A role of fear on diseased food web model with multiple functional response.

Abstract

In this paper, we analyze the role of fear in a three-species non-delayed ecological model that examines the interactions among susceptible prey, infectious (diseased) prey, and predators within a food web. The prey population grows in a logistic manner until it achieves a carrying capacity, reflecting common population dynamics in the absence of predators. Diseased prey is assumed to transmit infection to healthful prey by the use of a Holling type II reaction. Predators, alternatively, are modeled to consume their prey using Beddington--DeAngelis and Crowley--Martin response features. This evaluation specializes in ensuring the non-negativity of solutions, practical constraints on population dynamics, and long-term stability of the system. Each biologically possible equilibrium point is tested to understand the environmental stable states. Local stability is assessed through eigenvalue analysis, while global stability of positive equilibria is evaluated by the use of Lyapunov features to determine the overall stability of the model. Furthermore, Hopf bifurcation is explored primarily based on infection rate $\varepsilon$. Numerical simulations are carried out to validate the theoretical effects and offer practical insights into the model behaviour under specific conditions.