Is density really the driver of this epidemic or is the idea misplaced? When people are packed tightly into urban areas they come in contact more often, and thus have more opportunities to spread disease. This intuition coincides with our standard understanding of the spread of infectious disease—but only partly.
To understand how widely and quickly an infectious disease will spread, epidemiologists refer to something called the reproduction number or R. It measures the average number of people an infected person will pass the illness on to over the course of their infection. R is calculated by multiplying four average values: the contact rate of an individual, C; the probability of transmission when a susceptible person contacts an infected person T; the time it takes for an infected person to recover—referred to as the duration D—and the fraction of susceptible people in the population S.
The intuition that population density increases the propensity of an epidemic to spread in cities is correct in the sense that increased density likely leads to an increase in the contact rate of an individual, which makes the reproduction number larger and leads to larger infectious disease outbreaks in dense areas.
We have completed a statistical analysis of county-level COVID-19 cases along with several potential explanatory variables. Density does positively relate to the number of current cases, but the effect is relatively small. The density component of R doesn’t include the dynamic part of the story, which is more important at this stage of the epidemic.
As an epidemic grows, more people are infected and then recover to become immune. (In most viral infectious diseases like COVID-19, we are awaiting conclusive evidence on this however.) As the epidemic grows, there are fewer people left to infect; in terms of calculating R, this means that the fraction of susceptible people in the population S gets smaller. One can think of S as the amount of wood on a fire; once the wood burns up, the fire goes out. Once there are too few susceptible people to infect, the epidemic goes out. This happens when R becomes less than one. At this level, each infected person is passing the disease on to fewer than one person on average over the duration of their infection; once they recover, the number of infected people is smaller. Once an infectious disease enters into a population it will burn until S is sufficiently small and then it disappears into ashes.
If we think about this process across the spectrum of cities in the U.S., we expect to see a similar story play out in many areas of the country. Seattle, New York City and various Californian cities are just the first to go through this process. Miami and New Orleans may quickly follow with many others coming in the next few weeks.
For example, think of each city as a small forest of trees. Once lightning strikes anywhere in the city, the forest will burn until the wood runs out. Because dense cities have a larger value of contact rate of an individual C, they will burn a little faster and a little longer, but what happens in New York City will be replicated in cities across the country; New York City today will be Topeka or Tucson tomorrow.
The attention on the density of New York City and other large cities is misleading. The epicenter could have been anywhere. Lightning could have equally well struck in Chicago or St. Louis or Seattle first. Have we forgotten that it actually did land in Seattle first? In the second half of March we were focused on suburban New Rochelle, N.Y.—hardly the first city that springs to mind when one thinks of urban density.
Despite the fact that the first lightning bolt could have struck anywhere, large cities like New York, Seattle and Los Angeles have a bias to attracting them. They are all commercial hubs with a large influx of tourism and business travel. Infectious disease is not randomly placed across cities. They are aimed precisely at places such as New York City and Los Angeles first because so many people go in and out of them. It is not an historical accident that we see the COVID-19 outbreaks happen in these such cities first.
If we again return to the data analysis, we see this effect. Counties that had early cases of COVID-19 have much larger case counts today. This effect dwarfs that of population density. The timing of early case arrivals is much more important than that of population density. There are no low-risk counties; just counties that haven’t been found by the pandemic yet.
Placing too much weight on urban density is a mistake. We are early in an epidemic that is sweeping across the U.S. It may seem currently that density is a main driving force the hotspots infectious disease springing up across the country. But that is only because these urban travel hubs attracted the first bolts of lightning. It is likely that in two months we will focus less on the density of New York City as a driving force and instead notice cases across the country and note that places like Seattle, Los Angeles and New York City just happened to be the first wave of the curve. Cities and counties that appear immune today will not remain so tomorrow. They are only a lightning bolt away from becoming New York. They need to expect and prepare for the pandemic that is headed their way.