How much testing do we need to "re-open" the economy? Let's look at a comparison between countries to get an idea. But how do we take into account that countries are very different in size, and have very different numbers of COVID-19 cases? One way would be to simply divide tests by the number of confirmed cases. But there's a problem with this approach: some countries are known to not test everyone with COVID-19 symptoms, so their official "confirmed case" numbers understate the magnitude of the epidemic - sometimes by very large factors.
A better number to use for normalization is the number of COVID-19 deaths. There are also some differences between countries about what they count as a COVID-19 death, but they are not nearly as large as the differences in who gets tests. So here's a look at some countries:
The middle group with blue bars has done a few hundred tests per COVID-19 deaths. All three countries show a clear downward trend in new cases (more about that below).
The last group has states with fewer than 100 tests per COVID-19 death, and includes the US, Italy, and the United Kingdom. This group also has the highest number of COVID-19 deaths, relative to population size.
Overall, the relative number of tests is strongly correlated with how well a country managed to control the COVID-19 epidemic - but why? Simply put, more testing allows countries to find a higher percentage of those infected with the virus, so that they can be isolated, which prevents further transmissions. More testing generally goes hand-in-hand with earlier testing: if plenty of test capacity is available, everyone can get tested right away. For the countries in the green group, this includes not only anyone with symptoms, but also anyone who has been in contact with a confirmed case. These countries all have large and efficient "tracking" efforts to find such contacts, and test them before they can infect anyone else. This is very important for COVID-19, since many transmissions happen before the first symptoms appear, or are from persons who never develop significant symptoms - but can still infect.
The goal for test and track is clear: test every person who is infected as soon as possible, and if a test is positive, test every person that has been in close contact with him or her. How does that relate to deaths? Various studies have shown that about 0.5% to 1% of all people infected with the SARS-CoV-2 virus die. Therefore, we absolutely need to test about 100 to 200 people for every reported death. To also test everyone who has been in close contact with an infected person, we need to test maybe another 5-10 people per infected person. That brings us to about 500 to 2000 tests per COVID-19 death.
We know that the tests can sometimes be negative when they are done to soon after infection, so ideally, everyone who tests negative should be tested again a couple of days later. Similarly, anyone who tested positive should be tested at least a couple of times with negative results before he can be released from quarantine. This adds another factor of at least two, so now we are at a absolute minimum of 1,000 tests per death that need to be done, with a range up to 8,000 tests per deaths. That's exactly what we are seeing for Taiwan, Australia, Singapore, New Zealand, and South Korea.
For countries that have seen a larger case and death load than these countries, it is imperative to first reduce the number of active COVID-19 infections. Let's have a look at how some of the countries on our list have done. Let's have a look at Germany's daily cases, using a graph from the Worldometers web site:
There's definitely a downward trend, but the day-to-day variations make it difficult to quantify. So we need to smooth the data first, for example by using 7-day averages. We expect new cases to be proportional to current cases, which means we would have an exponential function; so we can take a log of the smoothed numbers, and try to fit a straight line through them - say, for sliding one or two 2-week periods. The slope of the line then corresponds to the growth rate of the epidemic - it tells us how fast the case numbers are going up or down. Here's a look at this curve for Germany:
Here's the graph for Australia:
Now let's look at a couple of states that have announced that they want to "re-open" the economy by gradually relaxing stay-at-home orders.
In conclusion, the observed trends in new case growth show that a containment of the COVID-19 epidemic has not been achieved at anywhere close to sufficient levels in most of the states that plan to re-open the economy soon. Relaxing social distancing restrictions will cause COVID-19 infections to accelerate in these states. However, the increases will only be picked up with a substantial delay; it will probably at least 10 days to 2 weeks before even a slight increase becomes noticeable above the day-to-day variations. It is very likely that the number of COVID-19 infections in each of these states will rise to a multiple of the current number before the governors in the affected states will even start to consider re-enacting restrictions that have been removed to early.