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All Journal JURNAL DERIVAT: JURNAL MATEMATIKA DAN PENDIDIKAN MATEMATIKA Al-Iqtishad : Jurnal Ilmu Ekonomi Syariah (Journal of Islamic Economics) Nature: National Academic Journal of Architecture Jurnal Ilmiah Ekonomi Islam BAREKENG: Jurnal Ilmu Matematika dan Terapan IKRA-ITH Humaniora : Jurnal Sosial dan Humaniora JTAM (Jurnal Teori dan Aplikasi Matematika) Al Qalam: Jurnal Ilmiah Keagamaan dan Kemasyarakatan Jurnal Kewirausahaan dan Bisnis JURNAL CEMERLANG: Pengabdian pada Masyarakat JEMPER (Jurnal Ekonomi Manajemen Perbankan) Inovasi: Jurnal Ilmiah Ilmu Manajemen BASKARA: Journal of Business and Entrepreneurship Jurnal Bimas Islam Jurnal Komposit : Jurnal Ilmu-Ilmu Teknik Sipil Jambura Journal of Biomathematics (JJBM) Kontigensi: Jurnal Ilmiah Manajemen Jurnal Ekonomi Trisakti Media Ekonomi Iltizamat : Journal Of Economic Sharia Law and Business Studies Journal of Mathematics, Computation and Statistics (JMATHCOS) Media Riset Bisnis Ekonomi Sains dan Terapan J-CEKI Jurnal Ekonomi, Manajemen, Akuntansi Taraadin : Jurnal Ekonomi dan Bisnis Islam MILANG Journal of Mathematics and Its Applications
Jaharuddin, Jaharuddin
Universitas Muhammadiyah Jakarta
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Journal : Journal of Mathematics, Computation and Statistics (JMATHCOS)

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Stability Analysis of a Time-Delayed Disease Transmission Model in Prey–Predator Populations Incorporating a Holling Type II Functional Response Rauf, Nurul Maqfirah; Sianturi, Paian; Jaharuddin, Jaharuddin
Journal of Mathematics, Computations and Statistics Vol. 8 No. 1 (2025): Volume 08 Nomor 01 (April 2025)
Publisher : Jurusan Matematika FMIPA UNM

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35580/jmathcos.v8i1.7428

Abstract

Abstrak. This article presents a comprehensive study of a mathematical model describing the spread of infectious disease within a prey–predator population, incorporating the Holling type II functional response and a delay parameter, denoted as τ, representing the incubation or infection period. The model captures the interactions among four population groups: susceptible prey, infected prey, susceptible predators, and infected predators. Through analytical investigation, six fixed points (equilibrium points) of the system were identified. The stability of these fixed points was examined using the eigenvalues of the Jacobian matrix, and one locally stable fixed point was found, while the others were identified as saddle points or unstable. To gain deeper insights into the model’s behavior over time, numerical simulations were conducted for different values of the delay parameter . The results indicate that the presence of a time delay significantly affects the dynamics of all four population groups. Specifically, the infection delay can suppress or slow the spread of the disease by delaying the transition from susceptible to infected classes. Oscillatory behavior emerged in certain population groups when the delay was introduced, especially among infected prey and predators, before gradually stabilizing toward the disease-endemic equilibrium. These findings highlight the critical role of time delay in disease transmission dynamics in ecological systems and provide a framework for further research on delay-induced phenomena in epidemiological models. Keywords: Prey–Predator, Disease Spread, Delay Time, Functional Response, Stability Analysis.
Co-Authors Abbie Pangestu Abdullah Najib Azzamani Adi Mansah Afifah Harisah Ahmad Rodoni AIN, N. Ainun Zamilah Al Anshari Alaik Rifqi Sidqon ALDILLA, I. Amalia, Imas Saumi Andry Priharta Anggraini, Dahlia Tri Aprianti, Euis ARDIANSYAH ARDIANSYAH Arsalan Bintang Romadi Aulia, Nabila Nur BAKHTIAR, T. Bambang Sutrisno BANO, E. N. Bib Paruhum Silalahi Blante, Trianty Putri Budi Asmita Cahyona, Dwizani Vinoma Darmawan, Azhar Janjang Darto Dyanti, Najwa Putri Ekaputri, Dhea Endar Hasafah Nugrahani Eti Rohaeti FAHRURRAZI, F. Fakhri Muhammad Ario Putra Faricha Noor Aida Fikri, Faiqul Firdasari Firdasari Firdausiyah, Salsabila Furqoni, Muhammad Ihsan Gani, Nur Asni Hadi Sumarno Hafidz Ainur Rofi Hajmi Almanfaluthi Salam Hakim, Ulil Akbar HANUM, F. Hartutik (Hartutik) HASANNUDIN, H. HERMANSYAH, H. Irfan Purnawan Purnawan Irmawati Irmawati Khulud Saadah Almadaniah KUSNANTO, A. L. Hakim M Za'im Musyaffa Maesarach, R. Melda Masthura, Lely Medo Maulianza Meri Prasetyawati Muchtar, Masruri Muhammad Fariz Abdullah Pelu Muhibuddin Mumtaz, Alisa Hana Nahya Astriana Natalia, D. Nur Asni Gani Nur Asni Gani Nur Aziezah Nur Hidayah Nurul Ramandini Nurul Syamsiah OKTAFIANI, L. D. Paian Sianturi Puja Trisena PUTRI PRATAMA R, Ria Wikantari Rahayu Dwi Lestari Rahmita Nurul Muthmainnah Rauf, Nurul Maqfirah Rega Saputra Rony Edward Utama Rony Edward Utama Rully Mujiastuti SAHAMONY, N. F. Setya Nugroho Isri Yuwono SIANTURI, P. SISWANDI, S. Sofyan Rizal Sudirman Sudirman Sugi Guritman Sukardi Sukardi Syifa Fauziyah, Syifa Tan, Elfina Taufik Arfan Toni Bakhtiar Tri Ananto Ulil Akbar Hakim Utama, Rony Edward Utama, Rony Edward Utama WIBOWO, A. T. Wulan Rindyana S Yahya, Muhammad Ridwan Yahya, Wardah