Dynamics of Predator-Prey Model Interaction with Harvesting Effort

  • Muhammad Ikbal Universitas Muslim Maros
  • Riskawati Universitas Muslim Maros
Keywords: Prey-predator; Intraspecific; Harvesting; Routh-Hurwitz


In this research, we study and construct a dynamic prey-predator model. We include an element of intraspecific competition in both predators. We formulated the Holling type I response function for each predator. We consider all populations to be of economic value so that they can be harvested. We analyze the positive solution, the existence of the equilibrium points, and the stability of the balance points. We obtained the local stability condition by using the Routh-Hurwitz criterion approach. We also simulate the model. This research can be developed with different response function formulations and harvest optimization.


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J. Alebraheem and Y. Abu-Hasan, “Persistence of predators in a two predators-one prey model with non-periodic solution,” Appl. Math. Sci., vol. 6, no. 17–20, 2012.

K. pada Das, “A Mathematical Study of a Predator-Prey Dynamics with Disease in Predator,” ISRN Appl. Math., vol. 2011, 2011, doi: 10.5402/2011/807486.

C. Li, Y. Zhang, J. Xu, and Y. Zhou, “Global Dynamics of a Prey-Predator Model with Antipredator Behavior and Two Predators,” Discret. Dyn. Nat. Soc., vol. 2019, 2019, doi: 10.1155/2019/3586508.

R. P. Gupta and P. Chandra, “Dynamical properties of a prey-predator-scavenger model with quadratic harvesting,” Commun. Nonlinear Sci. Numer. Simul., vol. 49, 2017, doi: 10.1016/j.cnsns.2017.01.026.

T. K. Kar and H. Matsuda, “Global dynamics and controllability of a harvested prey-predator system with Holling type III functional response,” Nonlinear Anal. Hybrid Syst., vol. 1, no. 1, 2007, doi: 10.1016/j.nahs.2006.03.002.

B. Mukhopadhyay and R. Bhattacharyya, “Effects of harvesting and predator interference in a model of two-predators competing for a single prey,” Appl. Math. Model., vol. 40, no. 4, 2016, doi: 10.1016/j.apm.2015.10.018.

J. N. Ndam, J. P. Chollom, and T. G. Kassem, “A Mathematical Model of Three-Species Interactions in an Aquatic Habitat,” ISRN Appl. Math., vol. 2012, 2012, doi: 10.5402/2012/391547.

R. K. Upadhyay and S. N. Raw, “Complex dynamics of a three species food-chain model with Holling type IV functional response,” Nonlinear Anal. Model. Control, vol. 16, no. 3, 2011, doi: 10.15388/na.16.3.14098.

N. Ali, M. Haque, E. Venturino, and S. Chakravarty, “Dynamics of a three species ratio-dependent food chain model with intra-specific competition within the top predator,” Comput. Biol. Med., vol. 85, 2017, doi: 10.1016/j.compbiomed.2017.04.007.

A. Rojas-Palma and E. González-Olivares, “Optimal harvesting in a predator-prey model with Allee effect and sigmoid functional response,” Appl. Math. Model., vol. 36, no. 5, 2012, doi: 10.1016/j.apm.2011.07.081.

A. Chatterjee and S. Pal, “Interspecies competition between prey and two different predators with Holling IV functional response in diffusive system,” Comput. Math. with Appl., vol. 71, no. 2, 2016, doi: 10.1016/j.camwa.2015.12.022.

R. D. Parshad, E. Quansah, K. Black, R. K. Upadhyay, S. K. Tiwari, and N. Kumari, “Long time dynamics of a three-species food chain model with Allee effect in the top predator,” Comput. Math. with Appl., vol. 71, no. 2, 2016, doi: 10.1016/j.camwa.2015.12.015.

C. Ji, D. Jiang, and N. Shi, “A note on a predator-prey model with modified Leslie-Gower and Holling-type II schemes with stochastic perturbation,” J. Math. Anal. Appl., vol. 377, no. 1, 2011, doi: 10.1016/j.jmaa.2010.11.008.

X. Y. Meng, N. N. Qin, and H. F. Huo, “Dynamics analysis of a predator–prey system with harvesting prey and disease in prey species,” J. Biol. Dyn., vol. 12, no. 1, 2018, doi: 10.1080/17513758.2018.1454515.

T. K. Kar and S. K. Chattopadhyay, “A dynamic reaction model of a prey-predator system with stage-structure for predator,” Mod. Appl. Sci., vol. 4, no. 5, 2010, doi: 10.5539/mas.v4n5p183.

How to Cite
IkbalM., & Riskawati. (2020). Dynamics of Predator-Prey Model Interaction with Harvesting Effort. Jurnal Matematika MANTIK, 6(2), 93-103. https://doi.org/10.15642/mantik.2020.6.2.93-103