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Stability and Bifurcation Analysis of Mathematical Models of Meningitis Transmission with Vaccination and treatment

Analisis Kestabilan dan Bifurkasi pada Model Matematika Penyebaran Penyakit Meningitis dengan Perlakuan Vaksinasi dan Pengobatan

Jurnal Matematika, Statistika dan Komputasi · Vol. 18 No. 3 (2022) · pp. 385–393

DOI
10.20956/j.v18i3.19714
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

Meningitis is an infectious disease that occurs in inflammation of the meninges and the spinal cord in consequence of bacteria and viruses. Vaccination and treatment using antibiotics is used to increase growth rate in infected people so that the spread rate can be reduced. This study aims to see the effect of vaccination and treatment using some compartments: susceptible, carrier, infected without symptoms, infected with symptoms, recovery without disability, and recovery with disability; show the sensitivity analysis in order to discover the parameter that affect basic reproduction number and bifurcations analysis. The result from sensitivity found the relation between parameter and that can increase and decrease the value. This study also showed the influence of stability change from equilibrium point caused by the parameter value change form bifurcations analysis. Models simulation show that the effect of vaccination and treatmen for spread of meningitis can be handled.

Bahasa Indonesia

Meningitis adalah suatu penyakit menular yang terjadi pada peradangan meninges dan sumsum tulang belakang yang disebabkan oleh bakteri dan virus. Upaya pengobatan berupa pemberian antibiotik dilakukan untuk meningkatkan laju penyembuhan bagi individu terinfeksi sehingga menekan laju penyebaran penyakit meningitis pada suatu populasi. Tujuan dari penelitian ini ialah untuk menentukan titik ekuilibrium dari model penyebaran penyakit meningitis dengan menggunakan beberapa kompartemen, yaitu susceptible, carrier, infected without symptoms, infected with symptoms, recovery without disability, dan recovery with disability yang menghasikan titik ekuilibrium endemik dan non endemik, menunjukkan analisis sensitivitas untuk mengetahui parameter yang berpengaruh pada bilangan reproduksi dasar dan analisis bifurkasi. Hasil yang diperoleh dari analisis sensitivitas dan bifurkasi, yaitu ditemukan hubungan parameter dengan yang dapat meningkatkan dan menurunkan nilai, pengaruh perubahan kestabilan titik ekuilibrium akibat perubahan nilai parameter. Simulasi model menunjukkan bahwa pemberian vaksinasi dan pengobatan dapat mengendalikan penyebaran penyakit meningitis

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
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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
Mutmainnah SyamsulAffiliation 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 and Bifurcation Analysis of Mathematical Models of Meningitis Transmission with Vaccination and treatment</dc:title>
	<dc:title xml:lang="id">Analisis Kestabilan dan Bifurkasi pada Model Matematika   Penyebaran Penyakit Meningitis dengan Perlakuan Vaksinasi dan Pengobatan</dc:title>
	<dc:creator xml:lang="en">Adawiyah, Rabiatul</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">Model of Meningitis Disease</dc:subject>
	<dc:subject xml:lang="en">Sensitivity of R_0</dc:subject>
	<dc:subject xml:lang="en">Bifurcations</dc:subject>
	<dc:description xml:lang="en">Meningitis is an infectious disease that occurs in inflammation of the meninges and the spinal cord in consequence of bacteria and viruses. Vaccination and treatment using antibiotics is used to increase growth rate in infected people so that the spread rate can be reduced. This study aims to see the effect of vaccination and treatment using some compartments:  susceptible, carrier, infected without symptoms, infected with symptoms, recovery without disability, and recovery with disability; show the sensitivity analysis in order to discover the parameter that affect basic reproduction number and bifurcations analysis. The result from sensitivity found the relation between parameter and  that can increase and decrease the  value. This study also showed the influence of stability change from equilibrium point caused by the parameter  value change form bifurcations analysis. Models simulation show that the effect of vaccination and treatmen for spread of meningitis can be handled.</dc:description>
	<dc:description xml:lang="id">Meningitis adalah suatu penyakit menular yang terjadi pada peradangan meninges dan sumsum tulang belakang yang disebabkan oleh bakteri dan virus. Upaya pengobatan berupa pemberian antibiotik dilakukan untuk meningkatkan laju penyembuhan bagi individu terinfeksi sehingga menekan laju penyebaran penyakit meningitis pada suatu populasi. Tujuan dari penelitian ini ialah untuk menentukan titik ekuilibrium dari model penyebaran penyakit meningitis dengan menggunakan beberapa kompartemen, yaitu susceptible, carrier, infected without symptoms, infected with symptoms, recovery without disability, dan recovery with disability yang menghasikan titik ekuilibrium endemik dan non endemik, menunjukkan analisis sensitivitas&amp;nbsp; untuk mengetahui parameter yang berpengaruh pada bilangan reproduksi dasar &amp;nbsp;dan analisis bifurkasi. Hasil yang diperoleh dari analisis sensitivitas dan bifurkasi, yaitu ditemukan hubungan parameter dengan &amp;nbsp;yang dapat meningkatkan dan menurunkan nilai , pengaruh perubahan kestabilan titik ekuilibrium akibat perubahan nilai parameter . Simulasi model menunjukkan bahwa pemberian&amp;nbsp; vaksinasi dan pengobatan dapat mengendalikan penyebaran penyakit meningitis</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/19714</dc:identifier>
	<dc:identifier>10.20956/j.v18i3.19714</dc:identifier>
	<dc:source xml:lang="en">Jurnal Matematika, Statistika dan Komputasi; Vol. 18 No. 3 (2022): MAY, 2022; 385-393</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/19714/8140</dc:relation>
	<dc:relation>10.20956/j.v18i3.19714.g8140</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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