A Diseased Three-Species Harvesting Food Web Model with Various Response Functions

Abstract

The purpose of this work is to present a three-species harvesting food web model that takes into account the interactions of susceptible prey, infected prey, and predator species. Prey species are assumed to expand logistically in the absence of predator species. The Crowley–Martin and Beddington–DeAngelis functional responses are used by predators to consume both susceptible and infected prey. Additionally, susceptible prey is consumed by infected prey in the formation of a Holling type II response. Both prey species are considered when prey harvesting is taken into account. Boundedness, positivity, and positive invariance are considered in this study. The investigation covers all the equilibrium points that are biologically feasible. Local stability is evaluated by analyzing the distribution of eigen values, while global stability is evaluated using suitable Lyapunov functions. Also, Hopf bifurcation is analyzed at the harvesting rate H1. At the end, we evaluate the numerical solutions based on our findings.

Keywords

• prey–predator
• Crowley–Martin type
• Beddington–DeAngelis form
• equilibrium
• stability
• bifurcation