Voronoi Diagram, Cholera Outbreak and Beer

“After careful inquiry, we see no reason to adopt this belief. We do not feel it established that the water was contaminated in the manner alleged; nor is there before us any sufficient evidence to show whether inhabitants of that district, drinking from that well, suffered in proportion more than other inhabitants of the district who drank from other sources.”

-William Farr, British Epidemiologist

Georgy Voronoy was Ukrainian mathematician, who came up with a spatial analysis technique which is named after him- Voronoi diagram.

It’s a diagram created by taking pairs of points that are close together and drawing a line that is equidistant between them and perpendicular to the line connecting them. That is, all points on the lines in the diagram are equidistant to the nearest two (or more) source points.

The figure shown below tells how a Voronoi diagram is made. It has number of applications in field of science and technology ex. in cell biology, astrophysics, geometry, ecology etc.

It is also used in field of epidemiology, where Voronoi diagrams can be used to correlate sources of infections in epidemics.

Infact a similar technique was used by British Physician Dr. John Snow even before George Voronoy was born.

In 1854, there was outbreak of Cholera in Soho district of London esp. in areas close to Broad Street. Soho district then was facing problem of large influx of migrants. There were no proper housing and sanitation facilities, resulting in dirt and filth. Lack of sewer lines resulted in all waste (human and animal) getting dumped in Thames River.


This filth and stench resulting from it gave rise to Miasma Theory. Miasma was considered to be a poisonous vapour or mist filled with particles from decomposed matter (miasmata) that caused illnesses. The miasmatic position was that diseases were the product of environmental factors such as contaminated water, foul air, and poor hygienic conditions. Such infection was not passed between individuals but would affect individuals within the locale that gave rise to such vapours. It was identifiable by its foul smell. This theory had its supporters including epidemiologist Willaim Farr.

foul air

It was easy to correlate filth in Soho district with outbreak of Cholera.


Dr. Snow has different theory. He did not believe in Miasma theory. He believed that Cholera was spread by contaminated water rather than foul air. To prove his theory, he studied map of Soho district and cases of Cholera in different areas of district.


“That is possible; but I believe that the poison of the cholera is either swallowed in water, or got directly from some other person in the family, or in the room; I believe it is quite an exception for it to be conveyed in the air; though if the matter gets dry it may be wafted a short distance.”

-John Snow, British Physician.

He found that maximum number of cases were in and around a water pump in Broad Street. Dr. Snow concluded that water from this pump was responsible for spreading Cholera in region. He told authorities to break handle of pump so that people could not draw water from this pump. This resulted in sudden drop in Cholera cases, supporting this theory that it was water from pump that was spreading Cholera.

cholera 4


Dr. Snow’s research is pioneering work in areas of spatial analysis and research methodology. Till then causative agent for Cholera was not identified. It was much later i.e. 1884, that German physician and microbiologist Robert Koch during his research in India was able to determine the causative agent of cholera, Vibrio cholera.

It was found that human and animal waste from Soho district was discharged in Thames River. This water got into wells, and pumps were installed to draw water from these wells. The pump at Broad Street was drawing water from well whose water was contaminated and whoever drank water from pump suffered from Cholera.

cholera 3


But task of doing extensive research in correlating contaminated water of pump with cases of Cholera was done by Reverend Henry Whitehead. Whitehead believed in the miasma theory of disease, he also felt that this disease was punishment from God. Initially Whitehead worked to disprove Snow, but after interviewing lot of people, he eventually started believing John Snow’s idea that cholera spreads through water contaminated by human waste. Snow’s work, particularly his maps of the Soho area cholera victims, convinced Whitehead that the Broad Street pump was the source of the local infections.

“You and I may not live to see the day, and my name may be forgotten when it comes, but the time will arrive when great outbreaks of cholera will be things of the past; and it is the knowledge of the way in which the disease is propagated which will cause them to disappear.”

-Reverend Henry Whitehead

There was one exception to this theory, there was a brewery situated near Broad Street pump- Lion Brewery, yet workers from this brewery did not suffer from Cholera.

On investigation it was found that workers in brewery were allowed to drink beer free of cost, so they never drank water. So though the brewery was situated just one block east of the Broad Street pump, workers drank beer instead of water; the fermentation killed the cholera bacteria, and none of the brewery workers contracted cholera.

Drinking beer proved to be life saver.


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