People had fleas, too.
"Once a human is infected, a progressive illness generally results unless specific antibiotic therapy is given. Progression leads to blood infection and, finally, to lung infection. The infection of the lung is termed plague pneumonia, and it can be transmitted to others through the expulsion of droplets by coughing."
The high death rates were human to human.
Btw, the rat flea was the carrier, not the human flea.
http://www.nps.gov/public_health/inter/info/factsheets/fs_plague.htm