NEW ORLEANS—Bill Gates says there are many lessons to be learned from the Ebola epidemic raging in West Africa. The biggest, he says, is that the world has far to go before it is prepared to combat an even-larger disease threat.

“The world as a whole doesn’t have the preparedness for epidemics, and we’ve had a few flu scares that got us to do some minor things, but not enough,” he said in an interview at the annual meeting of the American Society of Tropical Medicine and Hygiene here. “If this thing had been twice as transmissive,...