Dr John Snow:A Model of Disease Transmission

John Burkardt,Interdisciplinary Center for Applied Mathematics &

Information Technology Department,Virginia Tech.

..........“Farewell Address”

to Eric Beeson, Robert Hagan and Chris Metz,the Computational Science Directed Study Class,

Virginia Tech, 05 May 2009...........

http://people.sc.fsu.edu/∼jburkardt/presentations/death map 2009 vtcs.pdf

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The Death Map

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Cholera Becomes A Worldwide Disease

In the early nineteenth century, European doctors working in Indiareported a strange new disease called cholera.

Cholera was agonizing and fatal.

No one knew how it was transmitted. No one had any idea how totreat or prevent it.

Yearly reports showed that cholera had begun to move across Asia,and into southern Europe. Soon it showed up in England.

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Cholera Spreading Like a Dark Cloud

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The Miasm Theory

This picture, illustrating a cholera epidemic, displays one commontheory of cholera’s transmission: transmission by miasm.

A miasm was a hypothetical airborne cloud, smelling terrible, andcarrying the disease.

Miasm explained why cholera victims often lived in poor areas fullof tanneries, butcher shops, and general dirty conditions.

It also explained why cholera did not simply spread out across theentire population, but seemed to travel, almost like the wind,settling down to devastate a neighborhood, then moving on.

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The Miasm Theory

The miasm theory was accepted by doctors and public officials.

They assumed there was nothing they could do, except perhaps todrive out the bad air, using smoke or scented handkerchiefs, and totell people not to live in low-lying areas near swamps and marshes.

This was still 40 years before Pasteur and Koch and otherscientists were able to identify the bacteria associated somediseases, to show that bacteria caused those diseases, and thatkilling bacteria could prevent disease.

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The Cholera Bacteria: Vibrio Cholerae

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Dr John Snow

Dr John Snow argued that the miasm theory was unscientific.

Even though he could not show what was causing the disease, hefelt strongly that it was transmitted by water.

Without knowing about bacteria, this is somewhat like trying to dophysics without really understanding atoms!

But the important thing was that Dr Snow was trying to make animproved model of disease, one that explained the facts he knew.

If the model was good enough, it might also tell him how toprevent disease.

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Dr John Snow

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Evidence That Miasms Were a Bad Model

The miasm theory didn’t satisfy Dr Snow because it didn’t try toexplain the patterns he had noticed.

In one small outbreak of cholera, only people living near theThames river got sick. To Dr Snow, this suggested something inthe river water. To the miasm defenders, there must have been adisease cloud floating along the low-lying river areas.

A second outbreak occurred away from the river, in an area withpiped-in water. People getting water from one company werehealthy, while others got sick. The intake pipes for that onecompany were located upstream from London. Again, the miasmdefenders were not impressed by the small amount of data.

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Golden Square: Cholera Outbreak of 1854

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Golden Square:

For most people in London, there was no running water. Fordrinking, cooking, cleaning and bathing, they went to one of thetown pumps which drew water directly from the ground.

Most people had no sewage system. People used chamberpotsand buckets, which were emptied into cisterns and carted off by aninformal network of night-soil carters.

People were used to getting sick from the water now and then.

But when cholera bacteria arrived in London, and seeped from acistern into the water, people died by the hundreds.

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A Map of the Golden Square Area

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John Snow’s Investigation

Dr John Snow suspected the water pump on Broad Street, but heneeded hard evidence that would confirm the model of diseasetransmission he was developing:

He made a map of the district.

He marked every house where cholera victims had lived;

He paced the distance to the nearest pumps;

The houses closest to the Broad Street pump were circled bya black line.

This was the Death Map.

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The Broad Street Pump and its Neighborhood

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Investigating the Exceptions

He personally interviewed people to explain exceptions to thepattern he found:

healthy workers at a beer factory didn’t drink any water!;

some sick children lived outside the district, but came toschool there;

a woman who lived miles away had her son deliver “fresh”water from the Broad Street pump because she liked its taste.

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Focus on the Pumps

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It’s Obvious – Once You See It

Snow’s map strongly suggested that people who died were preciselythose for whom the Golden Square pump was the closest.

The miasmic cloud theory required the miasm, purely by chance,to settle only over people who used the Golden Square pump.

Dr Snow’s map destroyed the miasm theory, because it could showwhere deaths occurred in a way that suggested why.

It took another 30 years before the exact cause of the disease, thecholera bacterium, was actually identified.

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Just a Touch of Mathematics

There were two organizing principles in Dr Snow’s map:

the pumps were “centers” of the geometry

the distance to the nearest pump organized the inhabitantsinto “cells”

Dr Snow imagined every dead person walking back to the pumpthat was the nearest to them, and found most of them met atGolden Square.

Dr Snow was doing epidemiology, but also mathematics.His map is an interesting example of a Voronoi diagram.

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A Voronoi Diagram of 50 Random Points

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A Good Model Can Convince Others

We may care about the mathematics, but what was important toDr Snow was that by using this model, he was able to convincepublic health officials that he had explained the cause of thedisease.

Because his model was convincing, the public official acted - theylocked the Broad Street pump.

Dr Snow’s investigations drove the London authorities to find cleanwater supplies, a task that took years and tremendous amounts ofmoney.

But once people believed his model of disease, they were preparedto make these efforts.

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The John Snow Memorial

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References

The John Snow web site is maintained by the UCLA School ofPublic Health: http://www.ph.ucla.edu/epi/snow.html.

Sandra Hempel,The Strange Case of the Broad Street Pump

Steven Johnson,The Ghost Map

Peter Vinten-Johansen, Howard Brody, Nigel Paneth, StephenRachman, Michael Rip,Cholera, Chloroform, and the Science of Medicine:A Life of John Snow

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