I think the wave of human settlers appearing in the Middle East and Europe before the Ice Age Maximum of about 35,000 years ago brought hunting pressure and perhaps warfare, as stated by the author, but disease, if carried over to a previously isolated population of humans, like it did to the American Indian, could have easily wiped out our Neanderthal cousins.
In my opinion disease is not only possible, but probable. The time line seems to work better for disease than for warfare. There's not a lot of evidence I'm aware of for pre-agricultural warfare, although I could be out of date.