This study investigates an ecological epidemiological model of prey harvesting and predator switching with time delay. Firstly, the linearization of the system is performed, and the method of analyzing the eigenvalues is used to show that when the predator's digestion delay exceeds a certain bifurcation threshold, the system loses stability and exhibits a Hopf bifurcation. Secondly, based on the theory of normal forms and center manifold, computational steps describing the characteristics of the Hopf bifurcation in the system are derived. Thirdly, under the influence of linear time-delayed feedback control, it is shown that the occurrence of the Hopf bifurcation can be effectively delayed while keeping the original equilibrium point of the system unchanged. Finally, numerical simulations are conducted to support the analytical results.