I commonly hear 90 or 95% of the new world population died from infectious disease, but I've recently been studying mathematical models of epidemiology and I find it very implausible that any disease outbreak could kill so many. Mortality from smallpox is usually around 30%. The mortality in the new world (and likely the susceptibility as well) were probably significantly higher, but as an outbreak runs its course the survivors become immune and once a significant portion becomes immune (1-1/R*0) the disease free equilibrium becomes stable Given that R0* for smallpox is roughly 2.5 once around 60% of the (surviving) population is recovered the outbreak will wear itself off, that's not even taking into account the lower density. By the law of mass action when the total population is reduced collisions between infected and susceptible people will decline (thus reducing transmission). Given that the majority of the new world (with the exceptions of the Andes, Central America, and parts of the eastern US) were hunter gatherer societies that were fairly sparsely populated I can't imagine a high enough contact rate (outside of those locations) to spread a disease fast enough for enough people to die before a significant recovered population accumulates.

Where did this 90% or 95% figure come from? Estimates of the precolombian population are all over the map from what I've read (I've heard estimates ranging from a few million to over a hundred million, my guess is around 30 or 40 million or so) so how can historians be so confident that the new world epidemics killed more than 90% of the population?