[PUGACHEV]

It's probably by chance that the diseases Neanderthals had grown immune to were less deadly that the ones our ancestors had evolved to live with. Something similar happened in the Conquest of Mexico: Europeans had a higher degree of tolerance to Smallpox than did the native Mexicans, but no disease native to Mexico affected the Spanish as badly.

But, again, looking at the effect of European diseases on the New World, while they decimated populations to the point that native cultures were unsustainable, they did not exterminate them. A small number of people possessed natural immunity, just a a small number of Europeans had some type of immunity to the Black Death. I do not see an historical precedent to a disease wiping out an entire race; always some few survive, and later flourish.

[MHGinTN]

“... and later flourish.” Or mimngle with the stronger population until they become extinct as a singular species.