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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

A Lesli-Gower Type Predator-Prey Model with Allee Effect and Disease in Predator

Discontinuity, Nonlinearity, and Complexity 14(1) (2025) 39--61 | DOI:10.5890/DNC.2025.03.004

Manish Sarkar$^1$, Ashok Mondal$^2$, Anindita Bhattacharyya$^1$, A. K. Pal$^3$

$^{1}$ Department of Mathematics, Amity University, Kolkata, India

$^2$ Department of Mathematics, Sir Gurudas Mahavidyalaya, Kolkata, India

$^3$ Department of Mathematics, Seth Anandaram Jaipuria Collee, India

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Abstract

The present study considers the dynamical response of an eco-epidemiological model consisting of prey and infected predator species population. Here, Leslie–Gower type model is considered for predator–prey interaction where the most common mathematical form to express the Allee effect in the prey growth function is considered. The well-posedness, existence and stability of different equilibria were explored thoroughly. Each equilibrium is stable both locally and globally within some prescribed regions and parametric condition. Hopf bifurcation around the interion equilibrium is explored and Allee threshold plays a significant role as bifurcation parameter. Suitable set of parameter values were observed for which transcritical bifurcation is observed around the boundary equilibrium point. Our analytical findings are exemplified through computer simulation using MATLAB, which show that this model may be valuable for analysing the ecological and eco-epidemiological phenomena in our eco-system.

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