The authors consider an eco-epidemiological system consisting of three species, namely, the sound prey, the infected prey and the predator population. Persistence and extinction conditions of the populations are derived and conditions are determined for which the system enters a Hopf-type bifurcation. Moreover, the fact is observed for which the bifurcated branches are supercritical in some parametric region space in a special case when the predator response function is a Holling-type II function.