Beyond testing -- The central question for pandemic policy.

Two weeks of California lockdown have gone by and I do not see signs of plans being made for virus-safe reopening. The fight seems to be between lockdown and reopen -- with little thought to the only possible answer: reopen smart.

Today, my latest thoughts about how to reopen smart.

There is one goal to public health policy right now: Reducing the transmission rate, aka  reproduction number.

If one person gets it, how many does he or she pass it on to? If the transmission rate is over one, the virus grows exponentially. For example, if the transmission rate is 2, then we have 1000 cases this week, 2000 next week, 4000 the week after that, and so on. If the transmission rate under one, the pandemic ends. If the rate  is 0.5, then we have 1000 this week, 500 next week, 250 the week after that and so on.

(The second goal of health policy is to keep hospitals going so that those who do get it stay alive. That's what ventilators, masks and so on are about. As an economist, I'll focus on the first goal.)

So, the entire question is how to reduce the transmission rate at the least -- or at least reasonable, non-disastrous -- economic cost.

This simple framing could, I think, guide lots of policy.

We don't have to talk about lives vs. money. The lockdown is so disastrously inefficient, we can talk about more lives and less money.

We talk about the reproduction rate as if it is just a biological feature of the virus. That helps -- viruses that spread by airborne droplets pass on more easily. But most of the reproduction rate depends on human behavior -- and government policy.

Lockdown, quarantine, etc.  The point of a lockdown is to reduce the transmission rate. If you're at home, you can't get or give the virus. But as we are seeing a lockdown is an immensely costly policy. Lots of people are stuck at home and businesses failing that would not have spread the virus much had they been allowed out. We have to do better.

Fat tails. The reproduction rate is the average reproduction rate. But not everyone is average. Every interesting distribution has a fat tail.  In this lies a great danger and a great opportunity.

Suppose there are 100 people with a 0.5 reproduction rate, and 1 super-spreader with a 100 replication rate. The average reproduction rate is 1.5. Clearly, locking everyone down is wildly inefficient. It's much more important to find the 1 super-spreader and lock him or her down, or change the business or behavior that's causing the super-spreading.

This is exaggerated, but not far off the mark. I have not seen numbers on the distribution of reproduction rates across people, but it is a fair bet that it has an extremely fat tail. Most of us are washing our hands, social distancing, work in businesses that are shut down or are taking great steps to limit contact. And a few people and activities contribute to most of the spread.

This wide and fat-tailed dispersion is ignored in a lot of simulations I've seen. They take the average reproduction rate as the same for everyone. That's a big mistake.

The danger: we waste a huge amount of time and money moving you and me from a 0.5 reproduction rate to an 0.4 reproduction rate.

The opportunity: focus on the super-spreaders, and the super-spreading activities, and you bring down the reproduction rate at much lower cost.

Politicians sort of figured this out. They quickly closed bars, restaurants, and other gatherings where people are in close quarters breathing each others' air.

We're still opening and closing and not fixing enough. Food stores are open. But we aren't all wearing masks, the cashiers still don't have transparent barriers, and so on. Lots of businesses are closed that could easily open in ways that provide a reproduction rate under 1. Zero is not necessary. Under 1 is enough. Once it's under 1, it's not worth pushing harder -- go work on the super-spreaders. 

It's all about the probabilities. Lockdowns and extreme measures try to give zero chance of spreading  the virus. (Except that half the population is "essential," and from the looks of things not doing a very good job.)  All we need is to get the transmission rate under one. Activities with possible but very low transmission rates, and high economic benefits should go on. Don't separate to "essential" and "non-essential." Separate into "high likelihood of transmission" and "low likelihood of transmission."

Why are we not using masks everywhere? Sure, they're not perfect. Sure, an old hankerchief might only cut the chance of transmission by half. We're not all surgeons. Cutting by half is enough to stop the virus. 

Conversely, why did they close the state parks? Really? Just how dangerous is it to drive the dog to a hiking trail and stay 6 feet away from other people? Parks, ski areas, golf courses, all sorts of businesses that surely can be run with a reproduction rate far less than one are just shut down. I met a realtor on our dog walk yesterday. They're totally shut down. Just how hard is it to run a realty business with a 0.5 reproduction rate? One family in the house at a time, don't touch anything, an hour between showings, stay 6 feet from the realtor... But instead the whole business is just shut down.  

Testing Last week I got over-enthusiastic about testing as the key to virus-safe reopening.

Testing is just a high-tech approach to reducing the transmission rate at lower cost. If we could test everybody every morning and know the answer instantly, then we could send the healthy off to work, isolate the sick, and reduce transmission to zero at low economic cost.

But that's all it is -- one of many devices to lower the transmission rate more cheaply than a lockdown. There are many others.  Which is a good thing, seeing as we will not have a daily test for 325 million people for a long time.

Testing doesn't have to be perfect. For the question of deciding which sick patients should be isolated and treated, and which should not, yes, we need fast, accurate, individual tests. But for the public health question, imperfect testing is useful.

False positives are not really a problem. If 2% of the population has the virus, but 4% register positive, then 2% are sent home needlessly. That's a lot better than 100% sent home because we can't tell the 2% from the 98%.

False negatives are worse, but tests with false negatives help too. Suppose half of the people who have it test negative. If you give everyone a test and isolate those who test positive, then you cut the reproduction rate in half. Cutting the reproduction rate from 1.99 to 0.99 would be enough to stop the virus.

False negatives are also only a problem if the person has a high risk occupation or lifestyle. The reproduction rate of a Hoover  fellow is likely about 0.2. If the test misclassifies me, it makes little difference. Save the tests for the people and activities that must unavoidably have a very high reproduction rate.

Thermometers. There is a test that is simple and fast with lots of false positive and negatives. Why are we not asking every person to take their temperature every day, and self isolate if they have a fever? Why are we not using those infrared probes at the entrance to every food store, place of business and so forth? Sure quite a few covid-positive people with no fever will get through, and quite a few feverish people with something else will get sent home. But it cuts the probabilities at almost no cost.

Or a simple web form with symptoms? Fill this out, take your temperature, the web form says ok to work or stay home.

It's an indication of a very first-world attitude that public policy seems to be relying exclusively on DNA technology that didn't exist 10 years ago to provide us with perfect tests.

The goal is to let out people and activities with low reproductive rates, and keep at home those with high reproductive rates. Testing everyone with a perfect test and letting out those who pass is a magic bullet. But it's not the only bullet, and it's a bullet we don't have right now. There are lots of simpler low tech ways to let out people and activities who are likely to have low reproductive rates, and keep home those who are likely to have high reproductive rates. We don't have to wait for snazzy technology.

Economics So what'w the answer? I think it remains the same, and the one that our public policies seem not to be working on: reopen safely.  Phrasing it in terms of reproduction rate might help. For each business, how are you going to open in such a way that the reproduction rate among your customers and employees is less than one? Disinfect premieres every day, take the temperature of everyone coming in, everyone wears masks, move workstations six feet away, rotate workers from home, add barriers... Is that enough so that a sick person coming in infects no more than one other person? Good enough.

There must be a safe reopening plan. We're not going to get nationwide testing of well people any time soon,

Herd immunity The optimist case for this virus right now centers on the idea that many more people have got it than we think, and therefore are immune going forward. If half the people already have it, then this cuts the transmission rate in half. Again, everything is about the transmission rate.

While I hope this is the case, it will mean we dodged a bullet and just got immensely lucky. The virus is out there that makes everyone sick and kills 10%.

Good links

Larry Kotlikoff thinks through the practicalities of group testing, a way to cut the costs of testing by orders of magnitude.

Health and Pandemics working group on pandemic economics

Jim Stock's blog. Jim's March 23 paper is excellent. Jim also clarifies that policy is about one and only one thing: reducing the average transmission rate. Jim thinks about dynamics, making the point that reducing the rate early is better than reducing it late, and worth paying more to do so,

Becker Friedman blog. Good short fact-laden posts.

Update

Thanks to commenter "Fat Man," Jonathan Kay at Quillette writes on the skewed distribution of the transmission rate, and the fact that most models take it as a single number.

In a 2016 paper, South Korean doctor Byung Chul Chun noted that the MERS outbreak could be summarized as:

"an explosive epidemic by infrequent super-spreaders. The number of secondary cases in the transmission tree was extremely skewed. Among 186 confirmed cases, 166 cases (89.2%) did not lead to any secondary cases, but 5 (2.7%) super-spreaders lead to 154 secondary cases. The imported index case [i.e. original case] was a super-spreader who transmitted the MERS virus to 28 people (referred to as secondary cases), and 3 of these secondary cases became super-spreaders who infected 84, 23 and 7 people, respectively. Eighty-four secondary cases resulting from a single case is one of the largest numbers observed in a SSE since the SARS outbreak in Prince of Wales Hospital in Hong Kong. None of the super-spreaders in the MERS outbreak in Korea was a healthcare worker."...

... June, 2020 Centers for Disease Control and Prevention (CDC) report, Identifying and Interrupting Superspreading Events—Implications for Control of Severe Acute Respiratory Syndrome Coronavirus 2, by Thomas R. Frieden and Christopher T. Lee. Echoing points made by Dr. Chun and others, the authors note, “SSEs highlight a major limitation of the concept of R0,” since R0, being a mean or median value “does not capture the heterogeneity of transmission among infected persons.”...

From Seattle to South Korea, many of the biggest outbreaks were fuelled by a small handful of very sick, highly symptomatic people who drifted along for days before their condition was correctly treated and isolated. (In South Korea, some have noted, the problem was exacerbated by patients who went “doctor shopping,” spreading their germs in many different clinics.)...

While we are at it, we need to stop wasting resources on pointless measures such as closing remote parks and natural reserves, where few people come close to one another anyway. In an especially important section of the aforementioned CDC report, the authors note that even COVID-19 super-spreaders can’t seem to infect people effectively in open spaces: “Rapid person-to-person transmission of COVID-19 appears likely to have occurred in healthcare settings, on a cruise ship, and in a church. In a study of 110 case-patients from 11 clusters in Japan, all clusters were associated with closed environments, including fitness centers, shared eating environments, and hospitals, [where] the odds for transmission from a primary case-patient were 18.7 times higher than in open-air environments.” These closed environments represent the sort of scenario we need to target—not British couples out on a jaunt to Sugar Loaf, Pen-y-Fan and other rustic destinations...

Even long before COVID-19 was a thing, infectious-disease experts such as James Lloyd-Smith were arguing that “the distribution of individual infectiousness around R0 is often highly skewed”; that approaches accounting for super-spreaders do a better job modelling the sudden cluster-based boom-and-bust quality of many diseases; and, crucially for today’s policymakers, that such analyses show how, in these cases, “individual-specific control measures outperform population-wide measures.”

This piece goes half way, I think, to the right conclusion. Reproductive rate is not a low number plus a few super spreaders. It is a distribution with a very fat tail. The report seems to personalize the super spreaders as particularly ill behaved people. They are more likely normal people who participated in a particularly poorly structured activity, like the famous South Korean church.

Our first goal should be to stop that fat tail.

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