In 1840, British epidemiology pioneer submitted a paper to the British government outlining his findings that the outbreak of epidemics over time follow a bell curve, with infections falling roughly at the same rate that they rise. His observation has come to be known as Farr’s Law.
Farr’s Law has stood the test of time. One hundred eighty years after Farr laid out his observation, there have been a number of scientific papers applying Farr’s Law to the COVID pandemic. Most concluded that COVID is following this historic pattern.
It is important to note that Farr postulated his law at a time that vaccines were still in their infancy, the germ theory of disease was still not widely accepted and there was almost no understanding of the human immune system. His law was not based on an understanding of the mechanisms of epidemics but rather solely on his observations of their histories.
If you look at COVID outbreaks on a regional basis they almost universally follow a bell curve trajectory. The bell curve is sometimes camouflaged by charts that combine regions. For example, if you look at an epi curve for the entire United States, it appears that there have been three recurring waves. But when you separate the epi curves into the regional components, what you are actually seeing is the overlay of individual bell curves from multiple regional outbreaks.
There are, however, two important caveats to Farr’s Law to note. First, there is nothing in Farr’s Law that says there will not be subsequent outbreaks in the same population. These probably occur because the population had reached an effective herd immunity under the circumstances at that time, but the pathogen is reintroduced under circumstances more favorable to its spread. That is probably what we are currently seeing in the U.S. Northeast and Europe, as they relaxed their restrictions. Nonetheless, subsequent outbreaks will also ultimately conform to Farr’s Law.
Second, all of the non-pharmacological interventions (NPIs), such as social distancing, lockdowns, masks, etc., are designed to “flatten the curve.” It appears those have been successful to some degree in doing so, as most of the COVID epi curves where NPIs were widely used are “deformed” with a more gradually sloping decline than a classic Farr’s bell curve. For example, this is the epi curve for fatalities in Italy’s initial outbreak.
As we head into the holiday season with COVID spreading rapidly across the United States, it is easy to become despondent and “think the numbers will just keep rising.” But as Oxford reminds us, they will not. Some European countries have already seen their second waves begin to subside and hospitalizations in some states that were in the early part of the recent outbreak in the Midwest, like Wisconsin, have begun to decline. With rapidly growing naturally acquired immunity soon to be supplemented by vaccines, the light at the end of the tunnel is not as far away as some fear.
So, let all of us whose families have not been touched by the disease, give thanks for that today and remember our friends whose families have. But most of all, let’s give thanks, that courtesy of William Farr, we have the promise that there is an end in sight.
