Dynamics of a predator-prey model incorporating infectious disease and quarantine on prey

Anatasya Lahay, Muhammad Rezky Friesta Payu, Sri Lestari Mahmud, Hasan S Panigoro, Perry Zakaria

Abstract


In this article, the dynamics of a predator-prey model incorporating infectious disease and quarantine on prey population is discussed. We first analyze the existence conditions of all positive equilibrium points. Next, we investigate the local stability properties of the proposed model using the linearization method. We also determine the basic reproduction number using the next generation matrix. Finally, some numerical simulations are performed to validate the stability of each equilibrium point.

Keywords


Dynamics; Eco-Epidemiology; Predator-prey; Infectious Diseases; Harvesting

Full Text:

PDF

References


D. F. Bailey, W. E. Boyce, R. C. DiPrima, and M. Braun, Elementary Differential Equations and Boundary Value Problems., 1977, vol. 84, no. 8. ISBN 0471319996. DOI: 10.2307/2321040

C. Ummah and Abadi, “Analisis Kestabilan Model Ekoepidemiologi Dengan Pemanenan Sebagai Kontrol Penyebaran Penyakit,” MATHunesa, vol. 2, p. 8, 2013.

E. Rahmi, I. Darti, A. Suryanto, Trisilowati, and H. S. Panigoro, “Stability Analysis of a Fractional-Order Leslie-Gower Model with Allee Effect in Predator,” Journal of Physics: Conference Series, vol. 1821, no. 1, p. 012051, 2021. DOI: 10.1088/1742-6596/1821/1/012051. DOI: 10.1088/1742-6596/1821/1/012051

H. S. Panigoro and D. Savitri, “Bifurkasi Hopf pada model Lotka-Volterra orde-fraksional dengan efek Allee aditif pada predator,” Jambura Journal of Biomathematics, vol. 1, no. 1, pp. 16–24, 2020. DOI: 10.34312/jjbm.v1i1.6908

H. S. Panigoro, “Analisis Dinamik Sistem Predator-Prey Model Leslie-Gower dengan Pemanenan Secara Konstan terhadap Predator,” Euler, vol. 2, no. 1, pp. 1–12, 2014.

M. Su and H. Wang, “Modeling at the interface of ecology and epidemiology,” Computational Ecology and Software, no. 4, pp. 367–379.

F. Brauer and C. C. Chavez, “Mathematical Models in Epidemiology,” 2019.

S. A. Wuhaib and Y. A. Hasan, “A predator-infected prey model with harvesting of infected prey,” ScienceAsia, vol. 39, no. SUPPL.1, pp. 37–41, 2013. DOI: 10.2306/scienceasia1513-1874.2013.39S.037

A. S. Purnomo, I. Darti, and A. Suryanto, “Dynamics of eco-epidemiological model with harvesting,” AIP Conference Proceedings, vol. 1913, no. December 2017, 2017. DOI: 10.1063/1.5016652

H. S. Panigoro and E. Rahmi, “Modifikasi sistem predator-prey: dinamika model Leslie-Gower dengan daya dukung yang tumbuh logistik,” in SEMIRATA MIPAnet. UNSRAT Manado, 2017, pp. 94–103.

S. Maisaroh, R. Resmawan, and E. Rahmi, “Analisis Kestabilan Model Predator-Prey dengan Infeksi Penyakit pada Prey dan Pemanenan Proporsional pada Predator,” Jambura Journal of Biomathematics, vol. 1, no. 1, pp. 8–15, 2020. DOI:10.34312/jjbm.v1i1.5948

R. Ibrahim, L. Yahya, E. Rahmi, and R. Resmawan, “Analisis dinamik model predator-prey tipe Gause dengan wabah penyakit pada prey,” Jambura Journal of Biomathematics, vol. 2, no. 1, pp. 20–28, 2021. DOI: 10.34312/jjbm.v2i1.10363

W. O. Kermack and A. G. McKendrick, “A contribution to the mathematical theory of epidemics,” Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, vol. 115, no. 772, pp. 700–721, 1927. DOI: 10.1098/rspa.1927.0118

G. J. Olsder and J. W. van der Woude, “Mathematical Systems Theory intermediate third edition,” Delft University of Technology: Netherlands. DOI: 10.1002/rnc.1036

O. Diekmann, J. A. P. Heesterbeek, and M. G. Roberts, “The construction of next-generation matrices for compartmental epidemic models,” Journal of The Royal Society Interface, vol. 7, no. 47, pp. 873–885, 2010. DOI: 10.1098/rsif.2009.0386

N. Anggriani and L. K. Beay, “Modeling of COVID-19 spread with selfisolation at home and hospitalized classes,” Results in Physics, vol. 36, no. December 2021, p. 105378, 2022. DOI: 10.1016/j.rinp.2022.105378




DOI: https://doi.org/10.34312/jjbm.v3i2.17162

Copyright (c) 2022 Anatasya Lahay, Muhammad Rezky Friesta Payu, Sri Lestari Mahmud, Hasan S. Panigoro, Perry Zakaria

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Jambura Journal of Biomathematics (JJBM) has been indexed by:

                          EDITORIAL OFFICE OF JAMBURA JOURNAL OF BIOMATHEMATICS

 Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Negeri Gorontalo
Jl. Prof. Dr. Ing. B. J. Habibie, Moutong, Tilongkabila, Kabupaten Bone Bolango 96554, Gorontalo, Indonesia
 Email: editorial.jjbm@ung.ac.id
 +6281356190818 (Call/SMS/WA)
 Jambura Journal of Biomathematics (JJBM) by Department of Mathematics Universitas Negeri Gorontalo is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.  Powered by Public Knowledge Project OJS.