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All Journal JTAM (Jurnal Teori dan Aplikasi Matematika) Media Publikasi Promosi Kesehatan Indonesia (MPPKI)
Ramadani, Maya
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Mathematics Public Health

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A Stochastic Projection for Tuberculosis Elimination in Indonesia by 2030 Sasmita, Novi Reandy; Ramadani, Maya; Ikhwan, Muhammad; Munawwarah, Munawwarah; Rahayu, Latifah; Mardalena, Selvi; Ischaq Nabil Asshiddiqi, M.; Suyanto, Suyanto; Safira, Nanda
Media Publikasi Promosi Kesehatan Indonesia (MPPKI) Vol. 8 No. 11 (2025): November 2025
Publisher : Fakultas Kesehatan Masyarakat, Universitas Muhammadiyah Palu

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.56338/mppki.v8i11.8548

Abstract

Introduction: Indonesia, with the world's second-highest tuberculosis (TB) burden, has targeted TB elimination (65 cases per 100,000) by 2030. This study aimed to evaluate the feasibility of achieving this goal by projecting TB incidence trends using a stochastic epidemic model that accounts for the uncertainties inherent in TB transmission dynamics in latent TB infections. Methods: The initial values for state variables and parameters were derived from a comprehensive literature review and calibrated against publicly available epidemiological data from the Indonesian Ministry of Health reports from 2018-2022. A Susceptible, Vaccinated, Three Exposed, Three Infectious, Recovered (SVE3I3R) model was developed, incorporating Gaussian noise into the exposed compartments to simulate real-world unpredictability in latent infection dynamics. The model was solved numerically using the fourth-order Runge-Kutta (RK4) method in R software. Key outcomes measured were the projected incidence of drug-susceptible TB (DS-TB), multidrug-resistant TB (MDR-TB), and extensively drug-resistant TB (XDR-TB). Results: Model projections suggest that the overall TB incidence rate will fall from 387 cases per 100,000 people in 2023 to a projected 320 cases per 100,000 by 2030. However, this remains far above the national target. While DS-TB cases decreased to 730,283, MDR-TB and XDR-TB cases were projected to surge dramatically to 120,939 cases and 104,651 individuals, respectively. The estimation signals a critical shift in the epidemic's profile. Conclusions: Indonesia is not on track to achieve its 2030 TB elimination target under current interventions. The alarming rise of drug-resistant TB necessitates an urgent, aggressive, and multifaceted policy response. This study underscores the critical value of incorporating stochasticity into epidemiological models for more realistic forecasting and public health planning in high-burden settings.
Can Indonesia Eliminate Tuberculosis by 2030? A Deterministic Epidemic Model Approach Sasmita, Novi Reandy; Ramadani, Maya; Ikhwan, Muhammad; Rahayu, Latifah; Mardalena, Selvi; Suyanto, Suyanto; Safira, Nanda; Huy, Le Ngoc; Myint, Ohnmar
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 Huy, Le Ngoc Ischaq Nabil Asshiddiqi, M. Mardalena, Selvi Muhammad Ikhwan Muhammad Ikhwan Myint, Ohnmar Nanda Safira Raden Mohamad Herdian Bhakti RAHAYU, LATIFAH Sasmita, Novi Reandy Suyanto Suyanto