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Stability and Bifurcation Analysis of a Bird Flu Model with Vaccination in Poultry Farm

Jurnal Matematika, Statistika dan Komputasi · Vol. 22 No. 3 (2026) · pp. 686–699

DOI
10.20956/j.v22i3.47980
ISSN
2614-8811, 1858-1382
Published
2026-05-14
Publisher
Department of Mathematics, Hasanuddin University
Language
en
License
creativecommons.org/licenses/by/4.0

Abstract

We analyze a nonlinear compartmental model describing bird flu transmission dynamics within a poultry farm, incorporating susceptible, infectious, and removed compartments with vaccination. The basic reproduction number R0 is derived, and the local stability of the disease-free and endemic equilibrium is investigated using linearization techniques. Bifurcation analysis based on standard bifurcation theory is conducted to identify parameter leading to qualitative changes in disease dynamics, revealing the occurrence of a forward transcritical bifurcation. Numerical simulations are used to illustrate threshold behavior and assess the impact of vaccination as a mitigation strategy on outbreak persistence. The results provide insights into control thresholds and the design of effective on-farm intervention strategies

Keywords

Collaboration network of the authors

17 authors · 32 co-authorship links · 2 across different organisations

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

  • Politeknik TEDC Bandung
  • Andalas University
  • Universitas Halu Oleo
  • Affiliation unknown
  • Different organisations
  • Same organisation
  • Affiliation unknown
  • Thicker line = more joint articles · bigger circle = more articles
Show as table
Co-authorOrganisationJoint articles
Efendi EfendiUniversitas Halu Oleo2
Izzati RahmiAffiliation unknown2
Hazmira YozzaAffiliation unknown2
Muthiah As SaidahAffiliation unknown2
Elvathna SyafwanPoliteknik TEDC Bandung1
Shandy TresnawatiPoliteknik TEDC Bandung1
Julia Indah PertiwiAffiliation unknown1
Yana WulandariAffiliation unknown1
Prisca JasmineAffiliation unknown1
Riswan EfendiAffiliation unknown1
Nor Azah SamatAffiliation unknown1
Muhafzan MuhafzanAffiliation unknown1
Budi RudiantoAffiliation unknown1
Syafrizal SyAffiliation 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 a Bird Flu Model  with Vaccination in Poultry Farm</dc:title>
	<dc:creator xml:lang="en">putri, arrival rince</dc:creator>
	<dc:creator xml:lang="en"> Muhammad, Bala Muhammad</dc:creator>
	<dc:creator xml:lang="en">Syafwan, Mahdhivan</dc:creator>
	<dc:subject xml:lang="en">Avian influenza</dc:subject>
	<dc:subject xml:lang="en">Population dynamics</dc:subject>
	<dc:subject xml:lang="en">Stability analysis</dc:subject>
	<dc:subject xml:lang="en">Bifurcation</dc:subject>
	<dc:description xml:lang="en">


We analyze a nonlinear compartmental model describing bird flu transmission dynamics within a poultry farm, incorporating susceptible, infectious, and removed compartments with vaccination. The basic reproduction number R0 is derived, and the local stability of the disease-free and endemic equilibrium is investigated using linearization techniques. Bifurcation analysis based on standard bifurcation theory is conducted to identify parameter leading to qualitative changes in disease dynamics, revealing the occurrence of a forward transcritical bifurcation. Numerical simulations are used to illustrate threshold behavior and assess the impact of vaccination as a mitigation strategy on outbreak persistence. The results provide insights into control thresholds and the design of effective on-farm intervention strategies


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	<dc:publisher xml:lang="en">Department of Mathematics, Hasanuddin University</dc:publisher>
	<dc:date>2026-05-14</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/47980</dc:identifier>
	<dc:identifier>10.20956/j.v22i3.47980</dc:identifier>
	<dc:source xml:lang="en">Jurnal Matematika, Statistika dan Komputasi; Vol. 22 No. 3 (2026): May 2026; 686-699</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/47980/14419</dc:relation>
	<dc:rights xml:lang="en">Copyright (c) 2026 Jurnal Matematika, Statistika dan Komputasi</dc:rights>
	<dc:rights xml:lang="en">https://creativecommons.org/licenses/by/4.0</dc:rights>
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