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Stability Analysis of Prey-Predator Model With Holling Type IV Functional Response and Infectious Predator

Kestabilan Model Mangsa Pemangsa dengan fungsi respon Holling tipe IV dan penyakit pada pemangsa

Jurnal Matematika, Statistika dan Komputasi · Vol. 17 No. 2 (2020) · pp. 155–165

DOI
10.20956/jmsk.v17i2.11716
ISSN
2614-8811, 1858-1382
Published
2020-12-23
Publisher
Department of Mathematics, Hasanuddin University
Language
en
License
creativecommons.org/licenses/by/4.0

Abstract

English

Stability of equilibrium points of the prey-predator model with diseases that spreads in predators where the predation function follows the simplified Holling type IV functional response are investigated. To find out the local stability of the equilibrium point of the model, the system is then linearized around the equilibrium point using the Jacobian matrix method, and stability of the equilibrium point is determined via the eigenvalues method. There exists three non-negative equilibrium points, except, that may exist and stable. Simulation results show that with the variation of several parameter values infection rate of disease, the diseases in the system may become endemic, or may become free from endemic.

Bahasa Indonesia

Kestabilan titik ekuilibrium model mangsa-predator dengan penyakit yang menyebar pada predator di mana fungsi predasi mengikuti respon fungsional tipe IV Holling yang disederhanakan dianalisis. Untuk mengetahui kestabilan lokal titik ekuilibrium model, sistem kemudian dilinierisasi di sekitar titik ekuilibrium menggunakan metode matriks Jacobian dan stabilitas titik kesetimbangan ditentukan melalui metode nilai eigen. Ada tiga titik ekuilibrium non-negatif, kecuali, yang mungkin ada dan stabil. Hasil simulasi menunjukkan bahwa dengan variasi beberapa nilai parameter laju penularan suatu penyakit, penyakit dalam sistem dapat menjadi endemik atau bebas dari endemik.

Keywords

Collaboration network of the authors

40 authors · 98 co-authorship links · showing the 40 most connected

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
Kasbawati KasbawatiAffiliation unknown12
Khaeruddin KhaeruddinState University of Makassar3
Sulma SulmaAffiliation unknown2
Ainun Mawaddah AbdalAffiliation unknown2
Jeffry KusumaAffiliation unknown2
EDY SAPUTRA RUSDIAffiliation unknown2
Edy Saputra RusdiAffiliation unknown1
Naimah ArisAffiliation unknown1
Muhammad Ardiansyah AsrifahAffiliation unknown1
Nur Hilal A. SyahrirAffiliation unknown1
Aidawayati RangkutiAffiliation unknown1
Wahyudi RusdiAffiliation unknown1
I Nyoman WidanaAffiliation unknown1
Ita FitriaAffiliation unknown1
Illuminata WynnieAffiliation unknown1
Amil SiddikAffiliation unknown1
Mauliddin MauliddinAffiliation unknown1
Sulfayanti SulfayantiAffiliation unknown1
Syamsul AgusAffiliation unknown1
Mawardi BahriAffiliation unknown1
IIN SUTRISNAAffiliation unknown1
Asriadi NasrunAffiliation unknown1
Yusrianto YusriantoAffiliation unknown1
Himmatul Ulya FebriyantiAffiliation unknown1
Lilis Dwi Sapta AprilyaniAffiliation unknown1
Suriani SurianiAffiliation unknown1
Andi Muhammad Amil SiddikAffiliation unknown1
Syamsir MuarafAffiliation unknown1
Nita AnggrianiAffiliation unknown1
Andi Utari SamsirAffiliation unknown1
Hukmah HukmahAffiliation unknown1
Irawati IrawatiAffiliation unknown1
Hanni GarminiaAffiliation unknown1
Ismi Ra'yan SyarifAffiliation unknown1
Mutmainnah SyamsulAffiliation unknown1
Rabiatul AdawiyahAffiliation unknown1
Jeki SaputraAffiliation 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 Prey-Predator Model With Holling Type IV Functional Response and Infectious Predator</dc:title>
	<dc:title xml:lang="id">Kestabilan Model Mangsa Pemangsa dengan fungsi respon Holling tipe IV dan penyakit pada pemangsa</dc:title>
	<dc:creator xml:lang="en">Siddik, A. Muh. Amil</dc:creator>
	<dc:creator xml:lang="en">Toaha, Syamsuddin </dc:creator>
	<dc:creator xml:lang="en">Anwar, Andi Muhammad </dc:creator>
	<dc:subject xml:lang="en">prey predator model</dc:subject>
	<dc:subject xml:lang="en">disease</dc:subject>
	<dc:subject xml:lang="en">Holling response function</dc:subject>
	<dc:subject xml:lang="id">model mangsa pemangsa</dc:subject>
	<dc:subject xml:lang="id">penyakit</dc:subject>
	<dc:subject xml:lang="id">fungsi respon Holling</dc:subject>
	<dc:description xml:lang="en">Stability of equilibrium points of the prey-predator model with diseases that spreads in predators where the predation function follows the simplified Holling type IV functional response are investigated. To find out the local stability of the equilibrium point of the model, the system is then linearized around the equilibrium point using the Jacobian matrix method, and stability of the equilibrium point is determined via the eigenvalues method. There exists three non-negative equilibrium points, except , that may exist and stable. Simulation results show that with the variation of several parameter values infection rate of disease , the diseases in the system may become endemic, or may become free from endemic.
 </dc:description>
	<dc:description xml:lang="id">Kestabilan titik ekuilibrium model mangsa-predator dengan penyakit yang menyebar pada predator di mana fungsi predasi mengikuti respon fungsional tipe IV Holling yang disederhanakan dianalisis. Untuk mengetahui kestabilan lokal titik ekuilibrium model, sistem kemudian dilinierisasi di sekitar titik ekuilibrium menggunakan metode matriks Jacobian dan stabilitas titik kesetimbangan ditentukan melalui metode nilai eigen. Ada tiga titik ekuilibrium non-negatif, kecuali, yang mungkin ada dan stabil. Hasil simulasi menunjukkan bahwa dengan variasi beberapa nilai parameter laju penularan suatu penyakit, penyakit dalam sistem dapat menjadi endemik atau bebas dari endemik.</dc:description>
	<dc:publisher xml:lang="en">Department of Mathematics, Hasanuddin University</dc:publisher>
	<dc:date>2020-12-23</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/11716</dc:identifier>
	<dc:identifier>10.20956/jmsk.v17i2.11716</dc:identifier>
	<dc:source xml:lang="en">Jurnal Matematika, Statistika dan Komputasi; Vol. 17 No. 2 (2021): JANUARY 2021; 155-165</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/11716/6163</dc:relation>
	<dc:relation>10.20956/j.v17i2.11716.g6163</dc:relation>
	<dc:rights xml:lang="en">Copyright (c) 2020 Author and publisher</dc:rights>
	<dc:rights xml:lang="en">https://creativecommons.org/licenses/by/4.0</dc:rights>
</oai_dc:dc>