Historical Review: Megadrought And Megadeath In 16th Century Mexico (Hemorrhagic Fever)
"The epidemic of cocoliztli from 1545 to 1548 killed an estimated 5 million to 15 million people, or up to 80% of the native population of Mexico (Figure 1). In absolute and relative terms the 1545 epidemic was one of the worst demographic catastrophes in human history, approaching even the Black Death of bubonic plague, which killed approximately 25 million in western Europe from 1347 to 1351 or about 50% of the regional population.
"The cocoliztli epidemic from 1576 to 1578 cocoliztli epidemic killed an additional 2 to 2.5 million people, or about 50% of the remaining native population. Newly introduced European and African diseases such as smallpox, measles, and typhus have long been the suspected cause of the population collapse in both 1545 and 1576 because both epidemics preferentially killed native people. But careful reanalysis of the 1545 and 1576 epidemics now indicates that they were probably hemorrhagic fevers, likely caused by an indigenous virus and carried by a rodent host."
(You've probaly never seen or heard of this study because it doesn't blame the evil White people.)
From Wikipedia:
Although some areas continued an essentially Middle Mississippian culture until the first significant contact with Europeans, most areas had dispersed or were experiencing severe social stress by 1500. Along with the contemporary Anasazi, these cultural collapses coincide with the global climate change of the Little Ice Age.
So, it's a chicken or egg guess. Which came first? Perhaps cocoliztli was spread by rodents infesting these people BECAUSE of global cooling, when the natural food supply the rats relied on whithered up? This same disease (or the rodent carriers) spread Southward, reaching Mexico by 1545.