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Deterministic and stochastic study of an eco-epidemic predator–prey model with nonlinear prey refuge and predator harvesting

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Abstract

The present article deals with an eco-epidemic predator–prey model with infection in the prey population. The model system includes nonlinear prey refuges, harvesting in the predator, and assumes that the predator population preys on both prey populations following Holling type I functional response. After formulating the model system, the points of steady state are determined, and local stability and the global stability nature are discussed to examine the long-term behavior of the system. An expression for basic reproduction number is derived. By controlling the value of the basic reproduction number to be less than unity, it is found that the disease can be eradicated. Furthermore, Hopf-bifurcation with respect to important biological parameters and transcritical bifurcation are illustrated. An extension is introduced in the deterministic system by incorporating of environmental noise. Global positive solution as well as sufficient conditions for the extinction of species in the stochastic system are established. To validate the analytical findings of both the deterministic and stochastic model systems, we have executed numerical simulations.

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Data Availability Statement

This manuscript has associated data in a data repository. [Authors’ comment: The data that support the findings of this study are available from the corresponding author upon reasonable request.]

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Acknowledgements

The corresponding author Dr. Sarwardi is grateful to the Department of Mathematics and Statistics, Aliah University for providing necessary facilities to perform the present work. Mr. Islam is highly thankful to UGC (University Grants Commission), New Delhi, Govt. of India [NTA Ref. No.: 201610315672] for awarding doctoral scholarship. Mr. Nazmul is thankful to the Department of Mathematics, University of Kalyani for providing opportunity to do this research work.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Aliah University, IIA/27, New Town, Kolkata, 700160, India

    Md Sarijul Islam & Sahabuddin Sarwardi

  2. Department of Mathematics, University of Kalyani, Kalyani, 741235, India

    Nazmul Sk

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  1. Md Sarijul Islam
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Contributions

The conceptualization and formal analysis of this research article were done by MSI and SS. The authors MSI, SS, and NS contributed equally to the main results and numerical simulations. All authors have read and approved the final manuscript for submission.

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Correspondence to Sahabuddin Sarwardi.

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Islam, M.S., Sk, N. & Sarwardi, S. Deterministic and stochastic study of an eco-epidemic predator–prey model with nonlinear prey refuge and predator harvesting. Eur. Phys. J. Plus 138, 851 (2023). https://doi.org/10.1140/epjp/s13360-023-04476-2

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