Evaluating the Fiscal and Economic Cost of Lives Saved From Quarantine Benjamin Way Follow Mar 24 · 17 min read

“No cost too great” is a poor attitude for a society facing mortality from a variety of sources. At a certain point, “saving lives” costs lives on the balance. What, precisely, is the balance?

Spoiler: quarantine is at least worth the cost of stalling for additional research time to develop better estimates of irreversible scenarios before they occur.

These are very uncertain times. Everybody has valid concerns about COVID-19 and the havoc it can potentially wreak on our bodies, our families, or our fragile economic and medical systems. In fact, there are so many valid concerns that are so enormous that it can be hard to wrap one’s mind around them all meaningfully. We are now facing astronomical costs in our efforts to combat this epidemic, and many are beginning to question whether the benefits are worth the cost. I will do my best to lay out what those benefits are, and how we would go about evaluating the costs.

A fairly simple analysis of COVID-19 provides sobering conclusions. The mortality rate worldwide for the virus is variously estimated as being as high as 4%, although most experts predict that a fuller data set will reveal a much lower rate. The reasoning is that whereas all deaths are counted, most mild or asymptomatic cases will not even be tested, resulting in a skew toward extreme negative outcomes — perhaps a very large skew, as in, maybe making the problem look 10x worse than it is. (No, seriously.) Thus, although the official rate is currently 3.4%, that is expected to fall by as much as 90% with more data.

Still, if everybody caught it, even a 0.34% mortality rate would mean a staggering 1,100,000 deaths. 3.4% would mean an unfathomable 11.1 million deaths!!! For comparison, it would take twenty-eight WW2’s to kill that many Americans.

It gets worse. These rates are based on the presumption that only one in three patients requiring intensive care will die. If we run out of room at the hospitals, would the death rate increase to three out of three patients requiring intensive care dying? It is not unreasonable to assume that this is approximately so, with the margin filled in by regular hospitalization fatalities due to hospital overflow.

Thus, if everyone who is going to need intensive care needed it at the same time, the death rate could easily be TRIPLED. We are now talking about between 3 million and 33 million deaths. Let’s see how that stacks up against normal circumstances:

Definitely comparable to seasonal Flu.

It is hard to imagine an “overreaction” to this kind of situation. The minimal social distancing measures that we are calling “quarantine” do not seem to be outsize compared to something that is officially projected to kill as many as 10% of us if we do not act.

There are three — excuse me, two — main goals of quarantine:

0) Eradicate the disease entirely (completely unrealistic).

1) Hold out long enough for a treatment or vaccine to reduce mortality rates.

2) Space out the number of cases so that hospitals are not overwhelmed and mortality rates can be reduced with known care options.

Let’s just talk a little bit about the first goal. This is probably impossible. The disease has already infected hundreds of thousands of people, and perhaps millions. The number of cases is set to grow exponentially. This only took it a couple of months to achieve, because it is undetectable for so long while it is highly contagious. Absent a well-funded-and-coordinated global effort, and perhaps even despite one, this virus is here to stay.

Also, Gen Z is not taking this seriously, perhaps because of the 0% expected death rate among Gen Z, and perhaps because they don’t take anything seriously. Little twerps. (Millennials: it is now the dawn of our turn to be crotchety middle-aged adults. Finally, we can start making blanket statements blaming the younger generation for things far outside of their control!)

The second goal of developing a treatment is much more likely to be achieved. Although this particular virus is new, our tools for developing methods of combating viruses in general do not need to be redesigned so much as reapplied. If we are not unlucky, it is only a matter of time until the researchers of the world develop a method of treating this disease. How much time? Some are saying a year. That may be optimistic. Then there is the question of how much collateral damage we’re willing to accept to reduce mortality. Suppose a vaccine has a 0.004% death rate and unknown potential long term side-effects. Would it be good to use it or wait for a safer one or at least more information on the longer term effects? Millions of lives could hang in the balance; it would be a very tough utilitarian call to make, and yet there is a good chance somebody may have to make it next year.

If these guys are in charge, they’ll definitely push to use the first product they have “ready.” If they get the contract, you can probably expect a very different projected stock price. Always a silver lining, eh?

The third goal is pretty much guaranteed to work at least to some degree: if we are able to quarantine long enough to prevent hospital overflow, we can potentially lose two-thirds fewer people or even (unrealistically) 11/12th’s fewer.

You’ve probably seen some of these graphics about flattening the curve. There is a problem with these graphics: the healthcare system capacity line in the U.S. is much, much lower than depicted in this graph. We need to flatten the curve a lot more than that to stay within our capacity. This is in contrast to, say, South Korea, where they have an order of magnitude more staffed hospital beds per person than we do, and the world’s lowest mortality rate for COVID-19.

Because we need to flatten the curve so much in order to stay within our capacity limits, we need very strong protective measures for a very long time. Quarantine is therefore guaranteed to be extremely expensive because of how severe it must be and how long it will take. How expensive is it, exactly? I understand this may sound like a heartless question. Who could put a price on a life? The answer, of course, is somebody who can spend money in lots of different ways to reduce mortality in lots of different areas, i.e. the government.

For example, perhaps paying for more food quality inspectors, or more mine inspectors, or redesigning dangerous intersections, or building another hospital, or increasing funding for medical care and research could save more lives (or life-years) per dollar spent. Perhaps we should be using every available dollar to combat global warming, to save our way of life? Perhaps we should be investing heavily in technology to withstand the effects of global warming? Perhaps we need to be focused on cost-cutting measures to pay down the debt and to preserve our way of life. Some even argue that we need more weapons and preemptive wars to protect ourselves from war to preserve our way of life.

Existential threats aside, measures of poverty and unemployment track very closely with rates of mortality as well. Anything that causes a significant increase in rates of poverty is also likely to cause a significant increase in general mortality, as well as political and potentially geopolitical agitation. Very extreme economic shocks could cause cascading damage easily in excess of this particular pandemic crisis, although it may be hard to disentangle the two either way. How does one gauge the expected value of increasing the risk of systemic failure in economics or global diplomacy? Is this epidemic, if uncontrolled, less likely to destabilize the systems than uncontrolled spending to contain the epidemic would be? Despite all of these uncertainties, I will do my best to lay out an estimate for costs based on what we do know.

The main stated purpose of the quarantine is to prevent the number of new cases from being too high all at once. How much is too high all at once? In the United States, we currently have about 300,000 empty hospital beds available, of which a maximum of 100,000 are equipped for intensive care, and they are specialized for various kinds of care, so not all will be useful for this virus. I did not find data I wanted on what types of intensive care can be provided, so I am not sure about the proportion. I will just proceed looking at normal bed space without even worrying about overwhelming the ICU. This will underestimate the size of the problem, but I don’t know how to get around that.

Alright, so we’ve got about 300,000 beds free for 324,000,000 people, meaning we have enough beds for about an extra 0.1% of people to need to be hospitalized at once. The rate of hospitalization for COVID-19 has been estimated very widely, because we don’t know how many people got the virus mildly enough not to get tested and counted. The high estimate is 20% of people may need hospitalization. The low estimate is more like 1.25% of people. So, if everyone got it at once, we would have between 12.5 and 200 times too few beds available.

Yes, that little sliver there is what we have to work with. Thank you public/private healthcare monopoly.

As I was saying, those “flatten the curve” graphics are hiding the scale of the problem. Anyway, the idea of quarantine is that we can break that up into batches. Even if every bed is filled with perfect efficiency, this means we will need to turnover a minimum of 12.5 batches of recovered patients to prevent hospitals from being overwhelmed, and as many as 200 batches if the worst estimates for hospitalization are accurate. Recovery time from hospitalization of this virus has been reported as 3–6 weeks.

Putting together our hospital capacity with various possible rates of hospitalization and turnover time produces the following chart.

Minimum 9 months, maximum 25 YEARS? Hail Satan!

Best cast scenario, with every single estimate breaking heavily in our favor, we need to quarantine for 9 months. Much more realistically, we would not batch perfectly (by intention leaving a margin for error), and average turnover is likely to be between 4 and 5 weeks, so we are probably talking about more like 12–18 months as a true minimum. The batching issue would magnify all of these numbers proportionately by whatever margin we give ourselves to avoid overflow. If hospitalization rates are even a little bit higher than 1.25%, we are talking about a very, very long quarantine.

A little bit of “good news”: many of the people currently occupying beds in hospitals will be the most likely also to need hospitalization if they catch the virus, and they are more likely to die if they do. This can increase bed space estimates due to the overlap, plus those who die in under 3 weeks can bring down the turnover average. These are “good news” because as these people die, they reduce multiplicatively the duration of time we need to spend in quarantine to protect them from dying. So, there is negative feedback on these losses that will work in our favor, even as we bury our dead. If everyone in hospital now died at once, for instance, we would have 800,000–1,000,000 beds available instead of 300,000. The quarantine lengths could be slashed by 62–70%! “Good news!”

I apologize for my morbid sense of humor. That, and analysis, are my way of processing this kind of cataclysm. If I one day (maybe soon!) find out I’m dying, the first thing I’ll want to get done are some jokes for my funeral.

Alright, so with an acknowledgement that those numbers are a little bit fuzzy, they are the best I could cobble together, and we are going to use them.

Now for some actual good news! If we apply these published mortality rates for each age group to the age demographics of the U.S., this predicts that the mortality rate will actually be “only” 1.8%, not 3.4%! And if we are lucky and, as we suspect, 90% of cases are undetected, this would mean actually a 0.18% mortality rate instead!

Sorry, did I say actual good news? I meant, “Only half as bad news!” This means our BEST CASE scenario is 0.6 million to 6.1 million expected deaths if we avoid severe hospital overflow.

In a “Dark Day” scenario, we assume maximum hospital overflow and further that everyone who would have received intensive care would die without it, therefore tripling the mortality rate expected with hospital care.

In the “DOOMSDAY” scenario, we assume maximum hospital overflow, and further that everyone who would have been hospitalized, intensive care or not, would die instead without it. This would duodectuple the hospital care mortality rate. Thus, we have the following:

Hail Satan! Does that say 74 million American deaths? What in the Lake of Fire!?

Okay, thankfully, that DOOMSDAY scenario is probably impossible. Most people hospitalized who don’t go to critical care would probably recover without a hospital bed, too, and the actual rate of detection on which mortality rates are based is definitely less than 100%. But that middle row is actually a very likely although perhaps moderately overstated outcome, if we do not find a way to slow the rate of spread or mortality of the disease. It appears that a successful quarantine could easily save between one and twelve million American lives, depending how good our detection rate has been so far. For comparison, the death total for all causes of death combined in 2019 was a little under three million.

For the purposes of this model, we will assume that guaranteeing medical care for those with intensive needs can reduce mortality by two thirds. Thus, we can estimate the number of lives potentially saved per month of quarantine by dividing those potentially saved in total by the necessary length of quarantine to achieve it.

Wow, look at that spread! We do not have nearly enough information to make risky decisions.

So, as you can see, depending on the length of quarantine required to be effective and the total number of deaths we are expecting, there are extremely variable estimates for the value of this attempt. A few months of quarantine could be saving thousands of lives, or they could be saving millions. Not really sure yet, and we won’t have proper data until it’s too late. What a bind!

And — at last! — we are able to estimate cost per life saved by applying the costs per month of measures undertaken to reduce mortality through quarantine and dividing it by the number of lives that will be saved during that month of quarantine.

For example, let us consider the proposal to pay every American adult $1,200 and every child $500. With 209 million adults and 115 million children, that would cost us $308,300,000,000 a month.

Hail Satan! Does that say $75 million per life saved?! What in the Lake of Fire?!

Those costs do not take into account the interest we will have to pay on the loans we use to fund those checks, or the economic loss to production and consumption from ordering everyone home, which will also result in losses to tax revenue and decreases to quality of life. And, of course, this is just one spending measure among many intended to accompany it.

You may also notice something, which is fairly intuitive. The worse a disaster the virus would be, the more worthwhile quarantine measures are. The less bad the virus would be, the more of a waste quarantine measures are. Due to the extreme uncertainties plaguing our ability to predict the potential harm from the virus, it is impossible to make an informed decision. Are we paying $40,000 per life or $75,000,000 per life? How far in between those crazy extremes?

An unknown, potentially catastrophically large number of lives may be at risk, or maybe just a pretty manageable little fraction. Meanwhile, none of the many crises that were facing us immediately before COVID-19 rode in on a bat out of Hell have actually gone away, and still desperately need our fiscal attention.

We are now faced with an impossible decision. Several major issues await our attention and resources or else we will face consequences at some point in the future. National and individual debt could cause government or monetary system failure? Uncertain. Global warming could cause end of civilization as we know it? Uncertain. Overpopulation coupled with recession and environmental disruption of food supply could cause geopolitical conflicts? Uncertain. COVID-19 presents very serious consequences if we do not apply our attention and resources to it immediately. How serious will the consequences be? Uncertain. How serious would the consequences of the other looming crises be, and how likely are they to happen with what degree of severity if we focus on them now compared with if we wait to focus on them until after dealing with the COVID-19 crisis? Could failure to act on COVID-19 exacerbate the other issues more than our prioritizing them over it could ameliorate them? Uncertain, uncertain, uncertain, in interrelated ways. So uncertain that “completely unknown” might be a closer approximation.

We as a people are used to having disagreements about unknowable things that we will be able to improvise somewhat as they develop, or things that don’t have the potential to obliterate significant swathes of the population. That gives us some wiggle room for making mistakes and changing our policies. In contrast, this disease grows so rapidly and is so potentially dangerous that if we make a wrong step, we may not be able to respond to the consequences. This is why we are trying not to take any more steps, by quarantining everything possible. The possibility that the situation could almost instantaneously become an unstoppable catastrophe carries a lot of weight even if it is a much less likely one among the expected outcomes.

Yet, there is still another aspect to consider. Life-years saved vs. Lives saved.

(Note: I eschewed “productive life years” as a measurement, because I believe unquestioningly that people still have value even after they stop being “productive” and because it would lead to the fascist conclusion that we should sacrifice as many people over the age of retirement as possible to reduce the burden on entitlement programs; COVID-19 is a fascist godsend. That kind of inhuman reckoning is beyond even my detached, cynical capacity.)

For example, according to the Social Security Administration, an 11-year-old girl can expect about 70 more years of life, whereas an 85-year-old woman can expect 7 more years of life. Thus, saving the life of an 85-year-old woman garners 7 life-years, whereas saving the life of an 11-year-old garners 70 life-years.

Thus, saving one 11-year-old is “worth” as many life-years as saving ten 85-year-olds. This is intuitively true. It is unheard of for somebody to say that they would save two 80-year-olds from a burning building instead of one kid. But, twenty 80-year-olds? Thirty? Everyone has a point where they’ll start doing some calculations.

We are past the point where I had to do some calculations. I went with these death rates and these demographic numbers and these life-year expectancies to calculate how many life-years we would save, and then compared it if the death rate were equally applied across all age groups.

Fun fact! You might note that COVID-19 is likely to kill a lot more women than men. This is because so many men already died before they reached the ages of 70 or 80 that there aren’t as many left to be at high risk right now.

More importantly, along that line of thinking, you will notice the vast difference in life-years lost by COVID-19, which kills those who are already infirm at a very disproportionate level, as compared with something that kills indiscriminately. In this case, the heavy skew against the elderly results in 60% less life-years lost as compared with something indiscriminate. Something that targets the young would have an exaggerated impact on life years lost, obviously. When discussing lives lost, it is meaningful to include a consideration of life-years for this reason.

Furthermore, we must acknowledge that the life-years saved in this estimate will still very likely be highly overestimated. That is, the people most likely to die from the novel Coronavirus in each age bracket are also those who were already most likely to die from other things, among their cohort. If they survive this epidemic, they would still be those bringing the averages down for their group, discounting the life-years saved in this way — potentially reducing it close to 0 benefit, although the actual fraction is unknowable and the benefit probably significantly higher than nothing.

When this consideration is added into the analysis, it further reduces the value of each dollar spent on quarantine to prevent deaths, given that those deaths are, to some extent, unpreventable anyway in the slightly longer term. Nonetheless, the costs and values of various of quarantine responses have estimates with orders of magnitude in their ranges. Given the potential, exponentially growing severity of a failure to take decisive action in the immediate term compared against the high but known and linear near-term costs of taking early steps to prevent that, and the initially very high but exponentially decaying marginal value of stalling for more research time, it makes a lot of sense to gamble huge sums of money on insurance against cataclysm, at least until we can rule out the worst case scenarios with more research. If we end up ruling them *in* instead, we will be very appreciative of the money we are now throwing at quarantine, perhaps somewhat inefficiently.

We are very early in the stages of development of this epidemic, and we have very limited data from which to work and make decisions. As time passes, we will get much better data on hospitalization and mortality rates, and we will also have a better estimate on how long advances in treatment may take, we will have more time to build hospital space, train staff, and produce equipment, and we will be much better positioned to make a socially, morally, fiscally responsible decision. How can we guarantee we get that time? We’ll have to buy it with quarantine money.

And, finally, it is important to recognize that there was going to be an economic recession with or without the Coronavirus, and there would have been government stimulus packages and borrowing either way. It is impossible to know what policies would have been decided if COVID-19 had never been spawned. And, it is impossible to predict how markets would react to the uncontrolled spread of the virus. Quarantine measures are hurting production and consumption, likely more than people staying home sick from work would, but would failure to quarantine also hurt GDP, perhaps more? The answers are not knowable, but the possibility of severe panic at an epidemic is not to be ignored, either, and carries weight in these economic discussions, as well.

Ultimately, I may have opened up a lot more questions than I answered, but I think some important takeaways are as follows:

This is a serious disaster, unrivaled by all but the most major wars. The potential death toll is not known, but could be among the highest of anything in history. The amount we need to pay to insure against catastrophe is very high. Depending on what estimates a person is looking at, the economic cost of quarantine is either “easily justified” or “a much bigger disaster than the virus itself.”

There are a lot of unknowns here. The stakes are unfathomably high. Many different popular priorities are stacked against each other. Personal circumstances and histories are causing dramatic disparities in peoples experience of this crisis and response. Anxiety is running amok. Tempers are short. I guess I’m trying to say that there are a lot of well-supported, diametrically opposed viewpoints right now, and it’s really important that everyone try to be patient and understanding: with each other, with the government, with researchers, with their expectations for capital accumulation and immortality, and most importantly with forming any hardened opinions about what is the correct response to this virus. We need more time and more data! Quarantine will buy us the time to find out if further quarantine thereafter is economically viable.

For the time being, quarantine and whatever economic stimulus and income supports are necessary to accompany it are certainly worth the cost.

Links from which information was pulled for this analysis:

https://www.populationpyramid.net/united-states-of-america/2020/

https://www.ssa.gov/oact/STATS/table4c6.html

https://www.cdc.gov/mmwr/volumes/69/wr/mm6912e2.htm

https://www.cdc.gov/nchs/nvss/deaths.htm

https://www.businessinsider.com/coronavirus-death-rate-by-age-countries-2020-3

http://www.cidrap.umn.edu/news-perspective/2020/02/study-72000-covid-19-patients-finds-23-death-rate

https://www.aha.org/statistics/fast-facts-us-hospitals

https://www.geekwire.com/2020/scientists-find-86-percent-coronavirus-infections-go-unreported/

https://www.medscape.com/viewarticle/926089

https://bgr.com/2020/03/13/flatten-the-curve-what-does-it-mean-coronavirus-covid-19/