https://doi.org/10.1140/epjp/s13360-023-04476-2
Regular Article
Deterministic and stochastic study of an eco-epidemic predator–prey model with nonlinear prey refuge and predator harvesting
1
Department of Mathematics and Statistics, Aliah University, IIA/27, New Town, 700160, Kolkata, India
2
Department of Mathematics, University of Kalyani, 741235, Kalyani, India
Received:
6
July
2023
Accepted:
12
September
2023
Published online:
26
September
2023
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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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
