Here's the thing about Mole Rat disease, which I'm not going to hide because it's something the game really ought to tell you before you start into that area: you can get it from your companion. The basic mechanic is that if you get bitten even once, you get it. If your companion gets bitten, you get it. Presumably because you're sharing fluids or something. If you activate a Protectron and the Protectron gets bitten, you get it. I don't want to speculate what it is you're doing with the Protectron afterward to get infected.
The upshot of this is that before you venture into an area full of infected Mole Rats, dismiss your companion. The positive side is that disease-ridden Mole Rats are only in one place in the game, and you'll know about it before you go in.
The other thing is that while it's permanent, it's really not that bad. It's more like Fallout Herpes than Fallout AIDS, since it's -10 HP.