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ISSN:2325-6192 (print)
ISSN:2325-6206 (online)
Journal of Environmental Accounting and Management
António Mendes Lopes (editor), Jiazhong Zhang(editor)
António Mendes Lopes (editor)

University of Porto, Portugal

Email: aml@fe.up.pt

Jiazhong Zhang (editor)

School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi Province 710049, China

Fax: +86 29 82668723 Email: jzzhang@mail.xjtu.edu.cn

An Eco-Epidemiological Model with Harvesting and Discrete Delay: A Mathematical Study

Journal of Environmental Accounting and Management 11(4) (2023) 441--465 | DOI:10.5890/JEAM.2023.12.006

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

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Abstract

The present study deals with the study of the dynamics of an eco-epidemiological prey-predator mathematical system. The model that is proposed is an eco-epidemiological system of prey-predator association in consideration of discrete time delay where the prey population suffers from a disease which is modelled by the Susceptible-Infected (SI) epidemic scheme. We have assumed that the predator devours the vulnerable prey along with the diseased prey population in accordance with the modified Holling type II functional response. Harvesting of susceptible prey and predator have been considered and their effect has been analyzed also. To avoid the extinction of the prey population, refuge of prey is considered and its effect is observed on the stability of the system. Numerical simulation of the models reveals that the dynamical system undergoes Hopf-bifurcation due to the encounter rate, presence of refuge population and infection rate. Ecologically, the study discloses that harvesting, refugia and the rate of infection can be effectively used as a modulating parameter and may explain the reason behind the coexistence of prey-predator species and can remarkably affect the equilibrium of the dynamical system.

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