As hypothesized by Paul W. Ewald in his book, Plague Time, the spread seems more likely to have been an artifact of human actions, not only overcrowding in military hospitals and barracks, but also the worldwide failure of civilian authorities to appreciate the need for isolating/quarantining the ill.
(Ewald's logic involves an application of evolutionary theory that's too detailed for me to attempt a summary. But if you're seriously interested in the topic, I think you can't go wrong by reading his short book!)