Look at how the disease spread in Scandinavia. Literally, one day Iceland seals its borders, enforcing an armed quarantine, and the next day the disease is spreading virulently through the rest of the population. Within like 48 hours the rash has achieved almost total saturation through all the rest of northern Europe. That's fast. Basically all the characters we meet are already isolated in some way or another by the time we meet them. Everyone else already has the disease, they just don't know it.
So... sealed early, total isolation, total self-sufficiency, absolutely no contact whatsoever for days or weeks while the critical period passes, not even personnel changes... aside from Iceland, who does that sound like?
That's why the nuclear submarines seem the most likely to me. Carrier fleets could, too, but would they really have no contact at all for that long, not even people flying on and off? If they would, then yeah, it makes total sense that they would start doing island defense. Maybe some of the Hawaiian islands, near the big US naval base there?