The role of human shield in prey‎, ‎crop-raiders and top predator species in southwestern Ethiopia's coffee forests‎: ‎a modeling study

Volume 36, Issue 3, pp 333--351 https://dx.doi.org/10.22436/jmcs.036.03.08

Publication Date: August 10, 2024 Submission Date: February 05, 2024 Revision Date: April 14, 2024 Accteptance Date: July 08, 2024

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Authors

A. A. Thirthar - Department of Studies and Planning, ‎University of Fallujah, Anbar, Iraq. Sh. Jawad - Department of Mathematics‎, ‎College of Science, ‎University of Baghdad, Baghdad, Iraq. P. Panja - Department of Applied Science, ‎Haldia Institute of Technology, ‎Haldia‎, ‎721657‎, ‎W.B., India. A. Mukheimer - Department of Mathematics and Sciences, ‎Prince Sultan University, ‎P.O‎. ‎Box 66833, ‎11586 Riyadh, ‎Saudi Arabia. Th. Abdeljawad - Department of Mathematics and Sciences, ‎Prince Sultan University, ‎P.O‎. ‎Box 66833, ‎11586 Riyadh, ‎Saudi Arabia. - Department of Mathematics and Applied Mathematics‎, ‎School of Science and Technology, ‎Sefako Makgatho Health Sciences University, ‎Ga-Rankuwa, ‎South Africa. - Center for Applied Mathematics and Bioinformatics (CAMB), ‎Gulf University for Science and Technology, ‎Hawally‎, ‎32093, ‎Kuwait.

Abstract

‎In this work‎, ‎we have developed a model that describes the relationships between top predators (such as tigers‎, ‎hyenas‎, ‎and others)‎, ‎crop raiders (such as baboons‎, ‎warthogs‎, ‎and deer)‎, ‎and prey (such as deer) in the coffee forests of southwest Ethiopia‎. ‎Various potential equilibrium points are identified‎. ‎Additionally‎, ‎the model's stability in the vicinity of these equilibrium points is examined‎. ‎An investigation of the model's Hopf bifurcation is conducted concerning several significant parameters‎. ‎It is found that prey species may be extinct due to a lower growth rate and consumption by top predators in the absence of human interference in the carrying capacity of prey‎. ‎It is observed that top predators may be extinct due to human interference in their carrying capacity and their smaller dependence on humans in terms of prey and crop raiders‎, ‎respectively‎. ‎It is also found that there is an increase in intra-species competition among the top predators‎, ‎which may intensify the stability of the model‎. ‎Again‎, ‎it is also observed that the increase in the intrinsic growth rate of prey and top predators may improve the stability of the model‎. ‎Lastly‎, ‎some numerical simulation results have been shown to help visualize the model's dynamics‎.

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Keywords

• Human shield
• prey-predator model
• stability analysis
• Hopf bifurcation
• numerical simulation

MSC

•  37Dxx
•  34Dxx
•  76Fxx

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