Stability Analysis of Model tuberculosis Spread in Diabetes Mellitus Patients with Treatment Factors
DOI:
https://doi.org/10.20956/jmsk.v17i1.10245Keywords:
Tuberkulosis, Diabetes Mellitus, Titik KesetimbanganAbstract
Diabetes mellitus (Dm) is a disease associated with impaired immune function so it is more susceptible to get infections including Tuberculosis (Tb). Tb disease can also worsen blood sugar levels which can cause Dm disease. This study aims to analyze and determine the stability of the equilibrium point of the spread of Tb disease in patients with Dm with consideration nine compartments, which are susceptible Tb without Dm, susceptible Tb without Dm complication, susceptible Tb with Dm complication, expose Tb without Dm, expose Tb with Dm, infected Tb without Dm, infected Tb with Dm, recovered Tb without Dm, and recovered Tb with Dm with treatment factors. The result obtained from the analysis of the model is two equilibrium points, which are the non endemic and endemic equilibrium points. The endemic equilibrium point does not exist if , endemic will appear if . Analytical and numerical simulation show that the spread of disease can be reduced and stopped if treatment is given to the infected compartment.Downloads
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Wiraningsih, E.D., Aryati, W. L., Toaha, S. & Lenhart, S. (2010). Optimal control for SEIR rabies model between dogs and human with vaccination effect in dogs. Proceedings of the 6th IMT-GT Conference on Mathematics, Statistics and its Applications (ICMSA2010) Universiti Tunku Abdul Rahman, Kuala Lumpur, Malaysia. Vol. 6. 1161-1175
Wiraningsih, E. D., Agusto, F., Aryati, L., Lenhart, S., Toaha, S., Widodo & Govaerts, W. (2015). Stability analysis of rabies model with vaccination effect and culling in dogs. Applied Mathematical Sciens, 9(77), 3805-3817. doi:10.12988/ams.2015.53197
Beay, L., kasbawati & Toaha, S. (2017). Effects of human and mosquito migrations on the dynamical behavior of the spread of malaria AIP Conference Proceeding 1825, 020006.http://doi.org/10.1063/1.4978975
Hartati, H., Toaha, S. & kasbawati (2019). Stability analysis of SEISEIR-SEI modelling on the dynamics of spread dengue fever with vaccination and insectiside. J. Phy.: Conf. Ser. 1341 062033. doi:10.88/1742-6596/1341/6/062033
Muin, R.. M., Toaha, S & Kasbawati (2019). Effect of vaccination and treatment on the MSEICR model of the transmission of hepatitis B virus. J. Phys.: Conf. Ser. 1341062031. doi: 10.1088/1742-6596/1341/6/062031
Crofton, S. J. (2009). Crofton's Clinical Tuberculosis Third Edition. Oxford: Macmillan Publishers Limited.
Sembiring, S. (2019). Indonesia Bebas Tuberculosis. Jawa Barat: CV Jejak.
Wulandari, D. R., & Yani, J. S. (2013). Diabetes mellitus dan permasalahannya pada infeksi tuberkulosis. J Respir Indo, Vol.33, No.2
Soewondo , P. (2007). Hidup Sehat dengan Diabetes. Jakarta: FKUI.
Restrepo., Camerling, A. J., Rahbar, M. H., Wang, W., Restrepo, M. A., Zarate, I., Mora-Guz’an, F., Crespo-Solis, J. G., Briggs, J., Mc Cormika, J. B., & Fisher-Hocha, S. P. (2011). Cross-sectional assessment revels high diabetes prevelence among newly diagnosed tuberculosis cases. Bulletin of The World Health Organization, 89 (5): 352-359. doi:10.2471/BLT.10.085738359.
Moualeu, D. P., Bowong, S., Tewa, J. J., & Emvudu, Y. (2012). Analysis of the impact of diabetes on the dynamical transmission of tuberculosis. Math. Model. Nat. Phenom., Vol. 7. 117-146. doi:10.1051/mmnp/20127309.
Danumjaya, P., & Merina, D. (2019). Stability preserving non standard finite difference schemes for diabetes with tuberculosis infectious model. Letter in Biomathematics. doi:10.1088/23737867.2019.1618743.
Murray, J. D. (2012). Mathematical Biology: I an Introduction (Third Edition ed.). New York, USA: Springer.
Willems, J. L. (1970). Stability Theory of Dynamical System. London: Thomas Nelson & Sons.
Toaha, S. (2013). Pemodelan Matematika dalam Dinamika Populasi. Makassar: Dua Satu Press.
Driessche. & Watmough., (2002). Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences. Vol. 2002, No. 180, hal. 29-48.
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