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All Journal International Journal of Public Health Science (IJPHS) Journal of Fundamental Mathematics and Applications (JFMA)
Permatasari, Anindita Henindya
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Decision Sciences, Operations Research & Management Health Professions

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MATHEMATICAL ANALYSIS OF A TUBERCULOSIS MODEL WITH TWO DIFFERENT STAGES OF INFECTION Permatasari, Anindita Henindya; Utomo, Robertus Heri Soelistyo
Journal of Fundamental Mathematics and Applications (JFMA) Vol 6, No 1 (2023)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v5i2.15723

Abstract

Tuberculosis is an infectious disease. This disease causes death and the world notes that Tuberculosis has a high mortality rate. A mathematical model of Tuberculosis with  two infection stages of individuals, pre infected and actively infected, is studied in this paper. The rate of treatment considered in this model. The stability analysis of the equilibrium is determined by the basic reproduction ratio. Routh Hurwitz linearization is used for investigate the local stability of uninfected equilibrium. While the global stability of endemic equilibrium is investigated by construct Lyapunov function. The effect of treatment in pre infected and actively infected stages can reduce the spread rate of Tuberculosis as shown in numerical simulation.
Global stability of SEIM tuberculosis model with two infection phases and medication effects Pratama, Jovian Dian; Permatasari, Anindita Henindya
International Journal of Public Health Science (IJPHS) Vol 14, No 3: September 2025
Publisher : Intelektual Pustaka Media Utama

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.11591/ijphs.v14i3.25899

Abstract

Tuberculosis (TB), caused by mycobacterium tuberculosis (MTB), remains a significant global health issue, leading to high morbidity and mortality rates despite being a preventable and curable disease. The dynamics of TB transmission and the effects of treatment are critical to improving disease management. This study aims to analyze the global stability of a susceptible, exposed, infected, medicated (SEIM) model for TB transmission, incorporating the effects of medication and infection phases on disease progression. A deterministic SEIM model is proposed, dividing the population into four compartments: susceptible, exposed, infected, and medicated. The model accounts for treatment effects, including non-permanent immunity and the potential dormancy of MTB. Stability analysis was conducted using Lyapunov functions to evaluate equilibrium points, and the basic reproduction number (ℜ0) was derived to determine disease dynamics. The analysis reveals that when ℜ0 < 1, the system is globally asymptotically stable at the non-endemic equilibrium, indicating disease eradication. Conversely, when ℜ0 >1, the system converges to the endemic equilibrium, signifying sustained transmission within the population. These findings highlight the critical role of treatment and infection dynamics in controlling TB spread. The SEIM model provides a comprehensive framework for understanding TB transmission dynamics and emphasizes the importance of reducing (ℜ0) through effective public health interventions. Further research is recommended to validate the model with empirical data and explore its applicability in different epidemiological settings.
Co-Authors Pratama, Jovian Dian Robertus Heri Sulistyo Utomo