Three influenza pandemics struck the world in the 20th century, including the Spanish flu of 1918 that claimed anywhere from 50 million to 100 million lives. (There were no effective flu vaccines available at the time.) When a flu that contagious spreads across the world, how does it ever die out?

It runs out of victims. Infectious diseases like the Spanish flu spread exponentially as more and more people are infected and become contagious. As people develop immunities, receive vaccines, or otherwise shield themselves from infection, the pool of possible victims dwindles until the virus can no longer sustain itself.

Epidemiologists often describe the rate of infection in terms of a reproduction number, the average number of new people whom each sick person will infect. If this number is higher than one, even by a small amount, the disease is still spreading. (One study estimates that the reproduction number of the Spanish flu was 1.49 when the disease first hit Geneva and a whopping 3.75 in the second wave, which came shortly thereafter.) If the number is less than one, the disease is on the decline....