The Shape of Epidemics

Essay by David S. Jones and Stefan Helmreich: “…Is the most recent rise in new cases—the sharp increase in case counts and hospitalizations reported this week in several states—a second wave, or rather a second peak of a first wave? Will the world see a devastating second wave in the fall?

Such imagery of waves has pervaded talk about the propagation of the infection from the beginning. On January 29, just under a month after the first instances of COVID-19 were reported in Wuhan, Chinese health officials published a clinical report about their first 425 cases, describing them as “the first wave of the epidemic.” On March 4 the French epidemiologist Antoine Flahault asked, “Has China just experienced a herald wave, to use terminology borrowed from those who study tsunamis, and is the big wave still to come?” The Asia Times warned shortly thereafter that “a second deadly wave of COVID-19 could crash over China like a tsunami.” A tsunami, however, struck elsewhere, with the epidemic surging in Iran, Italy, France, and then the United States. By the end of April, with the United States having passed one million cases, the wave forecasts had become bleaker. Prominent epidemiologists predicted three possible future “wave scenarios”—described by one Boston reporter as “seascapes,” characterized either by oscillating outbreaks, the arrival of a “monster wave,” or a persistent and rolling crisis.

From Kristine Moore et al., “The Future of the COVID-19 Pandemic” (April 30, 2020). Used with permission from the Center for Infectious Disease Research and Policy, University of Minnesota.

While this language may be new to much of the public, the figure of the wave has long been employed to describe, analyze, and predict the behavior of epidemics. Understanding this history can help us better appreciate the conceptual inheritances of a scientific discipline suddenly at the center of public discussion. It can also help us judge the utility as well as limitations of those representations of epidemiological waves now in play in thinking about the science and policy of COVID-19. As the statistician Edward Tufte writes in his classic work The Visual Display of Quantitative Information (1983), “At their best, graphics are instruments for reasoning about quantitative information.” The wave, operating as a hybrid of the diagrammatic, mathematical, and pictorial, certainly does help to visualize and think about COVID-19 data, but it also does much more. The wave image has become an instrument for public health management and prediction—even prophecy—offering a synoptic, schematic view of the dynamics it describes.

This essay sketches this backstory of epidemic waves, which falls roughly into three eras: waves emerge first as a device of data visualization, then evolve into an object of mathematical modeling and causal investigation and finally morph into a tool of persuasion, intervention, and governance. Accounts of the wave-like rise and fall of rates of illness and death in populations first appeared in the mid-nineteenth century, with England a key player in developments that saw government officials collect data permitting the graphical tabulation of disease trends over time. During this period the wave image was primarily metaphorical, a heuristic way of talking about patterns in data. Using curving numerical plots, epidemiologists offered analogies between the spread of infection and the travel of waves, sometimes transposing the temporal tracing of epidemic data onto maps of geographical space. Exactly what mix of forces—natural or social—generated these “epidemic waves” remained a source of speculation….(More)”.