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)

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

Interactive Effects of Disease Transmission on Predator-Prey Model

Journal of Applied Nonlinear Dynamics 9(3) (2020) 401--413 | DOI:10.5890/JAND.2020.09.005

Md. Nazmul Hasan$^{1}$, Md. Sharif Uddin$^{1}$, Md. Haider Ali Biswas$^{2}$

$^{1}$ Department of Mathematics, Jahangirnagar University, Saver, Dhaka, Bangladesh

$^{2}$ Mathematics Discipline, khulna University, Khulna, Bangladesh

Abstract

This paper deals with predator-prey eco-epidemiological model where an infectious disease among fish population is non-linearly transmitted in a reserve area. Then the disease is transmitted indirectly to the predator population during their feeding process. At the time of harvesting, both the susceptible and the infected prey population are harvested. When the nonlinear disease transmission and the inhibition effect on the dynamical behavior of the prey are measured, the number of infected individuals increases. The model in this study is analyzed in term of boundedness, and local and global stability under certain conditions and Hopf bifurcation. For the determine of optimal conditions, we have compared the theoretical results with numerical results for different sets of parameters.

Acknowledgments

The first author gratefully acknowledges the financial support provided by the University Grant Commission, Bangladesh (UGC/1,157/ M.Phil and PhD/2016/5343).

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