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Stability Analysis of Mathematical Models of the Dynamics of Spread of Meningitis with the Effects of Vaccination, Campaigns and Treatment

Jurnal Matematika, Statistika dan Komputasi · Vol. 17 No. 1 (2020) · pp. 71–81

DOI
10.20956/jmsk.v17i1.10031
ISSN
2614-8811, 1858-1382
Published
2020-08-24
Publisher
Department of Mathematics, Hasanuddin University
Language
en

Abstract

Meningitis is an infectious disease caused by bacteria, viruses, and protosoa and has the potential to cause an outbreak. Vaccination and campaign are carried out as an effort to prevent the spread of meningitis, treatment reduces the number of deaths caused by the disease and the number of infected people. This study aims to analyze and determine the stability of equilibrium point of the mathematical model of the spread of meningitis using five compartments namely susceptibles, carriers, infected without symptoms, infected with symptoms, and recovered with the effect of vaccination, campaign, and treatment. The results obtained from the analysis of the model that there are two equilibrium points, namely non endemic and endemic equilibrium points. If a certain condition is met then the non endemic equilibrium point will be asymptotically stable. Numerical simulations show that the spread of disease decreases with the influence of vaccination, campaign, and treatment.

Keywords

Collaboration network of the authors

36 authors · 78 co-authorship links

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  • 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
I Nyoman WidanaAffiliation unknown3
Hukmah HukmahAffiliation unknown3
Suriani SurianiAffiliation unknown3
Jeffry KusumaAffiliation unknown2
Muhammad Rifki NisardiAffiliation unknown2
Ita FitriaAffiliation unknown2
Syamsul AgusAffiliation unknown2
Yusrianto YusriantoAffiliation unknown2
Himmatul Ulya FebriyantiAffiliation unknown2
Lilis Dwi Sapta AprilyaniAffiliation unknown2
Syamsir MuarafAffiliation unknown2
Nita AnggrianiAffiliation unknown2
Andi Utari SamsirAffiliation unknown2
Mutmainnah SyamsulAffiliation unknown2
Rabiatul AdawiyahAffiliation unknown2
Ni Luh Putu SuciptawatiAffiliation 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
Ismi Ra'yan SyarifAffiliation unknown1
Suriani MAffiliation unknown1
Harianto HariantoAffiliation unknown1
Dian FirmayasariAffiliation 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 Mathematical Models of the Dynamics of Spread of Meningitis with the Effects of Vaccination, Campaigns and Treatment</dc:title>
	<dc:creator xml:lang="en">Sulma, Sulma</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 Penyebaran Penyakit Meningitis</dc:subject>
	<dc:subject xml:lang="en">Titik Kesetimbangan</dc:subject>
	<dc:subject xml:lang="en">Nilai Eigen</dc:subject>
	<dc:description xml:lang="en">Meningitis is an infectious disease caused by bacteria, viruses, and protosoa and has the potential to cause an outbreak. Vaccination and campaign are carried out as an effort to prevent the spread of meningitis, treatment reduces the number of deaths caused by the disease and the number of infected people. This study aims to analyze and determine the stability of equilibrium point of the mathematical model of the spread of meningitis using five compartments namely susceptibles, carriers, infected without symptoms, infected with symptoms, and recovered with the effect of vaccination, campaign, and treatment. The results obtained from the analysis of the model that there are two equilibrium points, namely non endemic and endemic equilibrium points. If a certain condition is met then the non endemic equilibrium point will be asymptotically stable. Numerical simulations show that the spread of disease decreases with the influence of vaccination, campaign, and treatment.</dc:description>
	<dc:publisher xml:lang="en">Department of Mathematics, Hasanuddin University</dc:publisher>
	<dc:date>2020-08-24</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/10031</dc:identifier>
	<dc:identifier>10.20956/jmsk.v17i1.10031</dc:identifier>
	<dc:source xml:lang="en">Jurnal Matematika, Statistika dan Komputasi; Vol. 17 No. 1 (2020): JMSK, SEPTEMBER, 2020; 71-81</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/10031/pdf</dc:relation>
	<dc:relation>10.20956/j.v17i1.10031.g5708</dc:relation>
	<dc:rights xml:lang="en">Copyright (c) 2020 Sulma Sulma, Syamsuddin Toaha, Kasbawati Kasbawati</dc:rights>
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