Correction:
I couldn't find a saved game where I had the plague icon next to my name, so I went back to the latest autosave prior to the plague starting anywhere, and played forward from there, making saved games for you as I went.
It turns out that the plague icon never actually appeared next to my name on the score, even when (3 of) my cities became infected.
I'm emailing you (at your hotmail address in your profile) a saved game from 1898, one turn before the plague leaves the aztecs, and a saved game from 1862, one turn before the plague icon appears in the score for the first civ to be infected. Both will be in one attached zip file.
For the 1862 save, my empire is stable enough for you to just ignore my guys and end the turn repeatedly - and although I am at war with three civs, my enemies are wimps who won't actually bother to attack me - except Spain, who will unsuccessfully try to dislodge my army next to my former city that the world council gave to them.
For the 1898 save, it is (still) crashing for me after ending my turn in 1902. I can see the tech progress bar change prior to the crash, and Civ sits there for several seconds, seemingly doing nothing. Perhaps endless recursion.