As Lockdowns Are Lifted, Is the COVID-19 Reproductive Number Rising or Falling?

Two models generate strikingly different estimates.


If you are a critic of COVID-19 lockdowns, here are some numbers you will like. I also have some numbers you will not like as much, which I will get to in a minute.

According to a model by researchers at the University of Utah, the "real-time reproductive number" for the COVID-19 virus—the number of people infected by the average carrier—has fallen in Florida since the state began loosening its restrictions on businesses and individuals, from 0.98 on April 30 to 0.5 on May 26.

When the reproductive number falls below one, that indicates an epidemic is waning. The daily number of new cases can be expected to decline, and eventually so will the total number of active cases as previously infected people recover.

In Texas and Georgia, two other states with big populations that lifted their lockdowns on April 30, the pattern in the University of Utah model is initially similar but less encouraging in the last few days. In Texas, the model shows the real-time reproductive number falling from 1.13 on April 30 to 0.79 on May 22 and 23 before climbing to 1.32 on May 26. In Georgia, the number drops from 0.96 on April 30 to 0.78 on May 24, then rises to 1.01 as of May 26.

If you are a lockdown supporter, here are some numbers you will like better. According to a different model, this one produced by the independent data scientist Youyang Gu, the reproductive number in Florida rose from 0.96 on April 30 to 1.07 on May 26. Gu's model also shows the number rising in Texas (from 1.01 to 1.07) and Georgia (from 1.03 to 1.07) during that period.

Feel free to pick the numbers that reinforce your preexisting beliefs. If you want to support the view that lockdowns are overrated as a way to reduce transmission of the COVID-19 virus, the University of Utah model is for you. If you want to support the view that lifting lockdowns is reckless, Gu is your man.

Who is right? I don't know, but so far the Gu model has been remarkably accurate in predicting COVID-19 deaths, and the reproductive number figures into those projections.

The University of Utah model uses "a collated time series of daily state-wise positive
case counts from the COVID Tracking Project." The researchers calculate the reproductive number "using two complementary methods": the Wallinga and Teunis method, "which is forward-looking," and the Cori method, "which is backward-looking." The Gu model "builds machine learning techniques on top of a classic infectious disease model" known as SEIR, which starts by dividing the population into four groups: susceptible, exposed, infectious, and recovered.

As my colleague Ron Bailey has noted, the Gu model's projections "are considerably less optimistic" than the projections from other widely cited models. Historically, Gu notes, his model's COVID-19 death projections have matched the actual fatalities counted by the Johns Hopkins Coronavirus Resource Center much better than the model used by the University of Washington's Institute for Health Metrics and Evaluation (IHME). On May 2, for instance, the Gu model predicted 101,950 deaths in the United States by today, compared to the IHME projection (since revised) of 71,918. The current Johns Hopkins tally is 100,415.

The Gu model predicted that the death toll would reach 100,000 by May 25, and that happened just a couple of days later. It is now projecting more than 200,000 deaths by August 28. A projection by the U.S. Centers for Disease Control and Prevention, leaked to the press early this month, predicted that mark would be reached by June 1, which thankfully has proven to be excessively pessimistic. But if history is any guide, the IHME projections err in the opposite direction. They currently go only as far as August 4, when the predicted death toll is about 132,000, compared to more than 173,000 in the Gu model.

Since the Gu model's death projections incorporate its estimate of the reproductive number, it seems to have a pretty good handle on the latter, which suggests it is closer to the mark than the University of Utah model. Nationally, the Gu model shows the reproductive number falling from 2.26 on February 5 to a low of 0.91 on April 11, then beginning to rise on April 28 and reaching 1.02 today. The University of Utah model puts the national average at 2.66 on March 20, falling more or less steadily to 0.8 on May 24 and 25 before rising slightly to 0.85 as of May 26.

While I would prefer to believe the more optimistic scenario, the Gu model's historical performance makes a compelling case for (relative) pessimism. Furthermore, it is plausible that lockdowns had some impact on virus transmission and that lifting them would boost the reproductive number. Whether that means they were worth their enormous economic cost is another question, especially since many of the COVID-19 deaths they ostensibly prevented may simply have been delayed.