Dynamics and Bifurcation Analysis of an Eco-Epidemiological Model in a Crowley–Martin Functional Response with the Impact of Fear

This article describes a three-species food web model that was developed by considering the interaction between susceptible prey, infected prey, and predator species. It is assumed that susceptible prey species grow logistically in the absence of predators. It is assumed that predators consume susceptible and infected prey and that infected prey consumes susceptible prey. We consider the effect of fear on susceptible prey due to the predator species. Furthermore, the predator consumes its prey in the form of Holling-type and Crowley–Martin-type interactions. Also, infected prey consume susceptible prey in the form of a Holling-type interaction. The conditions of all biologically feasible equilibrium points were examined. The local stability of the systems around these equilibrium points was investigated. Furthermore, the occurrence of Hopf-bifurcation concerning fear ϱ in the system was investigated. Finally, we demonstrate some numerical simulation results to illustrate our main analytical findings.