I remember seeing this book in the summer of 1987, while working at a book wholesaler, and I have been long hunting around to try to figure out what title it was.
The book opens with some monks determining that rats were somehow connected to the spread of the bubonic plague (Black Death). The Catholic Church seizes upon this and decides to use a ship full of rats as a weapon in a new Crusade to reclaim the Holy Land. The ship was crewed by former convicts(?), pardoned by the Church, and apparently immune to the plague.
However, after departure, the plague mutated, killing the crew. The ship drifted and crashed into land somewhere in the Adriatic, releasing the rats back into Europe.
The net: instead of 1 in 3 European dead due to the plague, it is now 9 in 10, due to the more virulent strain of plague.
This was all a precursor to the main alternative history story, set in more-or-less present day, where the three superpowers are some Mayan/Incan/Aztec society, a Muslim society, and China.