Or at least their immune systems have the capacity to dismantle the virus very early in the load cycle. Perhaps derived from their endless multitude of hemorrhagic virii (Lassa, for example).
Or as Carlin put it...
“That’s what you gotta hope for, you know, that you get more than one cancer so they eat each other up instead of you. In fact, the way I look at it, the more cancer you got, the healthier you are.”