification. The change in market regime from bullish to bearish makes the portfolio more vulnerable, especially since some investors do not understand the concept of portfolio and the importance of determining optimal asset weighting. In addition, the allocation strategy used tends to be static and minimizes the utilization of sharia-based technical analysis, making investment decisions less responsive to market dynamics. This study aims to compare the performance of two portfolio allocation algorithms, which integrate Markov-switching models and Heiken Ashi candlestick patterns for trend identification, respectively. The research method used is a quantitative approach with experimental techniques or computational simulations that aim to test the performance of the algorithm in producing optimal portfolio weights. The portfolio model developed is an extension of the Markowitz model with two different integration approaches, namely the Markov-switching model and the Heiken Ashi candlestick pattern. Portfolio weight optimization on each algorithm is performed using the Generalized Reduced Gradient (GRG) method. The Markov-switching model is a time series model used to identify changes in the average market regime. In contrast, the Heiken Ashi pattern is used to detect trend changes in stock price movements. The time series data used consists of daily stock prices of Islamic stocks listed in the Jakarta Islamic Index (JII) during the period January 2019 to August 2022, obtained from the Indonesia Stock Exchange (IDX). This study finds that the Markowitz model integrated with the Markov-switching model is able to effectively identify market regimes and improve efficiency in portfolio weight optimization. These findings provide valuable insights for Islamic equity investors in their risk mitigation efforts while helping to align expected returns with long-term investment strategies that are adaptive to bullish and bearish market conditions.
COVID-19 RISK MAPPING AND LIFE INSURANCE ESTIMATION: MARKOV CHAIN MODEL FOR PREMIUMS AND BENEFITS IN BANDUNG CITY Nadwah, Hamidah Qurrotun; Mukhaiyar, Utriweni
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss1pp0239-0254

Abstract

The COVID-19 pandemic, first identified in China, rapidly spread worldwide and significantly impacted various sectors, including health and insurance. In Indonesia, regional disparities in case trends have highlighted the need for localized risk assessment. This study applies a Markov Chain model to estimate life insurance premiums and benefits by forecasting long-term COVID-19 transmission probabilities across 30 sub-districts in Bandung City. The analysis uses daily confirmed case data collected between September 18, 2020, and April 17, 2022, a period marked by multiple infection waves and heightened transmission risk. COVID-19 trends were categorized into discrete states—decrease, no change, and increase—and modeled to construct transition probability matrices and stationary distributions. These long-term probabilities were then used to generate a regional risk map and inform actuarial pricing of insurance products. The results reveal spatial heterogeneity in case increase probabilities, with Coblong, Arcamanik, and Antapani exhibiting the highest long-term risk. A strong correlation (R² = 0.9473) was found between case increase probabilities and projected insurance benefits and premiums. The practical implication of this study lies in its provision of a data-driven framework that enables insurance companies to align policy pricing with region-specific and evolving pandemic risks, including long-term health consequences such as post-COVID-19 conditions. This approach enhances both the fairness of premium structures and the financial resilience of insurers in managing future public health crises.
COMPARISON OF BINARY PROBIT REGRESSION AND FOURIER SERIES NONPARAMETRIC LOGISTIC REGRESSION IN MODELING DIABETES STATUS AT HAJJ GENERAL HOSPITAL SURABAYA Otok, Bambang Widjanarko; Zulfadhli, Muhammad; Pangesti, Riwi Dyah; Kurniawan, Muhammad Idham; Haryanto, Albertus Eka Putra; Darwis, Darwis; Kurniawan, Iwan
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss1pp0255-0270

Abstract

Diabetes mellitus is a chronic disease with a rising global prevalence, including in Indonesia. Early detection and accurate modeling are crucial for effective prevention and management. Binary Logistic Regression (BLR) is commonly used for binary outcome modeling; however, in practice, the relationship between binary outcomes and continuous predictors is often nonlinear, making BLR less suitable. To address these limitations, alternative methods such as Binary Probit Regression (BPR) and Flexible Semiparametric Nonlinear Binary Logistic Regression (FSNBLR) have been developed. This study aims to compare the performance of BLR, BPR, and FSNBLR models in classifying diabetes mellitus cases at Hajj General Hospital Surabaya. All three models were estimated using the Maximum Likelihood Estimation (MLE) method. Since the resulting estimators do not have closed-form solutions, numerical iteration using the Newton-Raphson method was applied. Model performance was assessed using Area Under the Curve (AUC), accuracy, sensitivity, and specificity. The FSNBLR model outperformed both the BLR and BPR models. It achieved the highest AUC value of 81.86%, while BLR (66.30%) and BPR (66.30%). That is indicated FSNBLR superior discriminative ability. In addition, the FSNBLR model recorded higher accuracy, sensitivity, and specificity compared to the other two models. The FSNBLR model demonstrated better predictive performance in identifying diabetes mellitus cases, especially in scenarios involving nonlinear relationships between predictors and the outcome variable. These findings suggest that flexible semiparametric approaches offer greater effectiveness in medical classification tasks, particularly for chronic conditions like diabetes mellitus.
PREDICTION OF THE INDONESIA COMPOSITE INDEX (ICI) USING THE ARCH GARCH APPROACH AND THE FOURIER SERIES Fadillah Mardianto, M. Fariz; Valida, Hanny; Putri, Farah Fauziah; Fauzi, Doni Muhammad; Pusporani, Elly
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss1pp0271-0286

Abstract

The Indonesia Composite Index (ICI) is a key indicator of stock market performance in Indonesia, often experiencing high volatility due to various domestic and global economic factors. In recent years, ICI has shown a significant upward trend, influenced by both local and international factors. In 2024, from June to October, the ICI saw a notable increase, reaching its highest value since 2020 at Rp 7,670. Despite fluctuations in stock prices, the rise in ICI reflects a positive outlook for the Indonesian stock market, attracting both domestic and foreign investors. This study aims to predict ICI movements using ARIMA-GARCH and Fourier Series approaches. The ARIMA model is employed to analyze time series data, while the ARCH-GARCH model addresses heteroskedasticity in residual variance. For comparison, the Fourier Series Estimator is applied to capture seasonal patterns in the data. Although ICI volatility is driven by a range of external macroeconomic and geopolitical factors, this study focuses on univariate modeling to evaluate the predictive capability of the index’s own historical movements, without involving exogenous variables. The data used comes from Investing.com. Weekly ICI data from March 2020 to June 2024 is used, split into training and testing sets. The analysis results indicate that the ARIMA-GARCH method provides higher accuracy, with a Mean Absolute Percentage Error (MAPE) of 5% (out-sample), compared to the Fourier Series method, which has a MAPE of 8.57%. This suggests that ARIMA-GARCH is more effective in predicting ICI trends, reflecting its ability to account for volatility and market changes more accurately.
MODIFIED STATISTICAL-BASED VALUE AT RISK FOR MULTI-OBJECTIVE OPTIMAL-BASED PORTFOLIO ANALYSIS OF INDONESIAN STOCK RETURN DISTRIBUTION Saputra, Wisnowan Hendy; Aqsari, Hasri Wiji
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss1pp0287-0298

Abstract

Basically, all stock investments aim to obtain maximum profit with low risk. The formation of a stock investment portfolio is always accompanied by measuring returns and risks that show its performance. Portfolio risk measurement is often faced with the challenge that returns are not normally distributed, so that measurements using the normality assumption cannot be applied. This study proposes the development of a modification of stock portfolio risk measurement so that it is not limited to the normality assumption. The development is carried out by modifying the calculation of Value at Risk (VaR) to consider the skewness and kurtosis values ​​(hereinafter referred to as modified VaR), so that the normal distribution assumption can be eliminated. As a method for compiling a stock portfolio, the Multi-Objective Optimization technique was chosen because it can modify risk averse so that the risk can be adjusted to the risk profile of each investor and is able to stabilize the mean return value. For its implementation, this paper uses real stock data which of course has returns that are not normally distributed, namely the four Indonesian stocks based on the largest capitalization recorded in January 2025 (blue chip), namely BREN, BBCA, BYAN, and BBRI obtained through finance.yahoo.com. The analysis method is divided into three steps, including multi-objective optimization completion, portfolio return calculation, and finally modified VaR estimation. The results of the study show that BBCA has the largest weight with a portion of more than 40% of the four stocks, so BBCA will be the priority stock for this portfolio. The portfolio formed using multi-objective optimization is proven to have a stable mean return because the portfolio mean return is between several of its constituent stocks (vice versa) which is around 0.01%, and the smallest estimated value of the portfolio modified VaR is 1.67%. Thus, a portfolio based on multi-objective optimization is not only able to create a portfolio that provides a small risk in risk measurement without assuming a normal distribution, but at the same time multi-objective optimization is also able to provide competitive returns with its constituent stocks.
ANALYSIS OF SMOKING AND COVID-19 MATHEMATICAL MODEL Oluwafemi, Temidayo Joseph; Miswanto, Miswanto
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss1pp0299-0312

Abstract

Smoking and COVID-19 have similar effects in the body system, i.e. damaging the airways and lung function. In this work, a mathematical model to study smoking and COVID-19 transmission was studied. The model was proven to have feasible region and it is well-posed mathematically and epidemiologically, the model was further proven to have positive solutions. The basic reproduction number was computed using the next generation method and sensitivity analysis was carried out. The results show that the disease-free equilibrium is locally and globally stable, the most sensitive parameter is the contact rate. The simulation shows that, curtailing rate of contact between exposed, infected individuals and susceptible human population will reduce the spread of the diseases, also giving attention to recovery strategies and controls will reduce to minimum the disease transmission. Therefore, it is recommended that stakeholders should give attention in controlling smoking habits, and prevention and treatment of COVID-19 infected individuals.
FORECASTING STATIONARY CLIMATE DATA USING AUTOREGRESSIVE MODELS AND HIGH-ORDER FUZZY Kayyisa, Alfien Diva; Sulandari, Winita; Slamet, Isnandar
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss1pp0313-0324

Abstract

Forecasting is essential for improving aviation safety, with air humidity being a critical factor influenced by air temperature. This study analyzes daily humidity data from I Gusti Ngurah Rai Airport, one of Indonesia’s busiest air stations, using two time series modeling approaches: Autoregressive (AR) and high-order fuzzy modeling. The objective is to evaluate and compare their forecasting accuracy. Historical daily data from the Meteorology, Climatology, and Geophysics Agency of Indonesia were used to build the forecasting models. The optimal linear AR model served as the foundation for constructing the AR high-order fuzzy model, which incorporates linguistic rules to capture nonlinear patterns. Both models were implemented and evaluated using the Mean Squared Error (MSE) metric. Results show that the AR(2) model outperforms the AR high-order fuzzy model, achieving a lower MSE of 13.23. This suggests that the AR(2) model provides more accurate humidity forecasts over the observed period. These findings offer practical insights for policymakers and decision-makers in forecasting daily humidity levels and supporting aviation operations. While the study confirms the effectiveness of traditional AR modeling, it also highlights limitations of the fuzzy approach, particularly its sensitivity to parameter tuning and data sparsity. The integration of high-order fuzzy modeling represents a novel contribution to this domain, though further refinement is needed to enhance its forecasting performance.

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