This study estimates parameters of the generalized modified Weibull (GM Weibull) distribution using the Maximum Likelihood Estimation (MLE) method with the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm. The GM Weibull distribution, which includes four parameters (lambda, theta, phi, tau), offers greater flexibility than Weibull distribution in modeling data with monotonic and bathtub-shaped hazard patterns. Parameter estimation was conducted on three datasets: simulated data with sample sizes of 50, 200, and 500 observations; survival data from 45 heart transplant patients; and health indicator data from 27 districts/cities in Central and South Kalimantan provinces. The results demonstrate that while the standard Weibull remains a parsimonious choice for simple monotonic data, the GM Weibull produces parameter estimates closer to theoretical values in small-to-medium samples and significantly lower deviance in complex datasets. Specifically, for the heart transplant data, the GM Weibull offered better modeling long-term survival tails (800--1,000 days), while for the health indicator data, it effectively accommodated central tendencies within asymmetric distributions. Although AIC and BIC favor standard Weibull, the GM Weibull accurately identifies underlying structural fluctuations and non-monotonic failure characteristics. This study confirms that the MLE-based GM Weibull distribution is one of the robust tools for researchers requiring a more representative model for complex survival and health data.

In insurance, risk can occur at any time, causing claims to sometimes have a large amount of value, so that insurance companies may not be able to satisfy claim payments. If these situations occur, insurance companies need claim reserves to prepare for such events. There are several methods to calculate claim reserves, such as aggregate claim reserving. However, certain claim characteristics involve dependencies among claims, which result in a lack of detailed information for individual claims. In addition, an increasing number of claims becomes more difficult to compute using traditional methods. Therefore, this research aims to calculate individual claim reserves using one branch of machine learning, namely the Backpropagation Algorithm. The Backpropagation Algorithm is believed to remain relevant compared to other algorithmic models because, in several studies, it produces relatively low values of Mean Absolute Percentage Error (MAPE), at approximately 2.70%. The data used in this research are simulated using R software, generating 10,000 claims over 20 years, consisting of 6,000 short-tailed claims and 4,000 long-tailed claims. The data model is evaluated using MAPE. The resulting MAPE value is 0.55%, indicating that the data are highly suitable for predictive modeling. The prediction results show that the total claims to be paid in the 21st development year reach Rp22,945,450,000,000, with an average claim amount of approximately Rp2,294,545,152. This research contributes to both informatics and actuarial science by developing an individual claim reserving approach to predict claim payments more efficiently.

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.

This study investigates the structure of conjugacy graphs formed from the conjugacy classes in the alternating group A4, the symmetric group S3, and their direct product A4 × S3. Using Mathematica, the conjugacy classes of each group are determined, and the corresponding conjugacy graphs are constructed to represent the relationships between the classes. The results show that the conjugacy graphs of A4 × S3 form a complete graph Kᵢ×ⱼ, where i and j are the number of conjugacy classes in A4 and S3, respectively. These findings indicate that the conjugacy structure of the direct product exhibits a distinctive combinatorial complexity derived from its component groups.

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.

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.

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.

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.

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.

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.