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Jl. Prof. Dr. Ing. B. J. Habibie, Moutong, Tilongkabila, Kabupaten Bone Bolango, Gorontalo, Indonesia
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Jambura Journal of Mathematics
Published by Universitas Negeri Gorontalo
ISSN : 26545616     EISSN : 26561344     DOI : https://doi.org/10.34312/jjom
Core Subject : Education,
Mathematics
Jambura Journal of Mathematics (JJoM) is a peer-reviewed journal published by Department of Mathematics, State University of Gorontalo. This journal is available in print and online and highly respects the publication ethic and avoids any type of plagiarism. JJoM is intended as a communication forum for mathematicians and other scientists from many practitioners who use mathematics in research. The scope of the articles published in this journal deal with a broad range of topics, including: Mathematics; Applied Mathematics; Statistics; Applied Statistics.
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Articles 165 Documents
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Parameter Estimation of Mixed Geographically Weighted Bivariate Zero-Inflated Negative Binomial Regression Model Islamiati, Mawadah Putri; Purhadi, Purhadi; Wibawati, Wibawati
Jambura Journal of Mathematics Vol 7, No 2: August 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v7i2.32711

Abstract

The Bivariate Zero-Inflated Negative Binomial (BZINBR) regression model is commonly used to analyze two correlated count response variables characterized by overdispersion and excess zeros. To account for spatial heterogeneity in predictor effects, the BZINBR model has been extended into the Geographically Weighted BZINBR (GWBZINBR) model. However, predictor effects are not always entirely local; certain global effects may persist across regions. This study proposes the Mixed Geographically Weighted BZINBR (MGWBZINBR) model, which integrates both global and local parameter structures for modeling spatially correlated bivariate count data. The theoretical framework of the MGWBZINBR model is developed, including the derivation of the log-likelihood function, parameter estimation procedures, and hypothesis testing. Parameter estimation is conducted using the Maximum Likelihood Estimation (MLE) method via the iterative Berndt–Hall–Hall–Hausman (BHHH) algorithm. Given the complexity of the likelihood equations and the absence of closed-form solutions, numerical optimization is employed to ensure convergence and stability. The MGWBZINBR model offers a flexible and robust framework for analyzing spatial count data with excess zeros and complex dependency structures. It can be applied in various fields, including public health, ecology, and transportation analysis, to understand the influence of both local and global predictors on spatial phenomena. As the focus of this paper is methodological, empirical and simulation-based applications are intentionally excluded.
Conditional Value at Risk Portfolio With Monte Carlo Control Variates Maga, Fahmi Giovani; Sulistianingsih, Evy; Satyahadewi, Neva
Jambura Journal of Mathematics Vol 7, No 2: August 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v7i2.30952

Abstract

Stock investment is one of the instruments investors favor due to its potential for high returns, but the risks stemming from stock price volatility cannot be overlooked. Value at Risk (VaR) is commonly used as a standard approach to measure and manage these risks. However, VaR has limitations in handling extreme risks, making Conditional Value at Risk (CVaR) is a more effective choice. This research measures the application of CVaR to a portfolio of banking sector stocks in Indonesia using the Monte Carlo Control Variates (MCCV) technique, with the Indonesia Composite Index (ICI) as the control variable. The portfolio consists of stock of PT Bank Rakyat Indonesia Tbk (BBRI) and PT Bank Negara Indonesia Tbk (BBNI). The purpose of this research is to compare CVaR calculation results using Standard Monte Carlo Simulation (MCS) and MCCV simulations. The data used includes the daily closing prices of BBRI, BBNI, and ICI stocks for the period from March 1, 2023, to February 29, 2024. The VaR and CVaR calculated in this study are for one day. The results of the analysis show that the MCS CVaR values at 90%, 95%, and 99% confidence levels are 1.730%, 2.050%, and 2.569%, respectively, while the MCCV CVaR values at 90%, 95%, and 99% confidence levels are 1.400%, 1.662%, and 2.084%, respectively. These values indicate that using the ICI as a control variable has successfully improved risk estimation by utilizing the ICI as a control variable.
Pemodelan Deret Waktu Menggunakan Non-linear Autoregressive Neural Network: Studi Kasus Prediksi Harga Saham Mandiri Najib, Mohamad Khoirun; Nurdiati, Sri
Jambura Journal of Mathematics Vol 7, No 2: August 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v7i2.33397

Abstract

Accurate stock price forecasting is critical for investment decision-making, yet the nonlinear and complex nature of time series data poses significant challenges. This study investigates the application of the Nonlinear Autoregressive Neural Network (NARNN) for modeling the monthly stock price time series of PT Bank Mandiri (Persero) Tbk (BMRI) from January 2011 to December 2023. The model is constructed by exploring combinations of feedback delays and hidden neurons to identify the optimal configuration based on the root mean squared error. The dataset is divided into training, validation, and testing. Evaluation results show that the configurations 8–12 and 8–13 yield the best testing accuracy with a MAPE of 4.71%. An ensemble mean strategy is also employed, producing competitive and stable performance. These findings demonstrate that the NARNN approach effectively captures nonlinear patterns in stock data and holds promise for financial forecasting applications.
Dynamical Analysis of Online Shopping with Beauty Influencer Andani, Meri Teri; Zulaikha, Zulaikha
Jambura Journal of Mathematics Vol 7, No 2: August 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v7i2.33363

Abstract

This study develops a modified nonlinear mathematical model of online shopping dynamics that explicitly incorporates the direct influence of beauty influencers through promotional content (F) and a parameter α for transition from offline to online shopping without the influence of influencers. The model comprises offline shoppers (L), online shoppers (O), and the amount of promotional content created by beauty influencers (F). Stability analysis shows two equilibrium points: an online shopping-free state E1 locally asymptotically stable when R0 1 and an endemic state E2 locally asymptotically stable when R0 1. Numerical simulations using MATLAB R2013a confirm the analysis, revealing that higher promotional content growth rates (k) and lower decline rates (θ) increase R0 and the online shoppers population. The novelty lies in explicitly modeling influencer-based promotional content as a driver of shopping behavior, offering strategic insights for sustained engagement and customer retention in beauty sector digital marketing.
Model Matematika Penyebaran Penyakit Demam Berdarah Dengue dengan Faktor Kesadaran Sosial: Analisis dan Simulasi Djuma, Clara Anggriani; Achmad, Novianita; Nuha, Agusyarif Rezka; Hasan, Isran K.; Arsal, Armayani
Jambura Journal of Mathematics Vol 7, No 2: August 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v7i2.33921

Abstract

Dengue haemorrhagic fever (DHF) is a serious health problem in many tropical regions, including Indonesia. The spread of this disease is influenced by various factors, one of which is the level of social awareness in the prevention and control of infection. This study developed a mathematical model of DHF spread by integrating social awareness as an additional compartment. The model was analysed by determining the equilibrium points and the basic reproduction number (R0), as well as stability analysis using the Routh–Hurwitz criterion. The analysis results show the existence of two types of equilibrium points: the disease-free equilibrium point (T1) and the endemic equilibrium point (T2). Point T1 is locally asymptotically stable when R0 1 and unstable when R0 1, while point T2 is locally asymptotically stable when R0 1. Sensitivity analysis shows that the social awareness parameter significantly influences the value of R0. Additionally, numerical simulations indicate that increasing social awareness can effectively reduce disease spread and drive the system toward a disease-free state. These findings underscore the importance of community-based awareness interventions in dengue control strategies.
Predator-Prey Dynamics in the Interaction of HIV Virus with CD4+T Cells Andika, Fadly; Sukarsih, Icih
Jambura Journal of Mathematics Vol 7, No 2: August 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v7i2.33911

Abstract

This study analyzes the interaction dynamics between the human immunodeficiency virus (HIV) and CD4+T cells using a predator–prey mathematical model, in which HIV is represented as the predator and CD4+T cells as the prey. The model aims to describe the long-term behavior of the immune system when challenged by the virus. Analytical results show that the system has two equilibrium points: a disease-free equilibrium E1 and an endemic equilibrium E2, whose explicit forms are derived in closed form. Stability analyses of both the disease-free and endemic states are conducted through system linearization, Jacobian matrix formulation, and application of the Routh–Hurwitz criteria. The disease-free state is found to be locally asymptotically stable when the viral elimination rate by the immune system exceeds a specific threshold determined by the balance between viral infection and CD4+T cell production, indicating that under certain conditions the immune system can suppress the virus naturally. The endemic state, representing chronic infection, is stable when the combined effects of viral replication and immune response surpass the rate at which healthy CD4+T cells are lost, implying that the virus can persist within the host. Numerical simulations in Python, using parameter values from previous studies, confirm the coexistence of the virus and host cells under specific conditions. The findings emphasize the influence of viral replication and immune response rates on system stability, offering insights into how HIV can maintain chronic infection without completely depleting CD4+T cells.
A Comparative Study of Linear and Quadratic Spline Regression Models for Predicting HbA1c Levels in Patients with Diabetes Mellitus Arifin, Samsul; Anggraini, Dewi; Salam, Nur
Jambura Journal of Mathematics Vol 7, No 2: August 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v7i2.33292

Abstract

HbA1c is widely recognized as a key clinical indicator for monitoring and controlling diabetes, as it reflects average blood glucose levels over the preceding 2–3 months and is closely linked to the risk of complications. This study compares linear and quadratic truncated spline regression models for predicting HbA1c levels in patients with diabetes mellitus. The analysis used retrospective medical record data from a hospital in Makassar, Indonesia, collected in 2023. Fasting blood glucose and LDL cholesterol were included as predictors, with HbA1c as the response variable. Truncated spline regression was applied to capture nonlinear associations between predictors and HbA1c, and the comparison focused on linear versus quadratic specifications. The selection of the best model was based on the minimum GCV value. The model selection process indicated that the best specification was the linear truncated spline regression with two knot points. For FBG, the optimal knots were located at 159 mg/dL and 368 mg/dL, yielding the lowest GCV value of 3.5798. For LDL cholesterol, the best fit was achieved with knots at 183 mg/dL and 191 mg/dL, resulting in a GCV value of 4.3325. The predictive performance of this model was further supported by an R² value of 0.3861, indicating that the linear spline with two knots provides a better fit compared with the quadratic spline alternative. The spline approach showed a better fit based on GCV in depicting the changes in the influence of predictors on HbA1c, suggesting its potential as a more accurate predictive model for clinical and epidemiological purposes.
Microclimatic Temperature Variability and Trends in Bengkulu Province: ANOVA and Regression-Based Analysis Norfahmi, Siti Hairunnisa; Samdara, Rida; Supiyati, Supiyati; Lestari, Wina Ayu
Jambura Journal of Mathematics Vol 7, No 2: August 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v7i2.33376

Abstract

This study investigates the microclimatic variability and trends of air temperature across three meteorological stations—Fatmawati, Bengkulu, and Kepahiang—in Bengkulu Province, Indonesia. Using five years of daily data (June 2020 to May 2025), minimum (Tmin), maximum (Tmax), and average (Tavg) temperatures were analyzed to understand both spatial patterns and temporal changes in surface air temperature. One-way ANOVA was conducted to assess whether mean temperatures differed significantly across stations, followed by Tukey  post hoc test for pairwise comparisons. The analysis revealed a consistent and statistically significant difference in all temperature variables (p 0.05), particularly between the inland highland station (Kepahiang) and the two coastal stations. In addition, monthly averages of Tavg were analyzed using simple linear regression, with significance tested via regression-based ANOVA. All three stations exhibited statistically significant warming trends (p 0.005), with slopes ranging from +0.0152 to +0.0213 °C/month (~0.18–0.26 °C/year), despite relatively modest coefficients of determination (R² = 0.14–0.24). These results highlight a dual climatic dynamic in the region: strong seasonal and spatial variability, overlaid with emerging baseline warming. The study underscores the importance of localized climate analysis for adaptation planning, particularly in topographically diverse tropical regions facing increased exposure to climate variability and change.
Estimasi Produksi Beras dengan Estimator Campuran Spline Truncated – Kernel di Jawa Timur Dani, Andrea Tri Rian; Putra, Fachrian Bimantoro; Budiantara, I Nyoman; Ratnasari, Vita
Jambura Journal of Mathematics Vol 7, No 2: August 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v7i2.33379

Abstract

This study aims to apply a nonparametric regression model using a mixed estimator of Truncated Spline and Kernel to estimate Rice Production in East Java Province. This model combines several predictor variables, namely Harvested Area of Rice Plants, Rice Productivity, Population, and Human Development Index. The selection of the best combination of variables is based on the lowest Generalized Cross-Validation (GCV) value to obtain a stable and accurate model. The results show that the model with a combination of variables Harvested Area of Rice Plants and Rice Productivity set as Truncated Spline components with three knot points, and Population and Human Development Index as Kernel components produces a minimum GCV value of 85,504,949, RMSE of 242,723.6, and R² of 91.24%. This model successfully captures non-linear relationship patterns and provides more stable estimates. The implication of this finding is that the resulting model can be used to design more efficient agricultural policies, by considering the factors that interact dynamically in rice production.
Stability Analysis and Numerical Simulation of Prey-Mesopredator-Apex Predator Dynamic Model with Supplementary Food for Apex Predator Resmawan, Resmawan; Handayani, Rizka Putri; Rosydah, Binti Mualifatul; Qur'ani, Fahma Mu'jizatil
Jambura Journal of Mathematics Vol 7, No 2: August 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v7i2.31345

Abstract

This study formulates and mathematically analyzes a three-species dynamic model involving prey, mesopredator, and apex predator, considering the presence of supplementary food available only to the apex predator. The model is expressed as a three-dimensional nonlinear differential equation system and analyzed by proving the existence and uniqueness of solutions, positivity, and solution limitations to ensure mathematical validity in the biological domain. Furthermore, we study the local stability of the six equilibrium points of the system using the eigenvalue approach and the Routh-Hurwitz criterion. We perform numerical simulations and find that the stability of the system is highly sensitive to the parameters of predation efficiency and the capacity to utilize additional food. In addition, species extinction, dominance, or long-term coexistence also occur. The model shows how the relationships between different species and the support from external energy sources can change the community structure and affect whether predator species survive.

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