Eur. Phys. J. Plus (2022) 137: 138
https://doi.org/10.1140/epjp/s13360-022-02348-9

Regular Article

Dynamics of an infected prey–generalist predator system with the effects of fear, refuge and harvesting: deterministic and stochastic approach

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

Received: 17 September 2021
Accepted: 3 January 2022
Published online: 19 January 2022

Abstract

A predator–prey model with infection in the prey population, including fear, refuge and harvesting factors, is proposed. An expression for basic reproduction number is obtained. Depending on reproduction number, global stability of disease-free and endemic equilibria is established. We have found that disease can be eradicated from the system by controlling the value of basic reproduction number less than one. In addition, deterministic model is analyzed for transcritical and Hopf bifurcations. Thresholds of parameters are identified which determine when the equilibrium is disease-free and when it becomes endemic. An extension is made in the deterministic model by including environmental noise. Sufficient conditions for extinction of species are derived based on environmental noise. We observed that the stochastic system fluctuates around the solutions of corresponding deterministic system when the intensity of white noise is low, whereas high intensity drive the populations to extinction. For justification of analytical results, we have performed numerical simulations and presented the results, which manifest the reliability of the model from ecological viewpoint.