Anthropology

I've said repeatedly I believe the Neanderthal's failure to survive as a species is multi-factorial and not due to a single cause from Homo sapien's presence or any other focus--particularly given the evidence that while they may have had violent encounters back and forth they obviously mated as well. And, of course, in terms of Darwinian explanations for survival of the fittest that you reviewed, all would apply.

A quick answer to your question, however with regard to disease transmission which is never unidirectional among two susceptible species, fully exposed. There can, however, be differences in susceptibility and thus infection rates and severity from genetically-conferred inherent advantages or obviously from prior exposure and thus immunity--whether full or partial--to the same or a closely related organism. Only infectious disease that quickly kills its host in nearly every instance would be unlikely to be spread to other populations, other geographical regions, or indeed to other susceptible species.

The original article tries to determine the cause of the disappearance of Neanderthals as a distinct species, but, in fact, Neanderthal DNA persisted. A better question, IMO, would be why, if the species was (in the mind of the author) inferior to Homo sapiens, then why did so much of its DNA persist within us? And, what benefits might that confer to the individual or be adapted in other areas of medicine in the future?