Stability Analysis of Tuberculosis Spread Model Co-Infected Diabetes Mellitus with DOTS Strategy
| Main Authors: | Syamsul, Mutmainnah, Toaha, Syamsuddin , Kasbawati, Kasbawati |
|---|---|
| Format: | Article info application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
Department of Mathematics, Hasanuddin University
, 2022
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| Subjects: | |
| Online Access: |
http://journal.unhas.ac.id/index.php/jmsk/article/view/19523 http://journal.unhas.ac.id/index.php/jmsk/article/view/19523/8137 |
Daftar Isi:
- Tuberculosis (TB) is an infectious disease caused by the bacterium Mycobacterium tuberculosis. Patients with symptoms of TB can be caused by immune disorders such as diabetes mellitus infection. Patients with diabetes mellitus can affect the clinical symptoms of TB patients and are associated with a slow response to TB treatment. This study aims to analyze and determine the stability of the equilibrium point of the TB disease spread model coinfected with DM by considering nine compartments, namely susceptible TB without DM, exposed TB without DM, infected TB without DM, recovered TB without DM, susceptible TB with DM, exposed TB with DM, infected TB with DM, recovered TB with DM, and treatment with DOTS. The research method used is a qualitative method by determining the basic reproduction number obtained with next generation matrix method to analyze the stability of the non-endemic and endemic equilibrium points. The non-endemic and endemic equilibrium points are said to be locally asymptotically stable if , and unstable if .The results obtained from sensitivity analysis show that the spread of disease can be reduced and eliminated if treated with DOTS in the infected compartment.
- Tuberkulosis (TB) adalah penyakit menular yang disebabkan oleh bakteri Mycobakterium Tuberculosis. Pasien dengan gejala TB dapat disebabkan oleh gangguan imunitas tubuh seperti infeksi diabetes melitus, seseorang yang menderita diabetes melitus dapat lebih beresiko menjadi pasien TB. Penelitian ini bertujuan untuk menganalisis dan menentukan kestabilan titik kesetimbangan dari model penyebaran penyakit TB yang koinfeksi DM dengan mempertimbangkan sembilan kompartemen yaitu susceptible TB without DM, expose TB without DM, infected TB without DM, recovered TB without DM, susceptible TB with DM, expose TB with DM, infected TB with DM, recovered TB with DM,dan treatment with DOTS. Metode penelitian yang digunakan adalah metode kualitatif dengan menentukan bilangan reproduksi dasar yang diperoleh dari metode next generation matrix untuk menganalisis kestabilan dari titik kesetimbangan non-endemik dan endemik. Titik kesetimbangan non-endemik dan endemik dikatakan stabil asimtotik lokal jika , dan tidak stabil jika .Hasil yang diperoleh dari analisis sensitivitas menunjukkan bahwa penyebaran penyakit dapat dikurangi dan dihilangkan jika diberikan pengobatan dengan DOTS pada kompartemen yang terinfeksi.