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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Impacts of Predator Harvesting on Extinction of Prey in an Eco-Epidemic System

Journal of Applied Nonlinear Dynamics 14(1) (2025) 31--52 | DOI:10.5890/JAND.2025.03.003

Banshidhar Sahoo

Department of Mathematics, Hiralal Bhakat College, Nalhati, Birbhum, West bengal, India

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Abstract

Through the development of a mathematical model, the impacts of predator harvesting in the presence of infectious prey are examined. It is commonly established that only harvesting or only infectious disease may cause species extinction. In contrast the combined effects of harvesting and infectious disease on species extinction in an eco-epidemic system was unexplored. In order to examine various dynamical circumstances, various predator harvesting strategies are included in this paper. The essential theoretical properties of the models such as dissipativity, local and global stability analysis of equilibrium points are done. The Hopf bifurcations and its continuations are evaluated with the variation of ecological parameters. The maximum sustainable yields are determined with the variation of harvesting effort. Numerical results of the system dynamics and bifurcation analysis are presented for experimentally obtained parameter values. The key observation is that uncontrolled harvesting of predator species not only cause predator extinction but also it may led to rapid extinction of prey species. The study's conclusion is that, in real-world eco-epidemic systems, the combined impacts of predation in the presence of infection in the prey can accelerate the extinction of prey species compared to the case of predation simply in the absence of infection.

Acknowledgments

The Jacobian matrix at $E_D^1$ is given by \begin {eqnarray} J(E_D^1)=\left(\begin{array}{ccc} 1-2\bar{s}- \frac{a\bar{p}}{(1+b\bar{s})^2} & -\beta \bar{s}+(\alpha+c) & - \frac{a\bar{s}}{1+b\bar{s}}\\ 0 & \beta \bar{s}-\gamma \bar{p}-(\alpha+d_1) & 0\\ \frac{\epsilon a \bar{p}}{(1+b\bar{s})^2} & \epsilon \gamma \bar{p} & 0\nonumber\\ \end{array}\right), \end{eqnarray}

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