Most diseases have a "reservoir" in nature, usually a species that is not effected or at least not strongly effected by the disease. Its these reservoirs that make it impossible to eradicate the disease species because they provide a continual source that re-infects the host species even if all of hosts are cured.
The only reason small pox could be eradicated was because it had no natural vector, it was only spread from humans to other humans.
Is varroa only spread from bees to bees? or does it survive on other insects in the wild?