  We consider a predator-prey population model with prey gathering together for
defense purposes. A transmissible unrecoverable disease affects the prey. We
characterize the system behavior, establishing that ultimately either only the
susceptible prey survive, or the disease becomes endemic, but the predators are
wiped out. Another alternative is that the disease is eradicated, with sound
prey and predators thriving at an equilibrium or through persistent population
oscillations. Finally, the populations can thrive together, with the endemic
disease. The only impossible alternative in these circumstances is predators
thriving just with infected prey. But this follows from the model assumptions,
in that infected prey are too weak to sustain themselves. A mathematical
peculiarity of the model is the singularity-free reformulation, which leads to
three entirely new dependent variables to describe the system. The model is
then extended to encompass the situation in which ingestion of diseased prey is
fatal for the predators.
