John Snow's cholera outbreaks revisited: from blackboard to bench
Joe Tien (The Ohio State University)
Cholera is a disease with a long history, with John Snow's investigations of the Broad Street pump and London cholera outbreaks during the 1800s as a celebrated example of research on the disease. Despite this long history, cholera outbreaks remain a serious public health concern today. For example, the cholera outbreak beginning in Haiti in October 2010 had caused nearly 700,000 cases as of November 2013. In addition to its public health relevance, several features of cholera make the disease of mathematical interest as well. These include multiple time scales, external forcing due to climatic conditions, and different connectivity networks, including the movement of both people and of surface waters. Understanding how these different features interact and affect cholera dynamics is a complicated question, which requires the interaction between mathematics and biology in both directions: mathematical modeling prompts the collection and analysis of new biological and epidemiological data, and biological questions stimulate new mathematical developments. Here we describe an example of this synergy between mathematics and biology by revisiting the cholera outbreaks from John Snow's time.
Data from the London cholera outbreaks of the 19th century exist in the Bills of Mortality, a remarkable record kept by the various parishes of London from the 1500s to the present and studied by mathematician David Earn (McMaster U.). Figure 1 shows a plot of weekly cholera deaths recorded in London from 1824 to 1901. There are two features of note. First, there is a clear seasonal pattern, with the majority of cholera deaths occurring during the late summer. Peak weekly deaths were on the order of ~100 for most years. However, unusually severe cholera outbreaks occurred in 1832, 1849, 1854, and 1866, of an order of magnitude greater severity. Three of these four severe outbreaks were preceded by unusually timed minor outbreaks occurring off-season, during winter or spring. These unusually timed outbreaks can thus be thought of as perturbations in phase of the typical cholera cycle. Why were these off-season outbreaks followed by such severe cholera outbreaks the following season?
One possible explanation suggested by a simple mathematical model is that these off-season outbreaks were caused by the arrival of new cholera strains, to which the human population had little prior immunity. A classical model for infectious disease dynamics is the Susceptible-Infectious-Recovered (SIR) framework, a simple ordinary differential equation model where the population is divided into compartments according to their immunological state. Extending this framework to include an environmental water compartment (SIWR ) and allowing for disease transmission to vary periodically allows for a good fit of the model to the London cholera data in "typical" years. Introducing a new strain of disease during the winter, for example, produces an outbreak, as a large proportion of the population is initially susceptible to the new strain. As winter conditions are not conducive to cholera transmission, seasonal effects curtail the outbreak before a large epidemic occurs. Because of this, the susceptible pool is not depleted, allowing for a severe outbreak when seasonal conditions for cholera improve the following summer. In this scenario, the off-season outbreaks "herald" the arrival of a new cholera strain .
Mathematical modeling of the London cholera outbreaks shows that the introduction of new strains is a plausible mechanism underlying cholera herald waves and the following severe outbreaks. This is, of course, only one of many possible explanations. A direct test of the new strain mechanism requires extraction and sequencing of cholera DNA from historical specimens from these 19th century outbreaks. In fact such historical specimens do exist: the Mütter Museum listed six cholera intestines collected from the 1849 cholera pandemic, preserved in alcohol (Figure 2). Led by Hendrik Poinar, an expert in ancient DNA at McMaster University, and Alison Devault, a PhD student in the Poinar lab, cholera DNA was successfully extracted from one of these specimens, and the genome of the 1849 cholera strain painstakingly reconstructed. This allowed identification of the 1849 strain ("Classical", with some deviations from 20th century Classical strains), giving important information on cholera evolution and suggesting further avenues for biological research regarding strain competition and virulence.
Exploration of historical records of the London cholera outbreaks investigated by John Snow prompted mathematical modeling, leading in turn to reconstruction of the cholera genome from a 1849 Philadelphia specimen. As for the identity of the cholera genomes from 19th century London? As this study demonstrates, the technology exists to answer this question, provided London specimens can be found.
 A. M. Devault, B. Golding, N. Waglechner, J. M. Enk, M. Kuch, J. H. Tien, M. Shi, D. N. Fisman, A. N. Dhody, S. Forrest, K. I. Bos, D. J. D. Earn, E. C. Holmes, and H. N. Poinar. Second-pandemic strain of Vibrio cholerae from the Philadelphia cholera outbreak of 1849. New England Journal of Medicine, 370(4):334–340, 2014.
 J. H. Tien and D. J. D. Earn. Multiple transmission pathways and disease dynamics in a waterborne pathogen model. Bulletin of Mathematical Biology, 72(6):1506–1533, 2010.
 J. H. Tien, H. N. Poinar, D. N. Fisman, and D. J. D. Earn. Herald waves of cholera in 19th century London. Journal of the Royal Society Interface, 8(58):756–760, 2011.