In my previous article I discussed some of the basic theories about how COVID spreads and how it can be effectively fought. This article does not require having read that article but will refer to the homogenous SEIR model and heterogenous models.

This article will argue that our current strategy of complete suppression is infeasible and not justifiable. Instead we need to adapt our strategy and find a sustainable level of infections and lockdown restrictions until we have an effective vaccine.

Why We Need a New Strategy:

The success of Asian countries in quickly suppressing COVID has led to the hope that a similar strategy could work elsewhere. After a short and sharp lockdown, we could reopen with minimal restrictions and rely on testing + tracing to keep our cases low.

In the US and Europe this strategy is not working. This is either because we have implemented the strategy poorly, or because it was never feasible in the first place. Either way, right now we are left with only the choice between two unpalatable options:

  • Herd Immunity - Remove essentially all lockdown restrictions and accept the large number of deaths.
  • Shelter until Vaccine - Retain essentially all lockdown restrictions until an effective vaccine is ready, which optimistically means another year of lockdown and pessimistically may not ever happen.

Measuring the Costs:

To decide between a full lockdown and herd immunity we actually need to compare the costs and benefits of both approaches. The costs between the two of them are not directly comparable, mixing economic costs, happiness costs and costs in human lives.

Combining these disparate concepts requires using the economic concept of the QALY. This combines a variety of costs (economic, health, happiness) into a single number.

Many people consider the idea of comparing health costs to economic costs to be abhorrent, and insist that it is immoral to tradeoff a human life for any amount of economic value. That is a valid perspective, but all public health decision making requires us to do this at some point even if only implicitly. For instance, the influenza kills around 50,000 people every year. We could impose a society wide lockdown every winter to reduce that number but obviously that would not be worth the cost and disruption.

The most controversial part of the adjustment is between dollars and years of life. The NIH values a single QALY at around $40,000 when considering which treatments to offer, while in the US a number closer to $100,000 is used. In this article we will use the value of $100,000 throughout our analysis.

The Cost of Herd Immunity:

If we choose to not react to COVID at all we would eventually reach herd immunity. In order to do this ~40-80% of the population would need to be infected. We will use the pessimistic assumptions from the homogenous model and assume that this would require 250 million infections and 3 million deaths in the United States. We could break down the costs into three clusters.

  • Deaths from COVID.
  • Long term health impacts from COVID.
  • Economic costs from treating COVID.

Deaths From COVID:

COVID disproportionately kills older people. Based on this demographic data we can estimate that the average person who dies from COVID would have otherwise lived ~10 years longer.

If we apply this to our estimate of 3 million deaths we get a cost of 30M QALYs or $3 trillion.

Long Term Health Impacts from COVID:

It is unclear what long term damages result from a case of COVID. Even if these complications are relatively minor, they still add up if we allow almost everybody to be infected.

A good way to estimate it might be to look at some of the research from an earlier H1N1 outbreak. In that case researchers used followup surveys to confirmed cases to estimate the quality of life reduction from a case of H1N1. They estimated an average cost of .01 QALY (or ~3 days). COVID is significantly more deadly than H1N1 so to be safe we will estimate it at .1 QALY (or ~1 month).

If we apply this to our estimate of 250 million cases we would have additional costs of 25M QALYs or $2.5 trillion.

Economic Costs of COVID:

Similarly we don't have a great idea of what the economic cost of COVID is. Again we can turn to the costs of the seasonal flu to get an estimate. Every year there are 30-35 million cases. These cost an estimated ~$10 billion.

To adjust this for COVID we can multiply this number by 80 (250M cases vs 30M and COVID being ten times more severe).

This would give us an economic cost of $800B or 8M QALYs.

Total Cost:

If we add these costs together we would get a total cost of 63 million QALYs.

Those costs are broken down as:

  • 30M QALYs from deaths.
  • 25M QALYs from long term consequences of non fatal cases.
  • 8M QALYs from economic costs.

The Cost Of Lockdown:

To balance against this we need to consider the costs of maintaining full lockdown restrictions until a vaccine is ready. We don't know what a lockdown sufficient to completely eliminate COVID cases would look like, but we can say that it would need to be at least as strict as the US's current lockdown.

The costs from this lockdown break down into four major components:

Direct Economic Costs:

In the United States the GDP has contracted by about 10% since COVID started. This corresponds to ~21.5M QALYs or ~$2.15T of economic costs per year of lockdown.

Lockdown Is Not Fun:

Something which dwarfs the direct economic costs is the loss of enjoyment associated with being in lockdown. This is something which is difficult to measure precisely but which obviously exists as a cost.

If the average person enjoys life 10% less while in lockdown (a fairly conservative assumption) then the cost of a year in lockdown is ~33M QALYs or ~$3.3T.

Loss of Education Opportunities:

Remote learning during lockdown is not as effective as in person learning. A common estimate is that the loss of a full year of education leads to a loss of ~$100,000 in lifetime earnings. If this is applied to the 76M students in the United States, then if remote learning is 10% less effective the economic cost would be ~7.6M QALYs or ~$760B.

Long Term Effects:

The long term effects on a post lockdown world are unclear. We have reason to believe that they will be negative (disruption of employment and businesses, loss of social cohesion). However they are hard to measure so we will ignore them for now.

Total Costs:

If we add up these costs with the same cost of $100K / QALY then the cost of a full year of lockdown ends up being around 62M QALYs.

This breaks down as:

  • 33M QALYs - Decreased quality of life under lockdown.
  • 21.5M QALYs - Economic cost of 10% lower GDP
  • 7.5M QALYs - Long term economic cost from 10% worse schooling.
  • 0M QALYs - Long term intangible costs.

Lockdown vs Herd Immunity:

If these were our only options, then on balance we should probably give up and go for herd immunity. Using very optimistic numbers for the costs of lockdowns (ignoring the long term economic costs, and assuming that this limited lockdown could completely eliminate all covid cases) and very pessimistic numbers for the costs of COVID (very high number of deaths and large long term health costs) it is still an extremely close choice. When you add in the possibility that effective vaccines may not be universally available within a year, it becomes even harder to justify this lockdown.

Can We Split the Difference?:

Under the assumptions of the standard SEIR model it makes no sense to try and split the difference with a partial lockdown.

Almost all of the gains come from reducing transmission from R0=1.5 (60% are infected) to R0=1.0 (almost nobody is infected).

At the start of the outbreak R0 was estimated to be > 3. This meant that even getting to R0=1.5 would require strict lockdown measures. If this is the case it makes no sense to consider a partial lockdown. If getting to R0=1.5 is worth it, then the few extra restrictions required to get to R0=1.0 would almost certainly be worth it. Conversely if the cost of getting to R0=1.0 is too high, there is little point in taking any half measures.

However heterogenous models behave differently.

Most of the focus has been on the reduced herd immunity (only 60% infected vs 95%). But perhaps more importantly, the slope is much more gentle and consistent than in the homogenous model.

Firstly this means that complete suppression is much more difficult than in the homogenous case. This is because no matter how low you bring the average transmission rate, some groups will transmit much more than average and spread among themselves.

Secondly there is no "critical region" where small reductions in R0 lead to large differences in the number of COVID cases. This means that each policy can be considered in insolation and the costs and benefits evaluated independently.

Splitting the Difference:

Splitting the difference between the lockdown and herd immunity policies allows us to reformulate our original question.

Originally we determined that both lockdown and herd immunity had similar costs associated with them. This meant that we were left with an intense dilemma as to which of the very divergent paths to choose. However if we can choose a middle path the problem becomes more manageable. If a policy would reduce transmissions by 10% it would be worth pursuing as long as it had less than 10% of the total costs of lockdown (and not otherwise). This doesn't solve the problem by itself (nobody actually has fully precise numbers), but it does make it more amenable to our standard tools of analysis.

Policy Suggestions:

This section is entirely my own opinions informed by the cost benefit analysis discussion above.

Reopen the Schools:

Keeping schools closed is one of the most obviously bad and damaging decisions that we have made so far in this pandemic.

Economists believe that the financial cost of losing a year of education is that you will earn roughly 10% less throughout your career. If properly discounted this amounts to roughly $100,000.

We don't have a good idea of how much worse remote learning is than in person, but it being 10% worse seems like a reasonable estimate. At that level the overall economic cost of moving schools to remote only for a year is $760 Billion. This number doesn't even capture all the other additional costs associated with leaving the schools remote (parents loss of productivity, emotional harm to children, the inequitable distribution of damage to poor and minority children).

Even if opening up schools were to cause 200,000 extra deaths, it would still be a close call. Fortunately we are gathering evidence that schools are nowhere close to that level of danger. Furthermore in many cases uncertainty means that we should act with caution. However in this case, the uncertainty involved in keeping schools remote is even larger. The estimate of remote being 10% worse is highly speculative, you could certainly justify a belief that it is 50% worse. If that was the case, the economic cost from keeping schools closed is $3.5 trillion or more than the rest of all the other economic damage combined.

Wear Masks:

From everything we know masks are not by themselves sufficient to prevent COVID transmission. However masks are extremely cheap and importantly do not prevent most activities. If the average person would value the discomfort of a mask at $500, then it would only need to cut cases by 3% to be worthwhile. The evidence we have on mask effectiveness is not especially strong but even conservative estimates put it at a 10-20% reduction which puts it comfortably in the worthwhile side of tradeoffs.

Discard What Doesn't Work:

Early on in the course of the pandemic we believed that surface transmission and casual outdoor contact were significant vectors for transmission. We now know that close indoor contact is the primary driver of the spread. Nevertheless we are still encouraging the use of expensive and largely pointless sanitation regimes and keeping outdoor recreation options closed. Instead we need to shift our focus and resources to more effective ways of reducing transmission.

Isolate the Elderly:

Although complete lockdown for society in general is hard to justify, for the elderly and vulnerable it is much more justifiable. 80% of the deaths are to those 65 and over, and even for non fatal cases, they are more likely to have significant health impacts. Furthermore, locking down the elderly has less of an economic or educational impact. Policies which concentrate on isolating those over 65 are 3X more cost effective than globally targeted policies.

Invest in HVAC:

There is speculative evidence that ventilation is related to the spread of COVID and that proper air filtering could reduce transmission. Improving the ventilation with filters is expensive but the potential benefits are so enormous that it is worth investing tens of billions of dollars for even a 1% reduction in COVID transmission. The partial reopening of schools gives us an enormous opportunity to test out this hypothesis as we can semi-randomly choose some number of schools to be upgraded and look for differences in transmission.

Take Vitamin D:

Again there is incomplete evidence on the topic, but Vitamin D has the potential to reduce the severity of COVID infections. In addition Vitamin D is generally considered safe as a supplement. A yearly supply of Vitamin D might cost $10 per person. This means that if this could reduce the costs of COVID by .05% it would be a worthwhile tradeoff.

Rush the Vaccine:

If we are going to try and remain in lockdown until a vaccine is ready, it is crucial that we speed up development as much as humanly possible. Every month in lockdown costs the United States 6M QALYs (5.2M from the lockdown, 700K from COVID). This equates to an economic cost of $600B. To put this number into perspective, the market cap of the top 20 pharma companies is roughly equivalent in value to getting a vaccine out 5 months quicker.

If we take this number seriously we should be taking extreme measures to accelerate this process, even at the cost of large risks. An effective but dangerous vaccine which killed 100,000 people would be better than a completely safe and equally effective vaccine if it could be released just one month sooner.

Effectively rushing the vaccine means that we need to do many things differently than our normal vaccine review process.

We need to use extremely large trials, and do as many things in parallel as possible. In normal vaccines we look to avoid even minor side effects and pause to carefully analyze every data point. With COVID vaccines minor side effects are relatively unimportant, only relatively common and serious side effects matter to the decision. China and Russia seem to have understood and internalized this point and dramatically accelerated the normal process while our own scientific and regulatory establishment is still in denial.

We need to use human challenge trials. Deliberately infecting people allows us to determine the efficacy of a vaccine much more quickly. Figuring out efficacy allows us to only do widescale accelerated safety testing on only the vaccines which are effective enough. A challenge trial which required deliberately infecting 100,000 people with COVID would be very clearly worth it, even if it sped up vaccine development by a single day.


The failure of contact tracing and testing strategies in the United States and Europe has left us with no good options. Unless a vaccine can be developed and distributed much more quickly than is currently planned the costs of lockdown will exceed the costs of reaching herd immunity.

If we want to salvage the best of our remaining options we need to find a partial lockdown which can be sustained until a vaccine is ready is the only way to adequately balance these costs. This will involve many COVID cases and deaths, but we will end up in a better place.

If you believe that saving human lives is the only value that matters and completely reject this economic reasoning you still need to figure out what restrictions matter most. The tolerance that society has for a complete lockdown is not infinite and is quickly becoming exhausted. When it runs out even the restrictions you find most important will be widely ignored.

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13 comments, sorted by Click to highlight new comments since: Today at 7:38 AM

Even if opening up schools were to cause 200,000 extra deaths, it would still be a close call. Fortunately we are gathering evidence that schools are nowhere close to that level of danger.

I would appreciate if someone could explain to me the linked thing, and check whether the methodology is sound.

Because it seems to me that schools are the obvious places where the virus spreads. First, many don't have good ventilation (ok, this may vary strongly geograhically), you need to remove the face mask when eating, etc. Second, whatever safety rules you make up, I don't really believe that 6-10 years old kids will follow them properly. So to me it seems like "in theory" schools should be safe, but in practice, they are anything but.

(It is hard to distinguish between all things that happen in the same time, but my anecdotal evidence is that in Slovakia, during spring the schools were closed immediately, and we had the best outcomes in the region. From September the schools are open again, and the infection graphs skyrocketed; now we are the second worst in the region. But of course, many other things happened too, so this is no hard evidence.)


My prejudices run the same way as yours. The most encouraging thing in the linked charts is that the fraction of staff infected doesn't seem outrageously large. (But I would be happier if I could compare with corresponding infection rates for the general population.)

I like the general approach and organization of this post.

I have some modest disagreements about the details.

I doubt that many schools will manage to get HVAC right even if someone does provide them with clear rules, and our system doesn't seem competent enough to provide such rules within a reasonable time.

Having schools be mostly outdoors would solve many problems. I expect that most people overestimate the costs of being outdoors.

I know that I am very reluctant to step out into the rain. But there are many situations where I've gone out hiking in light rain, and once I'm out there, the subjective costs feel dramatically lower than they feel when I'm just stepping out into the rain. That remains true even now that I'm aware of the effect. I suspect something like that is causing many people to mistakenly assume that outdoor schools are prohibitively unpleasant.


Schools make a lot of use of things made out of paper. Paper suffers in even quite light rain, especially after say 30-60 minutes.

My guess is that less than 5% of the value of schools depends on paper. I expect that the value of in-person school compared to remote comes from things like interaction with peers, or day care. See The Elephant in the Brain for more hints.

My local school system hired a contractor over the summer to improve the HVAC and also fix all the windows such that they can open if they were previously broken and stuck closed. I don't specifically know if they "got it right" but I'm not sure why you're so skeptical ... measuring air changes per hour, installing HEPA filters, etc. ... that's standard stuff in the same category as following electrical code, designing buildings with proper structural support, etc., I think, and I expect whatever overpriced building firm they hired did it correctly ... (This is in a medium-sized town in the USA.)

Depends a lot on where you are. In California, sure. But in the winter in Scandinavia or Canada?

Yeah, I don't think that HVAC in schools is something which will make a difference to their safety in time. My point was more

  1. We have a large set of buildings we should open regardless of safety
  2. We have an expensive intervention which may drastically reduce transmission.
  3. Here is an opportunity to experiment.

I would imagine that we could install experimental HVAC systems in a few hundred schools for not much money and get decent data.

Good post, saved to my hard drive, but this is clearly wrong: "Economists believe that the financial cost of losing a year of education is that you will earn roughly 10% less throughout your career. If properly discounted this amounts to roughly $100,000"- not if you believe, as many economists do, that education is signaling beyond lerning the 3R's.  It really does not matter if you learn calculus a year later than normal. 

I'm sympathetic to the case that education is signaling, but I think that case is less strong for early education. For instance this paper from Argentina uses teacher strikes to value a year of education at 6% of lifetime earnings.

That estimate is not wildly different and seems pretty immune to signaling.


In the United States the GDP has contracted by about 10% since COVID started. This corresponds to ~21.5M QALYs

It doesnt correspond to 21.5M QALYs actually lost , because you can't assume that the 100% money would have been spent on healthcare. About 18% does in the US.

"A common estimate is that the loss of a full year of education leads to a loss of ~$100,000 in lifetime earnings" - I find this very hard to believe