Effect of Prey Refuge and Harvesting on Dynamics of Eco-epidemiological Model with Holling Type III

Adin Lazuardy Firdiansyah


In this research, we formulate and analyze an eco-epidemiology model of the modified Leslie-Gower model with Holling type III by incorporating prey refuge and harvesting. In the model, we find at most six equilibrium where three equilibrium points are unstable and three equilibrium points are locally asymptotically stable. Furthermore, we find an interesting phenomenon, namely our model undergoes Hopf bifurcation at the interior equilibrium point by selecting refuge as the bifurcation parameter. Moreover, we also conclude that the stability of all populations occurs faster when the harvesting rate increases.  In the end, several numerical solutions are presented to check the analytical results.


Eco-epidemiology Model; Local Stability; Hopf Bifurcation

Full Text:

PDF [English]


P. H. Leslie and J. C. Gower, “The Properties of a Stochastic Model for the Predator-Prey Type of Interaction Between Two Species,” Biometrika, vol. 47, no. 3&4, pp. 219–234, 1960, doi: 10.2307/2333294.

Y. Cai, C. Zhao, W. Wang, and J. Wang, “Dynamics of a Leslie-Gower predator-prey model with additive Allee effect,” Appl. Math. Model., vol. 39, no. 7, pp. 2092–2106, 2015, doi: 10.1016/j.apm.2014.09.038.

H. S. Panigoro, E. Rahmi, N. Achmad, and S. L. Mahmud, “The Influence of Additive Allee Effect and Periodic Harvesting to the Dynamics of Leslie-Gower Predator-Prey Model,” Jambura J. Math., vol. 2, no. 2, pp. 87–96, 2020, doi: 10.34312/jjom.v2i2.4566.

M. Onana, B. Mewoli, and J. J. Tewa, “Hopf bifurcation analysis in a delayed Leslie–Gower predator–prey model incorporating additional food for predators, refuge and threshold harvesting of preys,” Nonlinear Dyn., vol. 100, no. 3, pp. 3007–3028, 2020, doi: 10.1007/s11071-020-05659-7.

S. Sharma and G. P. Samanta, “A Leslie-Gower predator-prey model with disease in prey incorporating a prey refuge,” Chaos, Solitons and Fractals, vol. 70, no. 1, pp. 69–84, 2015, doi: 10.1016/j.chaos.2014.11.010.

J. J. Zhao, M. Zhao, and H. Yu, “Effect of prey refuge on the spatiotemporal dynamics of a modified leslie-gower predator-prey system with holling type III schemes,” Entropy, vol. 15, no. 6, pp. 2431–2447, 2013, doi: 10.3390/e15062431.

A. S. Purnomo, I. Darti, and A. Suryanto, “Dynamics of eco-epidemiological model with harvesting,” AIP Conf. Proc., vol. 1913, 2017, doi: 10.1063/1.5016652.

X. Zhou, J. Cui, X. Shi, and X. Song, “A modified Leslie-Gower predator-prey model with prey infection,” J. Appl. Math. Comput., vol. 33, no. 1–2, pp. 471–487, 2010, doi: 10.1007/s12190-009-0298-6.

R. Bhattacharyya and B. Mukhopadhyay, “On an eco-epidemiological model with prey harvesting and predator switching: Local and global perspectives,” Nonlinear Anal. Real World Appl., vol. 11, no. 5, pp. 3824–3833, 2010, doi: 10.1016/j.nonrwa.2010.02.012.

N. Apreutesei and G. Dimitriu, “On a prey-predator reactiondiffusion system with Holling type III functional response,” J. Comput. Appl. Math., vol. 235, no. 2, pp. 366–379, 2010, doi: 10.1016/j.cam.2010.05.040.

A. A. Shaikh, H. Das, and N. Ali, “Study of a predator–prey model with modified Leslie–Gower and Holling type III schemes,” Model. Earth Syst. Environ., vol. 4, no. 2, pp. 527–533, 2018, doi: 10.1007/s40808-018-0441-1.

DOI: https://doi.org/10.34312/jjom.v3i1.7281

Copyright (c) 2021 A.L. Firdiansyah

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


 Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Negeri Gorontalo
Jl. Prof. Dr. Ing. B. J. Habibie, Tilongkabila, Kabupaten Bone Bolango 96119, Gorontalo, Indonesia
 Email: info.jjom@ung.ac.id
 +62-852-55230451 (Call/SMS/WA)
 Jambura Journal of Mathematics (p-ISSN: 2654-5616 | e-ISSN: 2656-1344) 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.