The Pareto Principle and COVID-19

The Italian economist Vilfredo Pareto noticed that 80% of the land in Italy was owned by 20% of the population. The management guru Robert Juran noticed that this type of inequality held true for many types of business data, such as 80% of work is produced by the top 20% of employees. It was Juran who gave this phenomenon the name the Pareto Principle. As it turns out, this principle applies to the spread of COVID-19. While the reproduction number, which is the average number of people who spread the virus to other people, has gotten much of the attention, a more important parameter is the spread in this reproduction rate. There is a significant amount of variation in how much people tend to spread the virus. As it turns out, this follows the Pareto Principle. Recent studies indicate that 10-20% of the people with the virus are responsible for 80-90% of the transmission of the virus. This explains in part why some events, like the protests, may not have led to an increase in the spread of COVID-19, while others, such as the Sturgis rally, may have resulted in a significant number of new cases. It also explains the asynchronous spread of the virus throughout the United States – it hit the northeast hard in late winter and early spring, the southeast and southwest during the summer, and is now spreading rapidly in the midwest.

The average income of people in a bar is one way to think of this. If most of us were to walk into a bar, the average income among everyone there would change very little. However, if Bill Gates of Jeff Bezos were to enter the same bar, the average would jump significantly. In terms of COVID-19, the Jeff Bezos and Bill Gates in the bar would be a superspreader. This would be someone who is much more likely than average to spread COVID-19.

The chances that someone contracts the virus are a function of coming into contact with someone with the virus, and contacting someone that is more likely to spread the virus. For example, the best COVID modeler, Youyang Gu, estimates that 0.6% of the DC population is currently infected with COVID-19. If someone in the nation’s capital ran across one random person, the chances of coming into contact with someone with the virus is very low, less than 1%. If that same person attended an event with five other people, the chances are a little higher, about 3%. (For those interested in the math, the probability of encountering a random person who is currently infected with COVID-19 in a group of n people is 1-(1-p)^n.)

However, because of the dispersion, the chances of encountering a superspreader are even lower. Assume that the number of superspreaders is 20% of the population of people currently infected. So in D.C., the percent of the population currently in the population is 0.12% of the population, or 1 in 833 people. The bigger the event a person attends, the more likely they are to encounter a superspreader, and the more events they attend, the more likely they are to encounter a superspreader. In the table below you can see a heat map of the probability of encountering a superspreader based on the size of the event and the number of events of that size a person attends.

For example, at an event with five people, there is a 0.6% change of a superspreader being present. A single event with 100 people has a 11.6% probability of having a superspreader at the gathering. As the number of events increases, the chance that a superspreader will be present increases. Just twenty-five large gatherings (75 people or more) is enough to achieve more than a 90% probability that a superspreader will attend at least one. With this phenomenon, it is easy for someone who attends several get-togethers and does not get infected to achieve a level of complacency. “I’ve done it before and never had any problems, so it must be OK.” However, given enough events with enough people present, and an outbreak will occur.

Something like this has occurred at the White House recently. The President, the First Lady, three senators, and several White House staff members have tested positive for COVID-19. This is not a political post, and I’m not going to comment except to say I hope everyone affected recovers quickly and has no long-term health effects. From a factual, data-driven standpoint, this was bound to happen sooner or later. Large gatherings, without uniform mask wearing and social distancing, have a chance of leading to an outbreak. Multiple events with many people present make that an inevitability.