The Calculus Diaries - Jennifer Ouellette [60]
I felt positive that sooner or later there must be an epidemic. There was no drainage. The soil on which the houses were built was becoming infected. The defecations, the waste water from kitchens, etc. went into wells 30 feet deep in the back patios. When one of these wells became full of filth and could hold no more, what was called a sangria (a bleeding) was made. A well was sunk to the same depth . . . and the sangria took place by pushing an iron bar through the full well . . . as the old well began to drain into the new. This went on for years, and some of the patios in the old houses were honeycombed by wells.
Darbyshire’s fears proved well founded when an epidemic broke out in the summer of 1868, brought about (he believed) by Brazilian ships tossing the bodies of those who had died from cholera into the River Paraná, contaminating the water supply. People fled to the countryside, bringing the disease with them, and Darbyshire advised his neighbors not to drink the water unless it was boiled, to bury all refuse, and to keep floors and patios clean. His own household did not contract the disease, which lent credence to his advice. Despite all the deaths, there was one positive outcome: The Argentine government overhauled the city’s drainage system and installed a proper water supply.
Darbyshire correctly identified a contaminated water source as the source of the outbreak. Initially the disease spread at a very rapid rate, and people panicked. With no quarantine in effect, those already infected brought the contamination to the countryside. Had that first city been quarantined, the outbreak would have been contained as the rate of removal (a) increased. Just as with an economic market, at some point, a critical threshold is reached, and the exponential growth rate of removal would level off as fewer and fewer people remained to be infected. Darbyshire had the foresight to put protective measures in place that limited the spread of infection. That caused the rate of removal to increase even faster, and thus the outbreak leveled off and died out much more quickly.
In the case of cholera, there was a single vector: the Broad Street pump, or, more specifically, the white flocculent particles contained in the water that came out of that pump. The disease spread to whomever drank from that particular source. A disease like the Black Death is much more complicated to model because there is more than one vector.
MASQUE OF THE BLACK DEATH
One week before Christmas in 1664, a comet streaked across the sky over England. Astrologers claimed it was an omen of impending apocalypse. One William Lilly predicted that this, combined with a lunar eclipse in January 1665, would bring “the sword, famine, pestilence, and mortality or plague.” Lilly was really hedging his bets—why not throw in a prediction of a zombie invasion or an asteroid strike while he was at it?—but his dire prediction came partially true. Pestilence was common in the rat-infested urban centers of England, and this led to a deadly outbreak of bubonic plague in London in the summer of 1665.
By October, one in ten Londoners had succumbed to the disease—over sixty thousand people. The government banned public meetings, but the epidemic spread to Cambridge, where the young Isaac Newton was in his second year of studies. The university closed, and Newton was forced to return to his country home in Grantham for over a year until the plague had run its course and the university opened its doors again in April 1667. And in that short time, he invented calculus, with no idea that it would one day be applied to study the spread of disease.
This was not the plague’s first appearance. Back in the Middle Ages, the plague decimated Western Europe, wiping out roughly one third of the population, some 25 million people. It could sweep through a region and wipe out