The Calculus Diaries - Jennifer Ouellette [59]
The man who solved the mystery was Dr. John Snow, a pioneer of modern epidemiology. He lived locally, on Fifth Street, and monitored the epidemic’s progress on-site. He was convinced that cholera was spread by a poison passed from victim to victim through tainted water; he’d already traced an earlier outbreak of contaminated water supplied by the Vauxhall Water Company. But authorities didn’t believe him, and the water company refused to admit culpability. He figured this was his chance to prove his theory was right.
Snow patrolled the district, interviewing the families of those who had died, and found that nearly all the deaths had occurred near a water pump on the corner of Broad Street and Cambridge Street—the epicenter of the outbreak. Houses closer to an alternate pump had only experienced ten deaths, and five of those were schoolchildren who occasionally drank from the Broad Street pump. Ever the scientist, Snow took a sample of the pump’s water, examined it under a microscope, and noted that it contained “white flocculent particles,” which he deemed the cause of the infection.
The Board of Guardians in St. James Parish reluctantly followed his advice and removed the pump handle as an experiment. The spread of the disease stopped dramatically. There were still a few unexplained deaths from cholera that appeared unrelated to the Broad Street pump. The most damning was a widow who lived in Hampstead, and her niece, neither of whom lived anywhere near Broad Street. Snow proved quite the detective: He found that the widow had once lived in Broad Street and liked the taste of that well water sufficiently that she had a servant bring her back a large bottle from it every day. The last bottle had been fetched on the day the Soho outbreak began.
Yet authorities were still doubtful of Snow’s findings. A local vicar, Reverend Henry Whitehead, thought the outbreak was the result of divine intervention—a very vicarlike approach to human calamity—and set about “proving” his case. In the end, Whitehead actually helped confirm a single probable cause of the outbreak: A young child living on Broad Street had been ill with cholera symptoms, and the child’s soiled diapers had been soaked in a tub of water that was then emptied into a cesspool three feet from the Broad Street pump. Underground leakage did the rest.
How do we model an outbreak of a disease? Let’s assume that a nasty flu virus strikes a university dormitory. The rate of infection will vary, depending on the nature of the disease and how it is transmitted. The flu is spread when an infected person, during the contagious period, coughs or sneezes near another person or touches another person. We can chart how the number of infected people (I ) changes over time (t)—in other words, I is a function of t, and for our purposes t will be measured in days. For epidemiology, there are two other parameters: how many people an infected person can infect per day, or rate of infection (r), and the rate at which the outbreak fizzles, as infected people recover—or die (a). So there will be a single equation for I(t), in which r and a will appear as parameters.
The end result is almost always the same: As more people recover or succumb and as precautionary measures kick in—quarantine, hand-washing, or just removing the handle of the offending pump—there are fewer new cases of infection. When r is less than 1, each infected person is, on average, transmitting the virus to fewer than one other person. This will not be sufficient to sustain the outbreak, and it will end. As for the flu, so for cholera.
Fourteen years after Snow’s discovery, a cholera epidemic hit Buenos Aires, Argentina. An account of the outbreak can be found in Charles Darbyshire’s My Life in the Argentine Republic 1852-1894. He moved his household