Is it true of false that a disease that wiped out the rabbit population in an enviorment would affect the coyote population in the same environment?

This question has an awkward wording, however, the answer is yes.

Obviously, if the rabbit population decreases, so will the coyotes. Because, in assumption, the coyotes rely on the rabbits for food for survival.

Another answer can be yes and no, because if we are talking about the same disease, the disease can probably only target this specific species (rabbit), and the coyotes will not be affected. Or it might spread to any other animal available. Then again, both species are affected and will decrease.