Dynamical behavior of a diseased predator-prey model with fear effect and prey harvesting

This article consists of a three-species food web model that has been 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 . We consider the effect of fear on susceptible prey due to predator species. Again, the harvesting of susceptible and infected prey has been considered. Furthermore, the predator consumes its prey in the form of Holling-type interactions. The positive invariance, positivity, and boundedness of the system are discussed. The conditions of all biologically feasible equilibrium points have been examined. The local stability of the systems around these equilibrium points is investigated. Furthermore, the occurrence of Hopf-bifurcation concerning the harvesting (h) of the system has been investigated. Finally, we demonstrate some numerical simulation results to illustrate our main analytical findings.