The best way to re-open the economy is to defeat the virus. Not by yelling slogans.

By Alex Tabarrok and Puja Ahluwalia Ohlhaver in the Washington Post

May 15, 2020 at 10:06 a.m. EDT

With the unemployment rate at its highest level since the Great Depression — 14.7 percent and climbing — many Americans are clamoring to reopen the economy, even if it means that thousands of daily covid-19 deaths become part of the backdrop to life. It’s time to move on as “warriors,” President Trump has said, because “we can’t keep our country closed down for years.” We, too, favor markets and share the president’s eagerness to stop economically ruinous shutdowns. But the choice between saving lives and saving the economy, the latter of which Trump has endorsed implicitly, is a false one.

In fact, framing the issue that way could kill many Americans and kill the economy.

The dangers of reopening without disease control — or a coronavirus vaccine or therapeutic breakthrough — are illustrated by events at the Smithfield Foods meatpacking plant in Sioux Falls, S.D. Smithfield offered workers a bonus if they showed up every day in April. Normally, bonus pay would increase attendance. But in a pandemic, encouraging the sick to haul themselves into work can be disastrous. The plan backfired. Hundreds of Smithfield employees were infected, forcing the plant to shut down for more than three weeks. If we stay the current course, we risk repeating the same mistake across the whole economy.

The economy consists of people who have hopes and fears. As long as they are afraid of a lethal virus, they will avoid restaurants, travel and workplaces. (According to a Washington Post-Ipsos poll last week, only 25 percent of all Americans want to “open businesses and get the economy going again, even if that means more people will get the coronavirus.”) The only way to restore the economy is to earn the confidence of both vulnerable industries and vulnerable people through testing, contact tracing and isolation.

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There is already a bipartisan plan to achieve this; we helped write it. The plan relies on frequent testing followed by tracing the contacts of people who test positive (and their contacts) until no new positive cases are found. It also encourages voluntary isolation, at home or in hotel rooms, to prevent further disease spread. Isolated patients would receive a federal stipend, like jurors, to discourage them from returning to workplaces too soon.

But our plan also recognizes that rural towns in Montana should not necessarily have to shut down the way New York City has. To pull off this balancing act, the country should be divided into red, yellow and green zones. The goal is to be a green zone, where fewer than one resident per 36,000 is infected. Here, large gatherings are allowed, and masks aren’t required for those who don’t interact with the elderly or other vulnerable populations. Green zones require a minimum of one test per day for every 10,000 people and a five-person contact tracing team for every 100,000 people. (These are the levels currently maintained in South Korea, which has suppressed covid-19.) Two weeks ago, a modest 1,900 tests a day could have kept 19 million Americans safely in green zones. Today, there are no green zones in the United States.


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Most Americans — about 298 million — live in yellow zones, where disease prevalence is between .002 percent and 1 percent. But even in yellow zones, the economy could safely reopen with aggressive testing and tracing, coupled with safety measures including mandatory masks. In South Korea, during the peak of its outbreak, it took 25 tests to detect one positive case, and the case fatality rate was 1 percent. Following this model, yellow zones would require 2,500 tests for every daily death. To contain spread, yellow zones also would ramp up contact tracing until a team is available for every new daily coronavirus case. After one tracer conducts an interview, the team would spend 12 hours identifying all those at risk. Speed matters, because the virus spreads quickly; three days is useless for tracing. (Maryland, Virginia and Washington, D.C., are all yellow zones.)


A disease prevalence greater than 1 percent defines red zones. Today, 30 million Americans live in such hot spots — which include Detroit, New Jersey, New Orleans and New York City. In addition to the yellow-zone interventions, these places require stay-at-home orders. But by strictly following guidelines for testing and tracing, red zones could turn yellow within four weeks, moving steadfastly from lockdown to liberty.


Getting to green nationwide is possible by the end of the summer, but it requires ramping up testing radically. The United States now administers more than 300,000 tests a day, but according to our guidelines, 5 million a day are needed (for two to three months). It’s an achievable goal. Researchers estimate that the current system has a latent capacity to produce 2 million tests a day, and a surge in federal funding would spur companies to increase capacity. The key is to do it now, before manageable yellow zones deteriorate to economically ruinous red zones.


States can administer these “test, trace and supported isolation” programs — but Congress would need to fund them. The total cost, we estimate, is $74 billion, to be spent over 12 to 18 months. That sum would cover wages and training for contract tracers, the cost of building voluntary self-isolation facilities, stipends for those in isolation and subsidies to manufacture tests.


That amount is a lot, but not compared to the cost of a crippled economy. In Congress’s latest relief package, $75 billion went to struggling hospitals alone, $380 billion to help small businesses and $25 billion toward testing. But hospitals and businesses will continue to hemorrhage money and seek bailouts as long as they can’t open safely. Not spending on disease control means new waves of infection followed by chaotic spikes in disease and death, followed by more ruinous cycles of economic openings and closures. Economists talk about “multipliers” — an injection of spending that causes even larger increases in gross domestic product. Spending on testing, tracing and paid isolation would produce an indisputable and massive multiplier effect.


States have strong economic incentives to become — and remain — green zones. Nations that have invested the most in disease control have suffered the least economic hardship: Taiwan grew 1.5 percent in the first quarter, whereas the United States’ gross domestic product contracted by 4.8 percent, at an annual adjusted rate. (Taiwan was fortunate to have its vice president, Chen Chien-Jen, a U.S.-trained epidemiologist; under his guidance, the island acted quickly with masks, temperature checks, testing and tracing.) The second quarter will be worse: The projected decline for U.S. GDP, at an annualized rate, is an alarming 40 percent.


Looking forward, we will see stark economic contrasts across states, depending on their investment in disease control. With $74 billion, Congress could close the gap between states and relieve pressure on state budgets hamstrung by collapsing revenues. In the spirit of federalism, states would then become laboratories for discovering the best ways to implement testing, tracing and isolation. States might choose to form interstate compacts that pool and move testing resources across state lines as the disease travels and surges; county health officials might tap firefighters or other municipal workers to build regional contact-tracing workforces (as is happening in Tyler, Tex.). When local and state governments become accountable for adopting strategies that work, we can expect more innovation.


How do we know that testing, tracing and supported isolation would work? It already has worked in New Zealand, South Korea and Taiwan — where there have been few to no new daily cases recently. Taiwan never had to shut down its economy, while New Zealand and South Korea are returning to normal. It would work here, too. Since March, Congress has passed relief bills totaling $3.6 trillion to support an economy devastated by a virus — and $3 trillion more is on the table. We should attack the disease directly so we can stop spending to alleviate symptoms. Following this road map, we can defeat the coronavirus and be celebrating life, liberty and livelihood by the Fourth of July.

How do we fix the CV19 testing problem? By re-testing everybody who tested positive!

I guess I’ve re-discovered a form of Bayes’ Theorem  regarding the problem that is posed by the high numbers of false negatives and false positives when testing for the feared coronavirus.  What I found is that it doesn’t really even matter whether our tests are super-accurate or not. The solution is to assume that all those who test negative, really are negative, and then to give a second test to all those who tested positive the first time. Out of this group, a larger fraction will test positive. You can again forget about those who test negative. But re-test again, and if you like, test again. By the end of this process, where each time you are testing fewer people, then you will be over 99% certain that all those who test positive, really have been exposed.

Let me show you why.

Have no fear, what I’m gonna do is just spreadsheets. No fancy math, just percents. And it won’t really matter what the starting assumptions are! The results converge to almost perfect accuracy, if repeated!

To start my explanation, let’s start by assuming that 3% of a population (say of the US) has antibodies to CV19, which means that they have definitely been exposed. How they got exposed is not important for this discussion. Whether they felt anything from their exposure or not is not important in this discussion. Whether they got sick and died or recovered, is not going to be covered here. I will also assume that this test has a 7% false positive rate and a 10% false negative rate, and I’m going to assume that we give tests AT RANDOM to a hundred thousand people (not people who we already think are sick!) I’m also assuming that once you have the antibodies, you keep them for the duration.

This table represents that situation:

math of CV19 testing

If you do the simple arithmetic, using those assumptions, then of the 100,000 people we tested, 3%, or three thousand, actually do have those antibodies, but 97%, or ninety-seven thousand, do not (white boxes, first column with data in it).

Of the 3,000 folks who really do have the antibodies – first line of data – we have a false  negative rate of 10%, so three hundred of these poor folks are given the false good tidings that they have never been exposed (that’s the upper orange box). The other 90% of them, or two thousand seven hundred, are told, correctly, that they have been exposed (that’s the upper green box).

Now of the 97,000 people who really do NOT have any antibodies – the second line of data – we have a false positive rate of 7%, so you multiply 0.07 times 97000 to get six thousand, seven hundred ninety of them who would be told, incorrectly, that they DID test positive for Covid-19 – in the lower orange box. (Remember, positive is bad here, and negative is good.) However, 90,210 would be told, correctly, that they did not have those antibodies. (That’s in the lower green box.)

Now let’s add up the folks who got the positive test results, which is the third data column. We had 2,700 who correctly tested positive and 6,790 who wrongly tested positive. That’s a total of 9,490 people with a positive CV19 antibody test, which means that of that group of people, only 28.5% were correctly so informed!! That’s between a third and a fourth! Unacceptable!

However, if we look at the last column, notice that almost every single person who was told that they were negative, really was negative. (Donno about you, but I think that 99.7% accuracy is pretty darned good!)

However, that 28.5% accuracy among the ‘positives’ (in the left-hand blue box) is really worrisome. What to do?

Simple! Test those folks again! Right away! Let’s do it, and then let’s look at the results:

math of CV19 testing - round 2

Wowser! We took the 9490 people who tested positive and gave them another round of tests, using the exact same equipment and protocols and error rates as the first one. The spreadsheet is set up the same; the only thing I changed is the bottom two numbers in the first data column. I’m not going to go through all the steps, but feel free to check my arithmetic. Actually, check my logic. Excel doesn’t really make arithmetic errors, but if I set up the spreadsheet incorrectly, it will spit out incorrect results.

Notice that our error rate (in blue) is much lower in terms of those who tested positive. In fact, of those who test positive, 83.7% really ARE positive this time around, and of those who test negative, 95.9% really ARE negative.

But 84% isn’t accurate enough for me (it’s either a B or a C in most American schools). So what do we do? Test again – all of the nearly three thousand who tested positive the first time. Ignore the rest.

Let’s do it:

math of CV19 testing - round 3

At this point, we have much higher confidence, 98.5% (in blue), that the people who tested ‘positive’, really are ‘positive’. Unfortunately, at this point, of the people who tested negative, only about 64% of the time is that correct. 243 people who really have the antibodies tested negative. So perhaps one should test that subgroup again.

The beautiful thing about this method is that it doesn’t even require a terribly exact test! But it does require that you do it repeatedly, and quickly.

Let me assure you that the exact level of accuracy, and the exact number of exposed people, doesn’t matter: If you test and re-test, you can find those who are infected with almost 100% accuracy. With that information you can then discover what the best approaches are to solving this pandemic, what the morbidity and mortality rates are, and eventually to stop it completely.

Why we don’t have enough tests to do this quickly and accurately and repeatedly is a question that I will leave to my readers.


Note that I made some starting assumptions. Let us change them and see what happens. Let’s suppose that the correct percentage of people with COVID-19 antibodies is not 3%, but 8%. Or maybe only 1%. Let’s also assume a 7% false positive and a 10% false negative rate. How would these results change? With a spreadsheet, that’s easy. First, let me start with an 8% infection rate and keep testing repeatedly. Here are the final results:

Round Positive accuracy rating Negative accuracy rating
1 52.8% 99.1%
2 93.5% 89.3%
3 99.5% 39.3%

So after 3 rounds, we have 99.5% accuracy.

Let’s start over with a population where only 1% has the antibodies, and the false positive rate is 7% and the false negative rate is 10%.

Round Positive accuracy rating Negative accuracy rating
1 11.5% 99.9%
2 62.6% 98.6%
3 95.6% 84.7%
4 99.6% 30.0%

This time, it took four rounds, but we still got to over 99.6% accuracy at distinguishing those who really had been exposed to this virus. Yes, towards the end our false negative rate rises, but I submit that doesn’t matter that much.

So Parson Tommy Bayes was right.

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