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Stability Analysis of Tuberculosis Spread Model Co-Infected Diabetes Mellitus with DOTS Strategy

Analisis Kestabilan Model Matematika Penyebaran Penyakit Tuberkulosis yang Koinfeksi Diabetes Melitus dengan Pengobatan strategi DOTS

Jurnal Matematika, Statistika dan Komputasi · Vol. 18 No. 3 (2022) · pp. 336–347

DOI
10.20956/j.v18i3.19523
ISSN
2614-8811, 1858-1382
Published
2022-05-15
Publisher
Department of Mathematics, Hasanuddin University
Language
en
License
creativecommons.org/licenses/by/4.0

Abstract

English

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.

Bahasa Indonesia

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.

Keywords

Collaboration network of the authors

31 authors · 61 co-authorship links

Hover or tap a name to highlight its co-authors. Double-click to open the author's page.

  • State University of Makassar
  • Affiliation unknown
  • Different organisations
  • Same organisation
  • Affiliation unknown
  • Thicker line = more joint articles · bigger circle = more articles
Show as table
Co-authorOrganisationJoint articles
Khaeruddin KhaeruddinState University of Makassar3
Sulma SulmaAffiliation unknown3
Jeffry KusumaAffiliation unknown2
Syamsul AgusAffiliation unknown2
Yusrianto YusriantoAffiliation unknown2
Himmatul Ulya FebriyantiAffiliation unknown2
Lilis Dwi Sapta AprilyaniAffiliation unknown2
Suriani SurianiAffiliation unknown2
Syamsir MuarafAffiliation unknown2
Nita AnggrianiAffiliation unknown2
Andi Utari SamsirAffiliation unknown2
Rabiatul AdawiyahAffiliation unknown2
I Nyoman WidanaAffiliation unknown1
Ita FitriaAffiliation unknown1
Sulfayanti SulfayantiAffiliation unknown1
Mawardi BahriAffiliation unknown1
IIN SUTRISNAAffiliation unknown1
Asriadi NasrunAffiliation unknown1
A. Muh. Amil SiddikAffiliation unknown1
Andi Muhammad AnwarAffiliation unknown1
Nur Suci RamadhaniAffiliation unknown1
Toaha ToahaAffiliation unknown1
Hukmah HukmahAffiliation unknown1
Ismi Ra'yan SyarifAffiliation unknown1
Sitti SahrimanAffiliation unknown1
Anisa KalondengAffiliation unknown1
M. Zaky Hisyam GozhiAffiliation unknown1
Aidul Fitri MustaminAffiliation unknown1

Affiliations come from OpenAlex; journal OAI-PMH metadata carries none. Authors without an OpenAlex ID are matched by name, which can merge or split people.

Metadata source: OAI-PMH (metadata jurnal) https://journal.unhas.ac.id/index.php/jmsk/oai, first harvested 5 Nov 2026, last seen 5 Nov 2026.
Original metadata (oai_dc) 
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	<dc:title xml:lang="en">Stability Analysis of Tuberculosis Spread Model Co-Infected Diabetes Mellitus with DOTS Strategy</dc:title>
	<dc:title xml:lang="id">Analisis Kestabilan Model Matematika Penyebaran Penyakit Tuberkulosis yang Koinfeksi Diabetes Melitus dengan Pengobatan strategi DOTS</dc:title>
	<dc:creator xml:lang="en">Syamsul, Mutmainnah</dc:creator>
	<dc:creator xml:lang="en">Toaha, Syamsuddin </dc:creator>
	<dc:creator xml:lang="en">Kasbawati, Kasbawati</dc:creator>
	<dc:subject xml:lang="en">Equilibrium point</dc:subject>
	<dc:subject xml:lang="en">Basic Reproduction Number</dc:subject>
	<dc:subject xml:lang="en">Tuberculosis</dc:subject>
	<dc:subject xml:lang="en">Diabetes Mellitus</dc:subject>
	<dc:subject xml:lang="en">Treatment with DOTS</dc:subject>
	<dc:description xml:lang="en">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.</dc:description>
	<dc:description xml:lang="id">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&amp;nbsp; 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.</dc:description>
	<dc:publisher xml:lang="en">Department of Mathematics, Hasanuddin University</dc:publisher>
	<dc:date>2022-05-15</dc:date>
	<dc:type>info:eu-repo/semantics/article</dc:type>
	<dc:type>info:eu-repo/semantics/publishedVersion</dc:type>
	<dc:format>application/pdf</dc:format>
	<dc:identifier>https://journal.unhas.ac.id/index.php/jmsk/article/view/19523</dc:identifier>
	<dc:identifier>10.20956/j.v18i3.19523</dc:identifier>
	<dc:source xml:lang="en">Jurnal Matematika, Statistika dan Komputasi; Vol. 18 No. 3 (2022): MAY, 2022; 336-347</dc:source>
	<dc:source>2614-8811</dc:source>
	<dc:source>1858-1382</dc:source>
	<dc:language>en</dc:language>
	<dc:relation>https://journal.unhas.ac.id/index.php/jmsk/article/view/19523/8137</dc:relation>
	<dc:relation>10.20956/j.v18i3.19523.g8137</dc:relation>
	<dc:rights xml:lang="en">Copyright (c) 2022 Author and publisher</dc:rights>
	<dc:rights xml:lang="en">https://creativecommons.org/licenses/by/4.0</dc:rights>
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