An Eco-Epidemiological Model Involving Prey Refuge and Prey Harvesting with Beddington–DeAngelis, Crowley–Martin and Holling Type II Functional Responses

Abstract

This paper represents a three-species food web model based on the connections between susceptible prey, infected prey, and predator species. It is considered that in the absence of predator species, prey species grow logistically. Predators consume susceptible and infected prey in the form of Crowley–Martin and Beddington–DeAngelis functional responses. Also, infected prey consumes susceptible prey in the form of Holling type II interactions. Here, prey refuge and harvesting in prey with disease in a prey population are taken into consideration. Positiveness, boundedness, and positive invariance are examined. All biologically feasible equilibrium points are investigated. The local stability of positive equilibria and their global stability are analyzed by the suitable Lyapunov functions. Finally, numerical solutions are analyzed according to our findings.

Keywords

• eco-epidemiological model
• Crowley–Martin functional response
• Beddington–DeAngelis form
• stability
• equilibrium