On Corona/Covid-19, herd immunity and WELLBY tradeoffs: key predictions and numbers

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In this note, I want to deal with three related issues: the main lessons on the corona virus from the reported deaths across countries with different policies; the feasibility of different “end games” relevant to this pandemic, including vaccines and herd immunity; and some key WELLBY numbers relating to loneliness, unemployment, and how government expenditures link to lives saved. Armed with these numbers you can generate your own estimates for how various policy scenarios change the numbers of happy lives lived by the population.

The take-away message is that I think most European countries will end up with a “Sweden, perhaps on steroids” strategy, openly adopt a not-much-to-truly-fear narrative, and that the key wellbeing consideration for the next two years will be jobs and social closeness. We will then also hopefully acknowledge as Westerners what the awful and totally predictable costs have been in the rest of the world of our attitudes and policies in dealing with this virus.

The dangers of the corona virus: on New York, Sweden, South Korea, and herd immunity.

In February / March, when many key policy decisions had to be made, it was still possible for a reasonable person to think more than 1% of the whole world would die if one didn’t lock down the majority of the population. With the benefit of all the research and information of the last 2 months, we now know much better what the risks are and what matters in terms of policies. The key information that is new is how many victims the corona virus has made in different countries following different strategies and with different circumstances. Though there are huge statistical issues with this data, including the fact that some countries are more strict than others when counting a death as covid related, and the large differences in just what part of the population was exposed, we can nevertheless turn to this data to help see the main contours.

One clear lesson is that death tolls have been highest in dense urban areas, and very low in rural and (sub)tropical areas, particularly in countries where infectious diseases are a very normal cause of death. In the dense cities, transmission rates are much higher than in other areas, and so a much higher percentage of the population is infected until some kind of herd immunity is achieved (which is basically when residual transmission rates are low, ie the “rho<1”).

The worst affected large region in the world is thus New York, with a death toll of around 0.15%, which is easily ten times higher than that of rural areas in the US. Importantly, the US basically let the virus roam around unhindered for over a month, which was long enough to spread all over New York, pretty much a worst case scenario. The latest estimates suggest there are several neighborhoods in New York that have over 40% of the population with observed anti-bodies. Since it takes a few weeks after infection to get anti-bodies and the reported numbers always related to measurements of several weeks ago, this means many areas of New York must at this moment be pretty close to herd immunity levels.

We don’t quite know why (sub)tropical areas have such low death rates, but its probably a combination of weather (the virus doesn’t like the sun), natural circulation in houses preventing the aerosols that carry the virus from hanging around, high humidity that prevents the contagious aerosols from hanging around, population density, and perhaps the fact that in most (sub)tropical areas, infectious diseases are plentiful and a very prevalent health hazard. Rich populations have dry inside places where it is far easier to catch the virus, and perhaps are not so used to infectious diseases. So it is a rich man’s disease where, for once, slum dwellers in poor countries are at the advantage. Having said that, within rich countries, its the poor who are most at risk.

In places like Vietnam, Thailand, the Indian countryside, South Asia, and Africa, total death rates from corona are thus below 0.01%.

We now also have a much better idea “what it takes” to get natural herd immunity because of Sweden. The Swedish ambassador to the UN claimed Sweden is now close to herd immunity, with more than 30% of people in its capital already immune by late April. It has a current death toll of around 0.035% and should thus be expected to have achieved herd immunity for a finalised death toll of around 0.05% (their death rates are well on the way down now). These numbers are of course not uncontested, with later research suggesting only 20% immunity in Stockholm by late May, whilst yet others think the immunity levels are far higher because the main immunity tests miss groups of people who are immune by having had similar diseases in the past or some genetic disposition. Still, these lower-than expected number might mean Sweden will have a death toll of 0.1% before it reaches herd immunity level, half of what New York seems to be heading for to get that outcome.

Relevantly, Sweden has a population density still higher than Australia, also has cities with lots of space, inside dry places, and has in previous decades also marginalised most other infectious diseases. So its reasonable to expect that Australia too could achieve herd immunity with a loss no higher than 0.05% to 0.1% of the population, ie 10,000 to 20,000 people. Ditto for other Western countries: one in thousand seems the maximum one “has to suffer” to get herd immunity, probably quite a bit less.

There are a few other lessons one can draw from the experience of other countries, though one should bear in mind that the international statistics have to be read with caution as different countries have totally different rules on whom to count as a corona death, which can easily lead to a factor of 5 difference in claimed deaths.

One lesson is that lock downs have had remarkably little benefit in preventing deaths in Europe. Their main failing is that they didn’t manage to truly shield the elderly and vulnerable population, possibly even the opposite: the vulnerable elderly who rightly had something to fear were those with lots of other health problems and in retirement/nursing homes. Their continuing need for help brought them into contact with infected elderly and infected health workers, thus spreading the virus precisely among the vulnerable population.

Lock downs were quite probably worse than asking their families to take them in for a month, and probably worse also than having the virus spread quickly among the healthy population so that the health workers would much sooner be in a herd immunity situation. Paradoxically, the lock downs prevented herd immunity among large groups which meant more health workers kept being infected, with hospitals and retirement/nursing homes some of the worst places one could be.

Now of course, smart lock downs can prevent this. The UK in that sense is the shining example of the worst of all worlds: economic and social devastation due to the lock downs, whilst the truly vulnerable population was not protected at all. Sick elderly patients were sent back to their nursing/retirement homes and infected hospitals and health workers helped spread the virus among the very group that truly had something to fear.

So it is now clear that blanket lock downs are a terrible idea and prevent few deaths, probably even causing corona deaths depending on various policy particulars.

Another lesson is that one should not see a country as a single herd, but as being made up of lots of different communities that have their own infection rates, vulnerabilities, and thus threshold levels of infection before herd immunity is hit.

The most useful way to see the issue of herd immunity is to realise that our societies have both places where there is a lot more interaction, as well as people that do a lot more interacting. Cities have high interaction rates, but there are also groups of workers and individuals that do a lot of traveling and interacting. Nurses for instance do a lot of interacting with different groups, and are highly efficient carriers of viruses since they will often be non-symptomatic. Traveling salesmen, university students, and businesswomen are also “high contact groups” that are very prevalent carriers and spreaders of the corona virus.

This means two crucial things: since the healthy ones among these groups run negligible risks when they get exposed to this virus, you actually want them to be exposed as quick as possible to this virus so that they build up immunity and can no longer accidentally spread the virus; and once a certain percentage of the high contact groups have built up immunity, a whole locality or community basically has herd immunity. Put in a language we have now all gotten used to: the high-contact people are the ones with a rho>1. Get them to be immune and further spreads peter out without any special intervention.

So in hindsight it is now much clearer what the optimal social strategy towards herd immunity is: to have the healthy individuals among the high-contact groups mingle as much as possible with each other so that they all get exposed to the virus and they all built up immunity. That would give all locations herd immunity. In a dense city, where there are far more high-contact people, this means one would need a much larger percentage exposed to the virus to achieve herd immunity than in other places. In the countryside or (sub)tropical countries, the group you’d need to have immunity would probably be no larger than 5-10% of the whole population and you’d already have widespread herd immunity. Incidentally, children seem hardly able to get it or carry it for a long time, so they would not be in the group one would want to deliberately expose. They are somewhat “inert agents” anyway when it comes to this virus.

We didn’t know this before: before, based on the experience with vaccines, we thought one would need something like 70% of the whole population to contract the virus in order to have herd immunity. Now our understanding is more nuanced: you only need the high-contact makers to be immune for the residual infection rates to become low enough so that a local upflare dies down, ie “rho<1 locally”.

This is also partially why the South Korean approach has worked well to contain the virus, though at the cost of huge economic and social disruption: the South Koreans tested lots of people on the motorways and in transit between places, thus picking up the high contact makers who were infected and were spreading it. By tracing them so quickly they managed to get the infection rates down and thus suppress the outbreaks. Yet, that kind of targeted track-and-trace would have to kept up indefinitely, thus incurring an indefinite economic and social cost. The South Koreans for instance will not be able to have large groups of tourists roaming around freely, nor lots of new international students and others: because South Korea does not have local herd immunity, bringing in infected people from outside would lead to run-away virus outbreaks. This will not in general be true for Sweden though, particularly not because international students and tourists will primarily interact with high-contact Swedes who will largely already be immune.

Finally, we now have a lot of potential vaccines in the pipeline. Something like 100 or more, with a human trial in Oxford as the front runner, hopefully giving us good news in 2 months or so. Their vaccine worked well in macaques and they hope to learn how it will fare in humans. Still, the odds are actually quite high that their study will fail to be definitive even if their vaccine works. This is because too few healthy people around Oxford might get exposed to the virus to say with certainty that those with the vaccine were less likely to get a full-blown infection than those without the vaccine in their trial. Also, it already seems the Oxford vaccine does not prevent someone from spreading it, limiting its use. Similar problems go for a lot of the other trials: it is probably more realistic to expect another 12 months before there is a vaccine that is actually rolled out to whole populations. We all hope, me included, for an autumn miracle, but I am not counting on it and its quite possible we’ll not find a vaccine for the next 10 years.

End-games, basic options around the virus going forward, and death tolls.

There are many end-game scenarios doing the rounds, but I find the three most important ones to be: i) the open adoption and conscious move towards herd immunity for the whole population (Sweden), ii) limited social distancing plus targeted track-and-trace till a vaccine (South Korea), and iii) indefinite or seasonal lock downs (suggested in the UK).

Let’s quickly dismiss the last of these options. The economic and social devastation, as well as their likely health ineffectiveness, of lock downs is such that we should just openly dismiss them as ridiculous and ill-conceived, as I have argued for 2 months now. They cost at least 10 times as much as they potentially give. For face-keeping purposes many of the elites and “scientists” in Western countries are loathe to accept this, but I actually doubt any country will truly repeat the mistake of the last two months of lock downs. I am willing to bet against it occurring in Europe if anyone wants to seriously suggest otherwise!

Nearly all Western countries locked down are now openly embracing either herd-immunity or some notion of limited social distancing and track-and-trace. So let’s not even bother talking about continued lock downs.

With the South Korean style track-and-trace, as well as their continued habits of social distancing, it is clear the total death toll of covid is very very low. They claim their death toll is 5 per million, ie 0.0005%, basically a few hours of the normal death toll of a single day. A bad flu year is much worse. South Korea is particularly relevant for many European countries because it is also rich, quite urban, well organised, and also has bad flu years (unlike Australia where flu and pneumonia are much less of a problem than in colder rich countries anyway). So South Korea offers an appealing, relevant, and replicable example to follow.

If one maintains the South Korean effort, one should basically expect no more than an ongoing death toll of about 0.0002% per month, essentially till a vaccine or another strategy/treatment emerges, which is quite possibly only 12 months from now. That is why so many countries are dabbling with these corona apps.

It does mean one has to copy the South Korean institutions around this: a very large, mobile, and intrusive test regime that can force the mobile parts of the population to get tested, and then to track their prior movements via their mobile phones to see who else might have been infected. This takes a while to set up and the intrusiveness may be less acceptable to some European countries than it is to South Koreans.

Also, one should bear in mind that the South Korean economy is being hit just as badly as the Western countries. They too are looking at over 10% additional unemployment, a GDP hit of close to 20%, and the almost total crash of the hospitality, tourism, business travel, and cultural sectors. Since the SK model comes without herd immunity, it basically cannot “open up” these sectors to their full prior extent.

So with the SK model one also extends the economic and social pain into the future. As I will show later on, the costs of doing so, however you want to put it (lives, healthy years, or happy years), far outweigh the benefits.

Then the herd immunity route. As hinted at before, one can do “stupid herd immunity” and one can do “smart herd immunity”. Stupid herd immunity could for instance be achieved very quickly by deliberately infecting the 70% healthiest part of the whole population. This can be done quickly by giving lots of people a nasal spray, but would probably have a rather large death toll as not everyone who seems healthy actually is all that healthy, and infecting people deliberately involves more risks than mild infection levels, which are often good enough to get an immune response.

Smart herd immunity can be achieved by actively encouraging the healthy part of the “high contact” part of the population to mingle in large crowds with each other, such as basically happens naturally in dense cities anyway. People know themselves whether they are high-contact people, but you could also target particular professions. They include the frequent fliers, the salesmen, the politicians, the sales people, the nurses, the police, market sellers, international and national students, etc. You basically can expose them to normal levels of the virus so that they get an immune response and no longer can get it later on. As a reward you can offer them an immunity passport with which they could travel. During this “quick spread” period, you would want these high-contact people to of course stay away from the truly vulnerable and preferably mainly mingle with other high-contact people.

We don’t know perfectly how many “should get it to achieve herd immunity” as the answer will vary by type of city and country, but Sweden and other places are suggesting the answer in big cities is at least 50% and in other places no more than perhaps 10%. That at least is my current best guess.

The expected death toll among those encouraged to get it would be minimal, probably well below 0.01%, which is a number based on the low death rates among prime-aged groups in Sweden, Germany, and elsewhere who have been found to be immune, often unaware they even had the disease. A high number would simply be the 0.05% found in Sweden already.

The option I am sketching is basically a “Sweden on steroids” scenario, where one tries to mimic the basic strategy and end-game of Sweden, but much quicker and with much less economic disruption than Sweden suffered. Btw, on the issue of economic disruption one should of course acknowledge that much of it is due to the reactions of individuals themselves rather than government choices, and that there are large economic spillovers between countries such that a region only has limited agency over its economic fate. That is why an anti-fear campaign and international cooperation matter.

However, if a smart herd immunity program is done successfully, the country as a whole can then return to normal life. You’d have a local outbreak now and then, just as with any infectious disease, and one might want new large groups of high-contact makers coming into the country, such as a new glut of international students, to be deliberately exposed when they come in, but otherwise life is lived as before. The corona virus would join the long list of other infectious diseases that now and then flare up but don’t make a lot of victims.

Whilst I think countries will tinker first with what looks like the South Korea option, I think the ongoing economic and social devastation inherent in that option will basically make them gradually move towards the herd immunity scenario.

Incidentally, I actually expect the United States to end up in roughly this herd immunity scenario also, though more out of incompetence at doing anything else than by design. The US too looks to me like it will hit herd immunity in many states and cities with an overall death toll below 0.05%, higher in the highly urban areas like New York and much lower in the warm spread out areas down South.

Unless a vaccine comes along the next 4 months or so (which is possible but unlikely), I think this is the scenario that will de facto be chosen by most countries, who will then also adopt the anti-fear narratives that come with it, essentially openly admitting the corona virus is not so dangerous after all.

Then some key numbers important for tradeoff calculations.

Important tradeoff-numbers: public services and WELLBYs, loneliness from lock downs, and cost of unemployment.

For one, we now know that the number of healthy life years (QALYs) of those dying from corona are probably between 3 and 6. Some journos think it is still above 10 years, because that is how long healthy people would still have to go on average if they died at the ages of the corona virus victims, but because of the high prevalence of multiple co-morbidities among the victims, this is just not the case. Whereas my initial guess based on the Italian data was that the corona victims had another 3 good years left, I would now revise that upwards to 4 as the most reasonable guess for the world as a whole, because the Italian victims were particularly frail. My best guess for why that is, is that Italy seems to have had people dying of corona who would have died of the flu in previous years had they lived in a place like the UK.

One years of a healthy life (=1 QALY) is 6 WELLBYs because a healthy life is spent with a life satisfaction of 8 and the level at which people are indifferent between living on another year or not is probably around 2. So the corona victims on average had another 24 WELLBY left. that is the loss one would count in a WELLBY approach of a corona virus victim.

Then public services. Crucially, the UK public service itself claims that 15,000 pounds spent on the National Health Service buys 1 QALY, ie 6 WELLBY. That claim is based on research into how costly it is to save people from cancer and other illnesses via chemo, operations, and other health services. I might add to this that the found “productivity” of health services is often found to be far higher than this. The introduction of GP services in Turkey for instance was easily ten times more productive than this. The WELLBY productivity of Obamacare was similarly found to be much higher than this.

So 15,000 pounds productions costs of 6 WELLBYs via health expenditure is not a crazy number but the simple reflection of how necessary government services are for maintaining a population with high health. And government is much better at this than the private sector, which is why the UK has a life expectancy of close to 82 which the US has one closer to 78 whilst the UK spends less than half on health than the US per person: the UK has a cheap government-provided service whereas the US has an expensive privately-provided one that forces lots of services on patients that they don’t need (like useless tests).

Now, the question is of course whether other government services are equally productive. If government spending was rational and based on where it did most good, the answer would be “yes, at least as productive”.

Indeed, we know that people who are higher educated look after their health better and that state education thus also buys health. We know that better roads, sewage works, clean water, clean air, and many other things that non-NHS government services pay for also buy a lot of health.

Importantly, even if the non-health expenditures of government were to buy no health directly at all and were merely there to “keep the place running”, one should still assign them the same marginal productivity as health expenses: if the place is not kept running, then by implication GDP and other tax-revenue-generating activity would come to a halt, basically leading to collapsing health services. So unless one buys into some notion of the idea that anything not directly spent on health is a total waste, one should credit non-health expenditure with the same marginal health benefit as health expenses.

In my initial calculations I thus took the argument seriously that government spending is roughly rational and the marginal health productivity of the NHS should be applied to all government expenses. So I argued that 15,000 pounds in government expenses buy 6 WELLBY in all areas of government expenses.

One can reasonably argue for other numbers, such as the often used number that it costs 30,000 pounds to buy 1 QALY and thus 6 WELLBY via life-saving medicines provided by pharmaceutical commpanies. Or one can use consumer willingness-to-pay numbers for 6 WELLBYs, which is basically 60,000 pounds (see the Handbook for Wellbeing Policy for references and details). Yet if one uses consumer willingness to pay, one should then apply it to all incomes, not just government incomes.

These numbers are crucial for getting a handle on how many lives and WELLBYs are lost with an economic depression: they capture the long-run relation between economic development and the length of life via government services. They do not capture the short-run relation because government expenses are often kept up artificially during recessions and many government expenses have very long-run continuing payoffs that do not change during a recession (like sewage, innoculations, clean water). So the “health costs” of a recession will be smeared out over decades. Some poorly-trained commentators seem to miss this entirely and stare blindly at the Ruhm papers which are about short-run relations. More informed studies acknowledge that the long-run relation between government spending and health is strongly and causally positive.

What this means is that a reduction in government expenditure by 4*15,000 pounds will probably in the long run cost the equivalent of a corona virus death. That is 60,000 pounds. Since government spends 40% of GDP, roughly speaking, that means a reduction in GDP by about 150,000 pounds will lead to the equivalent health loss of a corona virus death. If one wants to be conservative and use consumer willingness to pay, one would say that 240,000 pounds less in economic activity would count as a corona virus death. That’s about 300,000 US dollars or 450,000 AUS. And that’s the conversion rate in rich countries. In poor countries, where the average income is three times lower, the same economic contraction would cause three times more health damage.

This is a crucial conversion number because it means, for instance, that 1 trillion pounds less economic activity with have the long-run effect of a minimum of 4 million corona deaths, or 100 million WELLBY. Given how the recession in 2020-2021 alone is now expected to reduce the world economy by over 6 trillion pounds, that immediately gets you huge numbers of implied victims that dwarf the actual death tolls of the corona virus. The lost economic damage over the next ten years is much higher again as the lost productivity and jobs take a while to return (the long-term loss is easily a factor 5 of the loss in the next year). Even 10% more economic damage, which is what you’d at the minimum must expect if we’d continue with fractional lock downs or closed borders between countries for another year, would then be equal to 12 million corona deaths, higher than the 0.05% of the world population I calculated would be at risk in a smart herd immunity scenario. That would be 4 million corona deaths, and even that is, if we’re honest, a ridiculous over-estimate of the additional number of victims from a smart herd immunity strategy.

Another crucial WELLBY number is the effect of social isolation due to lock downs, which comes with depression, loneliness, and a sense of futility. I initially guessed this effect to be 0.25 WELLBY per year of social isolation based on the literature on how important social interactions were for wellbeing. We now have actual studies.

A recent Fujiwara study put the effect of the lock downs on the average member of the public at 0.8 WELLBY, essentially by looking at how strongly life-satisfaction declined over time in the UK before and after the lock downs. Yet he had to glue two datasets together because his post lock down data was gathered by a different company, and that is always tricky when it comes to wellbeing. Nevertheless, it’s a very large effect in line with the found effects of unemployment or a mild depression.

An even better estimate comes from the “State of Life” people who follow lots of groups in the UK over time as part of their business, which is to help thousands of small charities measure their WELLBY effects on vulnerable populations. They thus have the same survey design and measurement methods before and after lock downs, finding that the average effect is 0.4 WELLBY per year of lock down. Their number is particularly believable because they could distinguish between groups that kept on working (the “crucial sector” employees) and groups that were forced to stop working. They found no life satisfaction decrease in the group that kept on working, as their routines and their self-esteem hence kept intact, whilst they found a much higher effect amongst the groups forced out of work and sitting at home. Exactly as one expects, but also showing that the effect is truly of the lock downs and not merely of some general anxiety in the whole population.

This too is a crucial number because it means that per 1 million inhabitants, a 70% lock down (which is the UK variety: roughly 30% kept on working) causes a loss of 400,000 WELLBY per year. Per 20 million, that is 8 million WELLBY, or 1.33 million happy years of life, or 333,000 coronavirus deaths. That is an equivalent of about 28,000 corona virus deaths per month.

Because it applies to the social isolation that is time and place dependent, this is thus a crucial number for any scenario to do with marginal lock downs or smart tracking: it tells you what you should count as the general reduction in quality of life due to the stress and loneliness caused by forcing people to stay at home and keep their distance from other humans. It should be clear that this effect is so large as to make a mockery of any claim that lock downs were worth it or that any significant fraction of a lock down will be worth it in the future.

Finally, I should simply reiterate that a year in unemployment has long been found to cost around 0.7 WELLBY. That number comes from hundreds of studies looking at plant closures, unexpected unemployment, recessions, etc. So 100 million people unemployed for another year is worth 70 million WELLBY. You can convert that into QALYs and corona deaths.

In conclusion, with the numbers above you can build your own basic tradeoff calculation based on what you expect to happen in various economic and health policy scenarios.

1. in progress: will add more references, links and latest numbers when I get the time[↩]