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

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...

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Bibliographic Details
Published in:European physical journal plus 2023-09, Vol.138 (9), p.851, Article 851
Main Authors: Islam, Md Sarijul, Sk, Nazmul, Sarwardi, Sahabuddin
Format: Article
Language:English
Subjects:
Applied and Technical Physics
Atomic
Background noise
Complex Systems
Condensed Matter Physics
Disease transmission
Endangered & extinct species
Epidemics
Extinction
Hopf bifurcation
Infections
Investigations
Mathematical and Computational Physics
Mathematical models
Molecular
Optical and Plasma Physics
Physics
Physics and Astronomy
Predation
Predator-prey simulation
Predators
Prey
Regular Article
Species extinction
Stability
Stochastic models
Stochastic systems
Theoretical
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Summary: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.
ISSN:2190-5444
2190-5444
DOI:10.1140/epjp/s13360-023-04476-2