We should remember, however, that pigs, chickens, ducks, geese, and cows were not the only domestic animals raised during the Middle Ages. Rabbits, pigeons, and carp must also be recognized. Virtually every monestery and convent had a fish pond and castles and manor houses were outfitted with pigeon lofts when they were constructed. I would suspect that the vast majority of rabbits consumed were from domestic sources. IMO, the existence of rabbit fever in wild rabbits, if it were even known about, would not have have been a major influence in setting rabbit seasons.
Rabbits are carriers of several parasites.
These parasites tend to proliferate during warm months with the cycle being completed by late summer. That is the reason that I normally take rabbits only in the fall and cooler months. All wild meat at a certain point in history was considered venison. Archaic usage of venison is the meat of a game animal. From the Latin venatus, past participle of venari, to hunt.