Where are the Recoveries?

Posted on April 15, 2020

For the next few weeks, the number of active cases will be an important number to watch. We’re going to start to see the active case graph peak and then descend as more deaths and more recoveries get reported by state and local health authorities. Many, many hours have been spent talking about the number of total confirmed cases. Total case numbers are great for money-making headlines, but aren’t very helpful in terms of real-time analysis. Only active cases let us see what’s going on right now.

Here’s the formula for active cases:

Active Cases = Total Confimed Cases – Deaths – Recoveries

As of 4/15, this works out to be:

Active Cases = 615,995 – 27,458 – 47,639

Using the formula, we find that the total reported active cases today is 540,898

It’s a large number for sure. However, this number appears to be much higher than it should be. It appears that a large number of recoveries are not being properly reported. This isn’t an accusation of any kind of conspiracy. Under-reporting recoveries may simply be a natural result of recovered people not interacting with doctors anymore since they no longer need care.

Nevertheless, we can’t know the true number of active cases in the US unless we have an accurate count on the number of recovered individuals. To get an accurate count on the number of recoveries, we can use the COVID-19 average incubation time, the time from the end of incubation to death, and the death rate to estimate a more accurate number of recovered patients.

On average it takes about 5 days for someone with COVID-19 to develop symptoms (incubation period). It takes another 18 days on average after that point for death to take place. Currently the death rate is ~4% in the US.

If we use the day that someone tests positive for COVID-19 as the end of the incubation period, we would expect that 18 days later the person should have either died or recovered, on average.

Using this info, we can project a more accurate picture of daily recoveries using the following formula:

Day 18 Recoveries = Day 1 New Daily Confirmed Cases * Survival Rate (inverse of Death Rate)

For example, let’s take 4/14 and try to estimate the true number of recovered cases:

4/14 Recovered Cases = 3/27 New Daily Confirmed Cases (17,796) * 96%

Using the formula, we would expect something in the neighborhood of 17,000 recoveries on 4/14 alone. However, only around 2500 recoveries were recorded by state and local agencies. On 4/13, we would have expected around 17,000 as well, yet only about 4,000 were reported. Just in 2 days’ time, the difference between actual and projected recoveries is 27,500, not a small number. This trend of under-reporting recoveries has been going on for about a week now, leading to a difference of nearly 100,000 recoveries.

So, something appears to be missing in the tracking of recoveries on a state on local level. Whatever it is, it’s preventing us from getting a handle on how many people in the US currently have the virus. Since active cases are such an important metric, improvement on tracking recoveries is a must.