Hunting for the guinea pig infection

There's not much to study. Infected sims receive a moodlet (debuff) that tells you exactly how long they still have before they succumb and then they can order a cure at the computer ("Research Rodent Fever"). They leave a cool ghost, though. The pack lifestream should have some footage as has this video: https://www.youtube.com/watch?v=a-XOxxV4IwI

There should be a number of rodent fever ghosts in the gallery (I'd be surprised if there weren't), but with only basegame you won't be able to use them.

If you're interested in twists of infections in Sims games, look up the Strangerville expansion! It comes with a questline regarding a spores infection that will spread and can (but doesn't have to) stopped by the player. Quest-based gameplay of that kind is rare in Sims 4, in this form it occurs only in the Strangerville and Journey to Batuu packs.