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All Journal BAREKENG: Jurnal Ilmu Matematika dan Terapan Indonesian Journal of Statistics and Its Applications
Irfanullah, Asrul
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Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation Other

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APPLICATION OF COX PROPORTIONAL HAZARD REGRESSION FOR ANALYZING FACTORS INFLUENCING THE RECOVERY RATE OF PULMONARY TUBERCULOSIS PATIENTS Irfanullah, Asrul; Damamain, Ferina Lestari; Tuanaya, Nur Amaliya
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 2 (2024): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol18iss2pp0987-0996

Abstract

Pulmonary tuberculosis is a serious disease that requires special attention from the community and the Government of Indonesia, especially the Maluku Province. One commonly used analytical method in the health field is survival analysis. Survival analysis is a statistical method related to observing the period until the occurrence of an event or events. This study aims to model and identify factors that affect the recovery rate of patients with pulmonary tuberculosis in Ambon City using Cox Proportional Hazard regression. The results of the Hazard Ratio interpretation show that the variables that have a significant influence are chest pain and night sweats. Specifically, patients experiencing chest pain exhibit a recovery rate 0.487264 times faster than those devoid of such symptoms. Similarly, patients experiencing night sweats demonstrate a recovery rate of 0.619839 times faster than their counterparts not experiencing this symptom. This study highlights the imperative of recognizing and addressing symptoms like chest pain and night sweats in managing pulmonary tuberculosis in Ambon City.
COMPARISON OF SURVIVAL ANALYSIS USING ACCELERATED FAILURE TIME MODEL AND COX MODEL FOR RECIDIVIST CASE Arfan, Nuraziza; Irfanullah, Asrul; Hamidi, Muhammad Rozzaq; Mukhaiyar, Utriweni
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 1 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss1pp629-642

Abstract

Recidivists, or ex-prisoners who commit crimes after serving a prior sentence, pose a critical challenge to the criminal justice system. This study examines social and economic factors that may reduce the likelihood of recidivists being re-arrested. Using survival analysis, the probability that a recidivist could survive in society without being re-arrested could be estimated. The purpose of this work is to compare the AFT and Cox models to determine which provides a better fit to identify factors affecting the likelihood of re-arrest within one year after release and to statistically assess the impact of these factors. This study utilizes a stratified Cox model to address variables that violate the proportional hazards (PH) assumption. The analysis is limited to four types of AFT models: Weibull, log-normal, log-logistic, and exponential. Results show that the stratified Cox model provides the best fit, based on Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). This demonstrates the Cox model's robustness in analyzing survival data, accurately approximating the distribution of survival times without restrictive assumptions, unlike AFT models. The study reveals that recidivists who received financial aid upon release have a lower risk of re-arrest compared to those who did not, and each additional prior theft arrest increased the risk of re-arrest by 1.09193 times.
DYNAMIC MODELING OF CARBON DIOXIDE EMISSIONS USING HIGH-ORDER DIFFERENTIAL EQUATIONS AND NONLINEAR ESTIMATION Pasaribu, Udjianna Sekteria; Mahdiyasa, Adilan Widyawan; Irfanullah, Asrul
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/barekengvol20iss2pp1215-1228

Abstract

Carbon dioxide (CO₂) is one of the main factors contributing to global warming. As the second largest CO₂ emitter globally, the United States (US) faces increasing political and economic pressure to reduce its emissions. Historical emission data exhibits complex structural patterns characterized by linear growth, quadratic trends, and periodic oscillations. Most existing models fail to capture this multifaceted behavior. In this study, we propose a high-order differential equation to represent the dynamic behavior of CO₂ emissions in the US. The model integrates linear, quadratic, and oscillatory components to reflect both long-term and short-term fluctuations. Nonlinear parameter estimation techniques are employed to fit the model to historical emission data with high accuracy. The proposed model effectively captures historical emission behavior, demonstrating strong goodness of fit and identifying both trend and cyclical components. Model-based projections indicate a likely resurgence in emission growth over the next decade, raising concerns regarding compliance with climate commitments and potential exposure to international carbon pricing instruments. The findings highlight the value of combining differential equation modeling with nonlinear estimation in analyzing environmental systems. The main limitation of this study is that it focuses only on historical emission dynamics, without direct integration of socio-economic drivers. This gap, however, highlights opportunities for future research.
ARFIMA Modelling for Tectonic Earthquakes in The Maluku Region: Pemodelan ARFIMA untuk Kejadian Gempa Bumi Tektonik di Wilayah Maluku Kondo Lembang, Ferry; Sinay, Lexy Janzen; Irfanullah, Asrul
Indonesian Journal of Statistics and Applications Vol 5 No 1 (2021)
Publisher : Statistics and Data Science Program Study, SSMI, IPB University, in collaboration with the Forum Pendidikan Tinggi Statistika Indonesia (FORSTAT) and the Ikatan Statistisi Indonesia (ISI)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/ijsa.v5i1p39-49

Abstract

Maluku Province is one of the regions in Indonesia with a very active and very prone earthquake intensity because it is a meeting place for 3 (three) plates, namely the Eurasian, Pacific and Australian plates. In the last 100 years, the history of tectonic earthquakes with tsunamis that occurred in Indonesia was 25-30% occurring in the Maluku Sea and Banda Sea. Based on this fact, this study aims to analyze the incidence of tectonic earthquakes that occurred in the Maluku region and its surroundings using the Autoregressive Fractionally Integrated Moving Averages (ARFIMA) model which has the ability to explain long-term time series data (long memory). The results of the research data analysis show that the best model for predicting the number of tectonic earthquakes that occur in Maluku and its surroundings is ARFIMA (0; 0.712; 1) with an MSE value of 0.1156. Meanwhile, the best model for predicting the average magnitude of the number of tectonic earthquakes that occurred in Maluku and its surroundings is ARFIMA (0; -3,224 x 10-9; 1) with an MSE value of 0.01237. Based on the two best models, the prediction results obtained from the number of tectonic earthquakes and the average magnitude of the number of tectonic earthquakes that occurred in Maluku and its surroundings for the next three periods, namely the first period there were 31 tectonic earthquakes with an average magnitude of 4.38481 SR. the second period there were 32 tectonic earthquakes with an average magnitude of 4.38407, and the third period there were 32 tectonic earthquakes with an average magnitude of 4.38333.
Co-Authors Damamain, Ferina Lestari Ferry Kondo Lembang Hamidi, Muhammad Rozzaq Lexy Janzen Sinay, Lexy Janzen Mahdiyasa, Adilan Widyawan Nuraziza Arfan Pasaribu, Udjianna Sekteria Tuanaya, Nur Amaliya Utriweni Mukhaiyar