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Muh. Isbar Pratama
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Journal of Mathematics, Computation and Statistics (JMATHCOS)
Published by Universitas Negeri Makassar
ISSN : 24769487     EISSN : 27210863     DOI : https://doi.org/10.35580/jmathcos
Core Subject : Education,
Mathematics
Fokus yang didasarkan tidak hanya untuk penelitian dan juga teori-teori pengetahuan yang tidak menerbitkan plagiarism. Ruang lingkup jurnal ini adalah teori matematika, matematika terapan, program perhitungan, perhitungan matematika, statistik, dan statistik matematika.
Arjuna Subject : Matematika - Matematika Terapan
Articles 241 Documents
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Mathematical Modeling of Typhoid Fever Control Through Non-Pharmaceutical Interventions in South Sulawesi Fausiatul Iffa; Wahidah Sanusi; Alimuddin Alimuddin
Journal of Mathematics, Computations and Statistics Vol. 9 No. 1 (2026): Volume 09 Issue 01 (March 2026)
Publisher : Jurusan Matematika FMIPA UNM

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35580/74nj6t57

Abstract

Typhoid fever remains one of the major public health problems in Indonesia, particularly in South Sulawesi. This article discusses mathematical modeling of the impact of non-pharmaceutical interventions on typhoid fever control. This study aims to develop a mathematical model that represents the dynamics of typhoid fever transmission and to solve the model numerically using the Variational Iteration Method (VIM). The model applied is the SICRB compartment model, which divides the population into five groups: susceptible (S), infected (I), chronic carrier (C), recovered (R), and bacterial concentration (B). The analysis results indicate that the basic reproduction number R₀ > 1, suggesting that typhoid fever has the potential to persist in the population. Numerical simulations are carried out using Maple for analytical derivation and R Studio for visualization of the dynamics. The implementation of non-pharmaceutical interventions, including health education, environmental sanitation, and herbal treatment, demonstrates a significant reduction in infection cases, an increase in recovery, and a decrease in bacterial concentration. The model shows stability toward the endemic equilibrium and consistency between mathematical analysis and numerical simulations.
Comparison of Holt’s Exponenetial Smoothing and GARCH Models In Forecasting BNI Bank Stock Isma Muthahharah; Muhammad Fahmuddin; Muhammad Nusrang
Journal of Mathematics, Computations and Statistics Vol. 9 No. 1 (2026): Volume 09 Issue 01 (March 2026)
Publisher : Jurusan Matematika FMIPA UNM

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35580/a76hfv58

Abstract

This study aims to compare the forecasting performance of Holt’s Exponential Smoothing and the ARIMA–ARCH/GARCH models in predicting the stock return volatility of Bank Negara Indonesia (BNI). Accurate forecasting of financial time series is essential for investors, policymakers, and market analysts, particularly in emerging markets such as Indonesia, where volatility levels tend to fluctuate due to global and domestic economic conditions. The data used in this study consist of weekly closing prices of BNI stock from January 2020 to August 2025, which were transformed into weekly stock returns. The analysis began with descriptive statistics to examine the trend and volatility behavior of the return series. Holt’s Exponential Smoothing was employed to capture the level and trend components of the data. Meanwhile, the ARIMA–ARCH/GARCH modelling approach was applied to address conditional heteroskedasticity and volatility clustering, which are typical features of financial return data. Model diagnostics, including parameter significance, stationarity tests, and white-noise assessments, were conducted to ensure the suitability of the models. The forecasting accuracy of both models was evaluated using RMSE criteria. The results indicate that the ARIMA ([4],0,0)–ARCH (2) model provides the most accurate predictions, reflected by its lower RMSE value compared to Holt’s Exponential Smoothing. This finding demonstrates that volatility-sensitive models outperform trend-based smoothing methods when applied to financial data characterized by fluctuating variance. Overall, this study highlights the importance of selecting forecasting methods that align with the statistical behavior of financial time series. The findings offer valuable insights for investors, financial analysts, and economic policymakers seeking to improve forecasting accuracy and strengthen risk management strategies in dynamic market environments.
Development of a Hybrid ARIMA–Fourier Series Model for Air Temperature Forecasting at the Gorontalo Climatology Station Suci Tilome; Isran K. Hasan; Agusyarif Rezka Nuha
Journal of Mathematics, Computations and Statistics Vol. 9 No. 1 (2026): Volume 09 Issue 01 (March 2026)
Publisher : Jurusan Matematika FMIPA UNM

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35580/jmathcosv9i1.11462

Abstract

Air temperature is a key climatic variable that reflects environmental conditions and influences various human activities. Recent observations indicate a persistent upward trend associated with global warming, leading to greater variability in climate patterns. These changes highlight the importance of forecasting methods that can accurately represent the characteristics of air temperature time series to support planning and decision-making. Reliable prediction is therefore essential for understanding climate dynamics and anticipating potential environmental impacts. This study proposes an air temperature forecasting approach using a hybrid Autoregressive Integrated Moving Average (ARIMA) and Fourier Series Analysis (FSA) model. The ARIMA component is applied to model trend behavior and temporal dependence, while FSA captures the remaining seasonal patterns in the ARIMA residuals. By integrating these two approaches, the hybrid model aims to improve forecasting accuracy in the presence of both stochastic and periodic components. The results show that the hybrid ARIMA–FSA model achieves good forecasting performance, with a Mean Absolute Error (MAE) of 0.56, a Root Mean Square Error (RMSE) of 0.66, and a Mean Absolute Percentage Error (MAPE) of 2.07%. These findings indicate that the proposed model effectively represents air temperature dynamics and can be considered a reliable alternative for climate forecasting applications
Adaptive ANFIS–PSO Model for Forecasting Bird’s Eye Chili Prices in Gorontalo Province Nur Siyam Djibu; Isran K. Hasan; Agusyarif Rezka Nuha
Journal of Mathematics, Computations and Statistics Vol. 9 No. 1 (2026): Volume 09 Issue 01 (March 2026)
Publisher : Jurusan Matematika FMIPA UNM

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35580/jmathcosv9i1.11473

Abstract

Bird’s eye chili is one of the strategic food commodities in Indonesia with high price volatility and a significant contribution to food inflation, particularly in Gorontalo Province. The dynamic and nonlinear characteristics of bird’s eye chili prices often hinder accurate forecasting when using conventional methods, thereby requiring an adaptive approach capable of capturing complex data patterns. Therefore, this study applies an Adaptive Neuro-Fuzzy Inference System (ANFIS) optimized using Adaptive Particle Swarm Optimization (PSO) to improve the accuracy of bird’s eye chili price forecasting. This study utilizes daily bird’s eye chili price data in Gorontalo Province from 1 January 2019 to 31 October 2025, obtained from the National Strategic Food Price Information Center (PIHPS). The ANFIS model is optimized using adaptive PSO to obtain optimal parameter values that address local convergence problems and parameter sensitivity commonly encountered in conventional ANFIS models. Model performance is evaluated using the Mean Absolute Percentage Error (MAPE). The results indicate that the adaptive ANFIS–PSO model achieves a MAPE value of 17.4487% on the training dataset, which decreases significantly to 5.0741% on the testing dataset. The testing MAPE value below 10% demonstrates that the proposed model has excellent generalization capability in capturing bird’s eye chili price fluctuations. These findings confirm that adaptive PSO-based parameter optimization effectively enhances ANFIS performance in modelling nonlinear and highly volatile time series data. The proposed forecasting model can serve as a reliable analytical tool to support decision-making and regional food price stabilzation policies in Gorontalo Province.
Application of the Logistic Growth Model for Forecasting Population Dynamics in Makassar Pratama, Muhammad Isbar; Ja'faruddin, Ja'faruddin; Ansi, Ansi
Journal of Mathematics, Computations and Statistics Vol. 9 No. 1 (2026): Volume 09 Issue 01 (March 2026)
Publisher : Jurusan Matematika FMIPA UNM

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35580/abd0sq36

Abstract

The continuous increase in population requires accurate forecasting methods to support development planning. This study aims to apply the logistic model to forecast the population of Makassar City using data from the Central Bureau of Statistics (BPS) for the period 2015–2024. The research employed a quantitative descriptive method with logistic differential equation modeling. The carrying capacity (K) parameter was determined analytically, while the growth rate (r) was calculated annually, resulting in nine different logistic models. The accuracy of each model was evaluated using the Mean Absolute Percentage Error (MAPE) to identify the best model. The results indicate that the ninth logistic model produced the smallest MAPE value of 1,95% and was used to project the population for 2030–2035. Based on this model, the population of Makassar City is projected to reach 1,495,521 people in 2030 and increase to 1,510,058 people in 2035. These findings demonstrate that the logistic model can serve as an effective tool for population growth forecasting to support sustainable development planning.
SDF Mathematical Model as a Solution to Overcoming Difficulties in Completing Thesis of Students of Mathematics Department of Makassar State University Wahidah Sanusi; Syafruddin Side; Muh. Ishaq Firdaus
Journal of Mathematics, Computations and Statistics Vol. 9 No. 1 (2026): Volume 09 Issue 01 (March 2026)
Publisher : Jurusan Matematika FMIPA UNM

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35580/qh78b575

Abstract

This study aims to develop and analyze the SDF mathematical model in addressing difficulties faced by students in completing their theses at the Mathematics Department, Universitas Negeri Makassar, in 2023. The SDF model is derived from the SIR model, which is commonly utilized to analyze disease spread, by adapting specific assumptions relevant to the students' circumstances. The analysis of the model focuses on determining equilibrium points, model stability, and the basic reproduction number , which serves as a critical parameter in understanding the dynamics of the issue's spread. Data for the study were collected from students in the Mathematics Department, Faculty of Mathematics and Natural Sciences, Universitas Negeri Makassar, and were used for model simulations employing Maple 18 software. The analysis results indicate a basic reproduction number value of , implying that the number of students experiencing difficulties in completing their theses is expected to increase over time without intervention. These findings provide valuable insights for the university to comprehend the factors influencing the thesis completion rates among students. It is anticipated that this study can inform the design of more effective strategies and interventions to assist students in overcoming their challenges. The SDF model can also serve as a reference for similar studies in other contexts
A Mathematical Model with Time Delay for Addressing Online Game Addiction Through Family Time Intervention Based on Local Wisdom in South Sulawesi Muhammad Abdy; Syafruddin Side; Yusuf Ramadana; Andi Muh. Ridho Yusuf SAP
Journal of Mathematics, Computations and Statistics Vol. 9 No. 2 (2026): Volume 09 Issue 02 (June 2026)
Publisher : Jurusan Matematika FMIPA UNM

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35580/1qyqb214

Abstract

This study analyzes the dynamics of online game addiction among FMIPA UNM students using a modified time-delayed SEAFR (Susceptible–Exposed–Addicted–Family time–Recovered) mathematical model. Online game addiction is a growing concern that threatens academic performance and social well-being. The research applies a five-stage methodology: (1) literature review of SIR-based models and digital addiction studies to identify compartments and parameters; (2) data collection from 400 students through proportionate stratified random sampling; (3) model development incorporating time delay, cultural norms, and family-based interventions; (4) equilibrium and stability analysis using Jacobian matrices and Routh–Hurwitz criteria; and (5) numerical simulations with MATLAB to evaluate intervention strategies. The analysis yields a basic reproduction number, R₀ = 0.5, indicating that addictive behavior tends to decline without reinforcement of exposure. However, the endemic equilibrium remains locally asymptotically stable, suggesting addiction may persist if interventions are weak. Simulation results highlight that reducing exposure (β), enhancing recovery through awareness and cultural support (γ), and strengthening family-based activities significantly reduce addiction prevalence. These findings show the usefulness of mathematical modeling as a decision-support tool contextualized by local wisdom, offering practical insights for policymakers and educators in designing effective interventions to address student addiction.
Hybrid Machine Learning and Numerical Method Model (SVR-ABM-Milne-Simpson) the Influence of Unemployment on Poverty Rate Prediction Variska Anjani; Hisyam Ihsan; Syafruddin Side
Journal of Mathematics, Computations and Statistics Vol. 9 No. 2 (2026): Volume 09 Issue 02 (June 2026)
Publisher : Jurusan Matematika FMIPA UNM

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35580/dh80wh85

Abstract

The poverty rate in South Sulawesi Province remains a complex socio-economic issue that is closely linked to fluctuating unemployment levels each year. The imbalance between economic growth and labor absorption has increased the risk of poverty in several regions. Therefore, this study aims to analyze the effect of the unemployment rate on poverty in South Sulawesi Province through the development of a hybrid model based on machine learning and numerical methods, combining Support Vector Regression (SVR), Adams–Bashforth–Moulton (ABM), and Milne–Simpson approaches. The SVR model was employed to predict the Open Unemployment Rate (OUR), with the best performance achieved using the Radial Basis Function (RBF) kernel and k-fold = 8, resulting in a MAPE of 6.69% and R² of 0.92, indicating high predictive accuracy. Furthermore, the relationship between unemployment and poverty was formulated in the form of an ordinary differential equation (ODE) as follows: dp/dt= -1-0.195277U(t)-0.00907P(t). Where U(t) represents the unemployment rate and P(t) represents the poverty rate over time. Numerical simulations demonstrated that both the ABM and Milne–Simpson methods were capable of reconstructing the dynamic behavior of poverty levels with high accuracy, producing MAPE values of 2.09% and 4.04%, respectively. The results indicate that the hybrid SVR–ABM–Milne–Simpson model is effective in generating stable poverty predictions that closely approximate actual data. Among the two numerical methods, ABM outperformed Milne–Simpson, yielding smaller prediction errors and better numerical stability in terms of convergence behavior. In summary, this hybrid modeling framework provides a robust analytical and computational approach for understanding and forecasting the socio-economic interplay between unemployment and poverty in South Sulawesi.
Analysis of the Relationship between Literacy, Numeracy and School Accreditation Rankings in Sulawesi Using Ordinal Logistic Regression and K-Nearest Neighbors Andi Illa Erviani Nensi; Dela Gustiara; Shalshabilla Shafa; Budi Susetyo
Journal of Mathematics, Computations and Statistics Vol. 9 No. 2 (2026): Volume 09 Issue 02 (June 2026)
Publisher : Jurusan Matematika FMIPA UNM

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35580/mka1m371

Abstract

This study aims to analyze the relationship between literacy and numeracy achievement and school accreditation rankings in the Sulawesi region and to compare the performance of two classification methods, namely ordinal logistic regression and the nearest neighbor method. The data used came from the results of the 2023 and 2024 national school assessments with response variables in the form of tiered school accreditation rankings and predictor variables in the form of literacy and numeracy scores. The analysis began with data exploration to understand the characteristics of distribution and class imbalance, then continued with modeling using two scenarios, namely without and with extreme value handling. Ordinal logistic regression was constructed using a cumulative probability approach and tested through assumption checking, parameter significance, and performance evaluation. The nearest neighbor method was applied through data normalization and parameter tuning to obtain the optimal configuration, and compared between conditions with and without class balancing. The results showed that literacy, especially in 2024, had a significant effect on increasing the probability of higher school accreditation, with an ordinal logistic regression model accuracy rate of around 58% and a balanced accuracy of around 65%. The KNN method produced higher prediction accuracy, around 66%, but had limitations in distinguishing minority classes. These findings emphasize the importance of literacy as a key indicator of school quality and provide a basis for selecting classification methods according to the analysis objectives.
Modelling Extreme Stock Market Risk with Peaks Over Threshold-Value at Risk and APARCH Specifications Aulia Khairani Hutabarat; Ayu Sofia; Muklas Rivai
Journal of Mathematics, Computations and Statistics Vol. 9 No. 2 (2026): Volume 09 Issue 02 (June 2026)
Publisher : Jurusan Matematika FMIPA UNM

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35580/hcm5vr15

Abstract

The capital market plays an important role in a country's economy. Through the capital market, investors can also grow their wealth by investing in stocks, bonds, or other instruments. Investing in stocks in the capital market has high profit potential, but also carries significant volatility risks. One company that experienced significant volatility was PT Indofood Sukses Makmur Tbk., as in 2020 when the COVID-19 pandemic caused extreme volatility in global and local markets. Therefore, risk management is necessary to minimize risks using the Value at Risk method.This study also aims to analyze the risk of investing in PT Indofood Sukses Makmur Tbk. shares using the VaR method with APARCH modeling and the POT approach. The data used are daily closing prices from March 2020 to June 2025. The results show that the best model for forecasting is APARCH(1,1) with a better forecasting accuracy than the naive forecast, as indicated by the MASE value of 0,6131. The VaR estimate indicates that the longer the forecasting period and the higher the confidence level used, the higher the VaR value. This indicates that the extreme risk is higher for the next ten periods. The validity test (backtesting) also confirms that the VaR estimation results are accurate for the long term at a significance level of 1%, 5% and 10%.

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