Dynamical System of Tuberculosis Considering Lost Sight Compartment

  • Heizlan Muhammad
  • Paian Sianturi
  • Endar H. Nugrahani
Keywords: Tuberculosis, HIV, Equilibrium


In this study, a model for the tuberculosis infection considering vaccination and lost-sight compartement is formulated. there are six populations in this model, Susceptibled, vaccinated, exposed, lost sight, infected, and recovered. The lost sight populations are infected but do not get any treatment and still can spread the tuberculosis, the infected population are infected but already got a treatment and no longer spread the tuberculosis. The local stability are obtained by analyzing the epidemic threshold . The result shows that the disease-free equilibrium is locally asymptotically stable when the condition <1 is satisfied, and the unique endemic equilibrium exist and it is locally asymptotically stable if >1 is satisfied. The numerical simulation are also performed to support the analytical result.


Download data is not yet available.


Apriliani V. (2016). Dynamical system of tuberculosis with vaccination. Magister Thesis of Bogor Agricultural University.

Castillo-Chaves C & Song B. (2004). Dynamical models of tuberculosis and their applications. Mathematical Biosciences and Engineering, 1(2), 361-404.

CDC. (2019). Center for disease control and prevention. Available at: www.cdc.gov/tb/topic/drtb/drfault.html

Diekman O. et al. (2009). The construction of next generation matrix for compramental Epidemics Models. Journal of The Royal Society Interface, 7, 873-885.

Hymann JM & Stanley EA. (1988). Using mathematical models to understand the AIDS epidemic. Mathematical Biosciences, 90, 415-473.

Nakul C. et al. (2008). Determining important parameters in the spread of malaria through the sensitivity of a mathematical model. Bulletin ofMathematical Biology, 70(5), 1272-1296.

Ministry of Health Republic of Indonesia. (2016). Tuberkulosis: Temukan, obatisampaisembuh. Jakarta (ID). Ministry of Health.

Temgoua A. et al. (2018). Global properties of a tuberculosis model with lost sight and multi-compartment of latents. Journal of Mathematical Modelling, 6, 47-76.

TU PNV. (1994). Dynamical system, An introduction with application in economics and biology. New York (US): Spinger-Verlag.

Van DDP & Watmough J. (2002). Reproduction numbers and sub-threshold endemic equilibria for compartemental models of disease transmission. Mathematical Biosciences, 180, 29-48.

World Health Organization. (2018). Global tuberculosis report. Available at: https://apps.who.int/iris/bitstream/handle/10665/274453/9789241565646-eng.pdf

Ministry of Health Republic of Indonesia. (2018). Sinergisme pusatdan Daerah dalam mewujudkan universal health coverage (UHC) melalui Percepatan Eliminasi Tuberkulosis. Jakarta (ID). Ministry of Health.

How to Cite
Heizlan Muhammad, Paian Sianturi, & Endar H. Nugrahani. (2019). Dynamical System of Tuberculosis Considering Lost Sight Compartment. International Journal of Engineering and Management Research, 9(3), 1-6. https://doi.org/10.31033/ijemr.9.3.1