As in OTL, the outbreak of the Black Death happened in 1337 (3034, Yin Fire Ox in the Chinese calendar) in the province of Hubei, China. But because there was no world-spanning Mongol Empire without inner barriers, which helped trade enormously, and China itself was split too, it took much longer to spread.
Spreading in East Asia:
- 1340 (3037, Yang Metal Dragon): Black Death spreads all along the Yangtse.
- 1344 (3041, Yang Wood Monkey): Black Death hits Hong China.
- 1347 (3044, Yin Fire Pig): Black Death hits the South Chinese coast kingdom.
- 1349 (3046, Yin Earth Ox): Black Death reaches Szechuan.
- 1352 (3049, Yang Water Dragon): Black Death hits Dali in SW China.
- 1353-59 (3050, Yin Water Snake / 3056, Yin Earth Pig): Black Death sweeps through Jin China.
- 1355: Pagan empire struck by Black Death.
- 1360: Khmer hit by Black Death.
- 1362: Black Death in Goryeo.
- 1363/64: Black Death brought to Nippon by ships.
- 1365-71: Black Death sweeps through Sultanate of Delhi.
- 1372-75: Various South Indian states are struck by the Black Death.
Spreading in the Russian lands:
- 1394-96: Black Death sweeps through Southern Russian states.
- 1397: Western Russian states struck by Black Death.
- 1397-1401: Novgorod hit by Black Death.
- 1399-1402: Black Death reaches Vladimir-Suzdal and other eastern Russian states.
Spreading in the Muslim world:
- 1374: Black Death reaches Afghanistan.
- 1377-81: Black Death hits Persia.
- 1378-85: Black Death strikes Choresm, preventing a reconquest of Persia.
- 1384-90: Seljuk lands struck by Black Death, which helps them losing the Crusade. The little isolated country of Montenegro is spared by the plague, though.
- 1387-89: Egypt hit by Black Death.
Spreading in Central Europe:
- 1392/93: Black Death strikes Hungary, being introduced by returning crusaders. The king also dies of it.
- 1394: Black Death arrives in Venice.
- 1394/95: Black Death hits the Holy Roman Empire. Poland is also affected, but by imposing a quarantine it's mostly saved; so is Flanders. Persecuted Jews flee to Poland, Flanders, Seljuk Balcans.
- 1395: Other Italian states are hit by the Black Death (although there are some exceptions, like Florence and Savoy). The divine republic of Parma is especially shocked - their preachers promised them that God would spare them, which doesn't happen.
- 1396: The lands of the Teutonic Order are struck by Black Death.
Spreading in Western Europe:
- 1399: Black Death strikes Scotland.
- 1400: Ireland is hit by the Black Death.
As a fast result of the Black Death, two new addictions spread through Europe: Liquor, known by the alchemists for longer time already, was (mis-)used as a cure against the plague. So was tobacco, which was brought from the New World and sold for high prices.
And finally, in 1435 Black Death hit the New World, destroying some small European settlements too; other trade places had to be given up, since the Atlantean trade partners had died or didn't want to have contact with the Europeans any more.