Kotlikoff: Beating COVID-19 with Math

Containing the ever-mounting butcher’s bill from Covid-19 will be hard enough. Getting the economy back on track when universal testing is still months away seems an impossible dream. But there is a loaves-and-fishes-style shortcut — one not dependent on divine intervention — that could dramatically improve the efficiency of testing in separating the well from the unwell. Skeptical? Suspend your disbelief for just a few minutes.

The Abyss We Face

As this is being written, at least 56,000 Americans have died from the virus, and all the epidemiological models imply a lot more to come. As for the economy, there is good reason to believe we’re headed for a full-blown depression. Unemployment topped out at 25 percent at the nadir of the Great Depression, and output fell by an estimated 26 percent from the previous peak. But it took 3 years to plumb those depths. This time around, the likely 40 percent drop in GDP will take only a few months. Unemployment is likely already at 20 percent.

So, easy-go, easy-comeback? To the contrary: I believe we’ll wallow in the bottom until we take the offensive against the pathogen.

To date, the realistic target of responsible leaders has been to “flatten the curve” of new cases by means of social distancing, with the near-term goal of making sure that the health care system will be at least marginally adequate in preventing unnecessary deaths. But thereafter, things get murky.

Yes, eventually enough people — the best estimate now is north of 70 percent, which is miles from where we are right now — will have had the disease to create “herd immunity” in which the virus cannot on average infect a new victim to replace one who has recovered or died. Yes, an effective vaccine combined with more effective treatments that sharply reduce the lethality of COVID-19 would allow the wheels of production and commerce to slowly spin up to capacity.

But the longer the economy is on life support, the greater the dislocation and the slower the recovery will be. It took a decade to fully recover from the Great Depression, almost as long to vanquish the ghost of the Great Recession. I can’t imagine the recovery will be any faster this time around unless there is extraordinary, immediate intervention that ends the epidemic in the United States.

But what would that entail? The consensus view among epidemiologists is a national strategy along the lines of Singapore or Taiwan — a slow relaxation of restrictions in the context of massive testing and follow-up surveillance. Yet we don’t seem to have the will to sustain social distancing at the national level for long periods — and we certainly don’t have the testing capacity to exit from lockdowns without great risk of a new wave of infections.

Loaves and Fishes

Absent a coordinated national policy, our best hope is that at least one state goes on the offensive, making a slick end run around the reality of inadequate testing capacity. The approach is simple — and has worked before — but it is not intuitive.

In the best of worlds, a state could test every resident every day. All the negatives would get green bracelets and all the positives red bracelets. Those with red bracelets would be quarantined. Those with green bracelets would be free to reenter society, but for only as long as they tested negative. Within a matter of weeks, the virus, even if the testing involved substantial false negatives, would lose access to new victims.

But, you say, we don’t have 328 million tests available every day — or, for that matter, every month — to identify the infected. That’s where group testing comes to the rescue.

Frazier’s team developed a group testing protocol that could release 96 percent of the U.S. population back to society within four weeks, with this percentage rising even higher thereafter.

Group testing was pioneered by a brilliant economist from Harvard named Robert Dorfman in response to the army’s need to screen hundreds of thousands of recruits for syphilis in World War II. Running the requisite blood tests, recruit by recruit, was time consuming and costly. So Dorfman proposed mixing together the blood of, say, 50 recruits and testing the entire batch all at once.

If the test was negative, you could release all 50 recruits to the services with a single test. If it was positive, you could divide the 50 into two groups and so forth, using a minimal number of tests to the point you could no long eliminate another group. Only then would you need to move from “wholesale” to “retail” testing individuals in the syphilis-positive group.

We could follow a parallel strategy for extinguishing the novel coronavirus that’s been outlined by Cornell University’s Operations Research Professor Peter Frazier and colleagues. (Frazier, for what it’s worth, worked on the algorithms for Uber’s dynamic pricing model — aka surge pricing — that allocated scarce vehicles at peak demand.) In the context of the pandemic, Frazier’s team developed a group testing protocol that could release 96 percent of the U.S. population back to society within four weeks, with this percentage rising even higher thereafter.

Frazier envisions initially testing 62 households at a time, and assumes, to be conservative, a very high (30 percent false negative) test rate that would require some degree of redundancy to work efficiently. All told, though, the job could be done for the entire United States with only 6 million tests per week. That’s a large number, but just three to four times the test rate we’ve already reached. If we could build a B-24 heavy bomber every 63 minutes in 1945, when the U.S. GDP was roughly one-eighth the size it was in 2019, surely we can create the capacity to test 6 million residents for coronavirus every week.

In the absence of federal leadership on group testing, a single large state could lead the way. States with a higher disease prevalence would want to use somewhat smaller group sizes and a larger than proportionate number of tests. But the math behind Frazier’s protocol works with any set of state-specific inputs.

• • •

Donald Rumsfeld infamously lamented, “You go to war with the army you have, not the army you might want or wish to have at a later time.” That, alas, is as true of America’s war on COVID-19 as it was of the Bush administration’s impromptu war on Iraqi insurgents. But there’s one big difference. The only way to remedy the inadequacy Rumsfeld was alluding to — a shortage of fully armored personnel carriers in Iraq — was to reinforce one vehicle at a time. Today, we could remedy our failure to produce massive numbers of virus tests with mathematical statistics and a time-proven solution — group testing.