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All Journal JTAM (Jurnal Teori dan Aplikasi Matematika)
Selvi Mardalena
Department of Statistics, Universitas Syiah Kuala
Mathematics

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Understanding Spatial Variability of Human Development Index in Aceh: A Geographically Weighted Regression Approach Selvi Mardalena; Latifah Rahayu; Novi Reandy Sasmita; Raihan Hayati; Arhamun Nisa; Nurul Ummah; Septia Devi Prihastuti Yasmirullah
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 2 (2026): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i2.35734

Abstract

The Human Development Index (HDI) is an important indicator in measuring people's quality of life, which includes education, health and economic dimensions. In Aceh Province, HDI achievements show inequality between regions, especially between coastal and inland areas. This study employs a quantitative spatial analysis to examine socio-economic determinants of HDI across districts using the Geographically Weighted Regression (GWR). The analysis utilized 2023 secondary data from the Central Bureau of Statistics (BPS), integrating HDI with key indicators of labor conditions, poverty, education, health, and regional economic performance. The global linear regression model was compared with GWR models using adaptive Gaussian and bisquare kernel weighting function, with model selection based on the Akaike Information Criterion (AIC). The results show that the GWR model with an Adaptive Gaussian Kernel weighting function outperformed the global regression model, indicating strong spatial non- stationarity in the relationships between HDI and its determinants. The average years of schooling, labor force participation rate, open unemployment rate, percentage of poverty, life expectancy, expenditure per capita, gross regional domestic product, and expected years of schooling have a significant effect on HDI in Aceh, but their contribution varies across districts. This study contributes to the literature by providing spatially explicit evidence to support region-based development policies, emphasizing the need for differentiated interventions to reduce interregional inequality and promote more equitable human development across Aceh Province.
Can Indonesia Eliminate Tuberculosis by 2030? A Deterministic Epidemic Model Approach Novi Reandy Sasmita; Maya Ramadani; Muhammad Ikhwan; Latifah Rahayu; Selvi Mardalena; Suyanto Suyanto; Nanda Safira; Le Ngoc Huy; Ohnmar Myint
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 1 (2026): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i1.35252

Abstract

Indonesia, bearing the world’s second-highest tuberculosis (TB) burden, has mandated a national target to eliminate TB by 2030, aiming for an incidence rate of 65 per 100,000 population. This study aims not only to project future transmission dynamics but also to systematically explore the specific epidemiological barriers, namely, drug resistance and relapse mechanisms, that hinder achieving this goal. To address the heterogeneity of TB transmission, we developed a novel deterministic SVE3I3R model. This framework stratifies the population into vaccinated, latent Tuberculosis Infection (LTBI), and infectious compartments, explicitly distinguishing among Drug-Susceptible (DS-TB), Multidrug-Resistant (MDR-TB), and Extensively Drug-Resistant (XDR-TB) strains. The resulting system of ordinary differential equations was solved numerically using the fourth-order Runge-Kutta (RK4) method to ensure stability and accuracy in simulating long-term epidemiological trends from 2023 to 2030. Parameters were calibrated using national reports and literature specific to the Indonesian context. Projections indicate that Indonesia will miss the 2030 elimination target by a significant margin. The model forecasts a TB incidence rate of 321 per 100,000 population by 2030, nearly five times the national benchmark. The analysis reveals that failure to reach the target is mechanistically driven by a "relapse trap" among recovered individuals and an alarming exponential surge in resistant strains (MDR-TB and XDR-TB). These findings suggest that current control strategies are insufficient not merely in scale but in structure. Evidence-based policy must urgently shift from standard intervention to aggressive interruption of resistance pathways and enhanced management of the latent reservoir to prevent the projected demographic resurgence.
Co-Authors Arhamun Nisa Latifah Rahayu Le Ngoc Huy Maya Ramadani Muhammad Ikhwan Nanda Safira Novi Reandy Sasmita Nurul Ummah Ohnmar Myint Raihan Hayati Septia Devi Prihastuti Yasmirullah Suyanto Suyanto