Increase of the prey may decrease the healthy predator population in presence of a disease in the predator,

We propose here a predator-prey model with an epidemics spreading only among the former by contact between a sound individual and an infected. An infected cannot recover, once contracted the disease. The prey are assumed to grow logistically, the predators are distinguished between disease carriers and sound individuals. Both feed only on the prey species, with saturation effects in the predation functions. The local stability analysis of the equilibria is carried out together with a bifurcation analysis. In addition to a saddle node and a transcritical bifurcations occurring in a couple of different equilibria, we also show that a supercritical Hopf bifurcation arises. A detailed comparison with some specific particular cases is performed, showing that the introduction of the disease may very well alter the demographic system's behavior, allowing the collapse at least of the predators. Also altering the system's coexhistence equilibrium value by increasing the prey has an adverse effect on the predators population, in that the infected predators will increase.