This is a back-of-the-envelope calculation to estimate how many Iowans currently have covid-19. To begin with, as of July 23, here is the rolling 7-day average for the daily number of positive covid-19 test results, and the 7-day average for the daily number of deaths due to covid-19 (all data from the covid tracking project).
According to this data, Iowa has a bit over 500 new covid cases per day right now, slightly under the all-time peak. However, this data is confounded by the variation in test supply. The following figure is the share of test results that came up positive, over the prior 7 days. As you can see, it varied substantially. In early May, it was as high as 25%, compared to 9% at the second peak.
How many covid cases are we missing, due to inadequate testing? To get an idea, let’s assume the deaths data is basically accurate. Because there is a gap in time between when someone is infected and when they get tested, another gap between when they get tested and they die of covid (if they do), and another gap between when someone dies and when their death is reported, we need to adjust the date of deaths to use it to estimate case counts.
The covid tracking project suggests deaths may be reported 14-21 days after symptom onset.
If someone dies of covid-19, they will first experience symptoms 14-21 days before their death. If we push back the deaths time-line by 18 days (about halfway between 14 and 21), we get the following chart.
Now, the trends for deaths and new cases match much more closely. They both peak in early May and hit their nadir in late June.
We know a lot more today about how deadly covid-19 is than when we started, with most estimates converging on 0.5-1.0% of people infected eventually dying. Let’s take the low end of this, since Iowa’s medical system was never overwhelmed or short on ventilators, and estimate that 0.5% of Iowans who contracted covid-19 died. Since we know the actual number of deaths, we can calculate the likely true number of cases by dividing this by 0.5%. That generates the following figure.
According to this estimate, there were a total of 160,000 covid cases in Iowa by July 5, compared to an official count of 31,000. That is, the actual number is 5x the reported number. This is also within the bounds of estimates about how many cases are being missed, which is as high as 9 out of 10. It also suggests, as of July 5, only about 5% of Iowans have had covid-19, which suggests there is a long way to go before we can think about things like herd immunity.
This figure also suggests the decline in covid cases was much swifter in the month of May then official tests indicate, because through this period our testing supply increased and we began catching more and more of the actual cases. And on June 19, this suggests we may have been close to capturing 100% of the covid cases.
Nowcasting Covid-19
One problem with this data is that it only gives you an estimate of how bad things are 18 days ago. What about right now? I took a stab at it, but it involves a lot of assumptions, so take this with a heaping spoonful of salt.
To estimate the real number of covid cases in Iowa right now, I use the following formula:
(# of positive covid test results) = (# of actual covid cases) x (share identified by testing)
We know the # of positive test results, so we can estimate the actual number of covid cases by dividing that by the share we identify with testing. But we don’t know the share testing identifies. So we have to estimate that.
I’ll assume there is a stable relationship between the share of cases identified by testing, and the percent of tests that show up positive, at least once testing gets up to speed. I use the date of May 21, when Governor Reynolds said anyone in Iowa who wants a test can now get one. Specifically, I assume:
log(share identified by testing) = A + B*log(% of covid tests that are positive) + e
where I estimate A and B, and e is a random error. Using data from May 21 to July 5, here’s what the scatterplot looks like.
This suggests A = -6.08 and B = -1.94. As we would expect, the relationship is negative – the higher the percent of cases that are positive, the fewer of actual cases are being captured. The estimated relationship is:
share identified by testing = 0.002/(% positive)^1.94
With an estimate for the share of actual cases identified, I can estimate how many actual cases there are from the number of positive test results. The estimate of the number of actual cases, based on this testing data, is in yellow.
Thus, according to my estimates, this second wave peaked a bit below 2,500 new cases per day in mid July, and has since dipped to 2,000 cases per day.
Validation
There are two ways I can think of to see if these estimates are right.
First, according to this model, the daily number of deaths should rise to a peak of about 12 per day (on average over a week), by early August, and then fall to about 10 per day (on average over a week) by mid August.
Second, if Iowa ever does widespread testing for antibodies, I estimate that, as of July 24, about 196,000 Iowans have had covid-19, or 6%.