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COVID-19: The Dilemma in Pictures
We’d all like this to go away so we can get back to normal life. This is an attempt to show what’s involved graphically. Here’s a chart of what lets the virus expand its human footprint, or causes it to shrink:
The horizontal axis is the famous ‘R’ – the replication number, which is how many other people a COVID-19 victim will infect, on average.
The vertical axis is the percentage of immunity in the population. The line is the critical frontier. Any combinations of R and immunity that plot downright means the virus is winning. To the top left, the famous ‘herd immunity’ has been reached and the virus will lose ground with each generation.
The logic is pretty easy. Take a look at the R = 2 hash line. Follow it up to the critical line and read over to the Immunity level: 50%. If a COVID victim would ordinarily infect two others, but on average one of them is immune, then the virus won’t grow. The actual formula is Critical Immunity = 1 – (1/R)
To start heading back to normal, we need to be in the upper left of the chart. Where are we, actually, and what might it take to get to the promised land? Let’s start with R. Next slide, please…
Here we’re looking at R-sub-t, that is, the probable R at a specific time. I’ve rolled time back to mid-March, and I’m taking estimates from this paper. There are a few dozen countries in their list. I’m using only those that had an infection count of 1000 or more at the time, which are Western democracies. That gives more confidence in the data and some cultural similarity to the US.
It’s quite a range. Spain is on the high end. The virus got into retirement homes there early, and this data was taken the day a lock-down was finally enforced. Italy is on the low end – by the time of this data, parts of northern Italy had been locked down for three weeks, and a national quarantine had been in effect for almost a week. Remember, this is an effective R at the time.
The US estimate is towards the middle. At the time, school closings had begun, but there was no national lock-down effort as yet. It’s probable that the US would have a somewhat lower beginning R anyway since its population density is considerably lower than European countries. So it makes sense that we’d be in about this spot.
How about immunity levels? Now I’ll use more current data. As of this writing, approximately .2% of the US population has been tested positive for COVID-19. Since there has been rationing of tests, we can assume the vast majority of these patients had notable symptoms of their infection.
What about those that didn’t get tested? It’s now well known that many, probably most, who get the virus never display symptoms, or have cases mild enough that they don’t bother to enter the healthcare system. Before going any further, I need to note a major assumption here: That a mild or asymptomatic case of COVID-19 will confer effective immunity once the virus has been cleared from the victim’s system. If that’s false, or only partially true (resistance, not immunity) then the discussion below on the costs of immunity will be worse.
To get from positive tested cases to total infections, we need an estimate of the ratio of unreported (asymptomatic + mild) infections to reported positive cases. What do we know about that? Appallingly little, at this point.
So little that I’m not going to put down a marker for the US, but instead show a range. As the bottom, I’m taking data from the Diamond Princess cruise ship that was struck by the virus. All of the passengers were tested, and of those testing positive for the virus, about half were asymptomatic. I’m taking this as a worst case, as the passengers were generally elderly and more likely to develop symptoms.
At the other end, I’m taking the recently concluded Stanford study by Bendavid and Bhattacharya, of 3300 subjects recruited in Silicon Valley. They reported a range of 50 to 85 times (!) more non-reporting virus carriers than positive tests. As to why I am taking this as the upper limit, I refer you to the able discussion by @mendel starting here.
Wow, a range of 2x to 85x, we’ve got this nailed, right? (More testing, more testing!) Applied to the known positive test rate, it suggests the actual infection level in the US is currently somewhere between .4% and 17%. On the chart, you can see it’s still a long way from beating the virus, even at the high end.
Now I put the two together, so you can see the rather large range of possibilities for our situation. While the range on the Immunity axis seems large, remember that the R-value is an exponent, not a multiplier.
Getting from there to the upper left, beating the virus, is the problem at hand. Here is the dilemma in stark terms:
Since there is no vaccine, we get immunity by having more people infected. Since some fraction of the infected will die, we pay in blood. How much? This is why the ratio just above is so important:
As of right now, we’ve endured 38,244 deaths to get to the current immunity level, whatever it is. If the 2x ratio above is true, and we’ve only achieved .4% immunity, then we’re going to pay about 95,000 deaths for each 1% increase in average immunity. If the 85x is true, then we pay 2250 deaths per 1%. We need to know that number, badly.
Beyond the human cost, there’s a dollar-cost on this axis as well. While some abhor the idea of assigning dollar values to life, we do it all the time. The US government assigns a cost between $7 and 9 million to premature death. I’m going to discount that heavily, since the victims of COVID average older, and because Federal regulators have an incentive to inflate that number to justify their meddling. I’ll use $2m per death. So we have a range of $190 billion on the bad end, to $4.5 billion on the good end, to achieve a one percent increase in immunity, plus the costs of healthcare for the sick and dying.
How about the other axis, R? While the virulence of the coronavirus can’t be changed directly, R can be affected by reducing the number of potential contacts per victim, and the chance of transmission per contact. Hence quarantines, distancing, masking and all the rest. The initial R values above showed that effect, it’s real. But how much does it cost? No one really knows, but there’s a gross figure in the news: About $2 trillion on the Federal tab for the COVID stimulus package, to cover one month of Full Monty lock-down. That probably doesn’t cover it all, but it was undoubtedly stuffed with pork, so call it a wash.
How effective are the individual ‘non-pharmaceutical intervention’ measures at reducing R for the coronavirus? We don’t know. And because of that, we don’t how cost-effective they are. Masking and hand washing are undoubtedly cheaper than shutting down whole industries, but what’s the relative benefit? Putting on all these measures at once may have made sense once, but it’s stopping us doing that evaluation.
If there’s a silver lining in the pictures above, it’s that they are averages for the point of the illustration. The pandemic does not deal in averages. On one hand, you have New York City, which has lost about 1 in 1000 inhabitants to COVID in a month. On the other, you have Adams County here in Idaho, with one case who is resting at home. Applying the same policies to them is ridiculous, but they offer an opportunity to reduce the ignorance of our actual state of affairs. The less impacted areas are a laboratory to test backing off on social control and measuring the effects, New York and others heavily infected are the logical places to nail to down the infection levels and death rates. Let’s be about it.
Published in Healthcare
Tagging @mendel since it doesn’t seem to work in the OP editor…
I appreciate your efforts and insights. Thank you.
I can’t argue with the logic of your graphs of R-values and population infection: math is math. What I might quibble about is the size of the font used in your final graph to when you write “Death.” I think I’d use a smaller font, and probably pick a different color.
Because I think the reality is that the population at the greatest risk, the elderly, is both small (3% of Americans are 75+) and the most easily isolated population in America. We can expect that a combination of improved treatment options and more effective isolation will drive down the mortality rate (whatever it actually is).
In other words, I think we can assume that there need not be an alarming number of COVID-19 deaths moving forward, and certainly nothing to overwhelm our critical care facilities. So if you reduce the point size on “Death” and increase the point size on “$$$,” the dilemma becomes a lot less dilemma-y pretty fast, in my opinion.
So let’s isolate the old and at-risk people, and get the rest of us back to work. Herd immunity will happen or not, eventually. We’ll survive.
18% of NY deaths are under 60.
Not exactly “elderly”.
Also death isn’t the only negative outcome.
Evidence is starting to come out there may be significant long term damage to lungs, liver, kidney, and heart.
We just don’t know yet.
Looking at your picture, welcome to the “elderly at risk group”.
Thank you for catching my error: the 75+ group in NYC is not the majority of cases, merely the population with the highest rate of death, by a factor of two or more.[Looking back at my original comment, I see that I did not actually make an error. I was mistaken when I thought I had. ;) ]The 60+ group constitutes 82% of the mortality (assuming the NYC statistics don’t overstate COVID-19 deaths, which they almost certainly do). The 70+ group is 63% of the mortality.
I’ll stand by my original point: let’s isolate the retirees and let the rest of us get back to work.
And I’m actually in the under-60 set, though I’ll probably cross that threshold before we get a vaccine.
We all will as the next time we invent a workable vaccine for a corona virus will be the first time.
Conversely the under 60 group represents 18% almost 1 in 5 deaths.
And in fact they have been understating the deaths by quite a bit.
See the pattern in deaths by month in NY going back to 2000?
Notice the previous spike? 9/11.
Now look at the big red spike ending April 4.
Under reported.
The Swedish plan. For the next 12 months we’ll all need to act Korean.
How is R0 estimated? I can see that extensive testing and contact tracing would work at the beginning. I can see calculating from herd immunity level at the end. But what is the method in the middle?
We have a story about 1000 of 2000 sailors on a French aircraft carrier being infected.
We have a story about 1/3 of a small survey in north Boston showing antibodies.
Look. I am not arguing that we can keep the country locked down much longer. It won’t work.
I just don’t want anyone to imagine this is going to happen without an awful lot of bodies, and potentially chronically ill people who manage to survive.
Damn the Chicoms.
Damn the CDC.
And damn the “flu bros”.
We did not have to be here.
I don’t find that convincing. First, why was April 4th chosen as the cutoff? NYC began attributing at-home deaths to COVID-19 after April 8th, when, as NPR put it, the city experienced “a staggering increase in the number of people dying at home but not included in the official tally….”
Secondly, how many of those who died at home, and who therefore are counted in the excess mortality, would have survived if normal hospital services had not been shut down while treating COVID-19 patients? For example, NYC reduced services to cardiac arrest victims on or about April 2nd. How many people died because they didn’t seek care that they would have sought under normal circumstances?
My assertion that NYC “almost certainly” overstates COVID-19 deaths is too strong, just as your assertion that they are under reported is too strong. Neither of us knows, either for NYC or for the nation as a whole.
Agreed.
“95,000 deaths for each 1% increase in average immunity”???
This is way too high when you consider there have been 160k deaths world wide so far.
The US total is currently around 38k.
Andrew Cuomo said R is now 0.9 in NY.
Belgium has a higher death per capita than Spain and Italy now.
NY and NJ are higher than Belgium.
An R-sub-t (effective R at a particular time) can be estimated by taking a time series of infection numbers, call it I(0) through I(t) and doing a linear fit to log(I(0)…I(t)). That works because I(t) ~ I(0) * R ^ t, it’s an exponential series. It’s always going to be an approximation because of limits of testing, changing conditions (lock-downs, etc.) and noise. If your testing coverage is partial – which is true now – you’re also assuming that the ratio of untested infections to tested positive cases stays pretty much the same for the time period.
As I said, that’s an extreme case. I used it because someone brought up the Diamond Princess in another thread. The 85x result is also extreme. Truth is also certainly somewhere in between. Sure wish we knew where.
Exactly the same questions: If hospitals have radically curtailed normal patient treatment, and if deaths are counted as COVID-19 deaths absent actual testing, then how do we know how to attribute excess mortality?
Let me make those questions clearer.
We know that COVID-19 is killing lots of people, and that there is therefore a substantial increase in year-on-year mortality for hard-hit areas, including both London and NYC.
What we don’t know is, when we subtract the deaths attributed to COVID-19 from the observed excess mortality, what percentage of the remaining deaths are caused by COVID-19, and what percentage are caused by other conditions, conditions presumably not treated because of the reduction in health care.
And, finally, we don’t actually know what percentage of the deaths attributed to COVID-19 are not in fact caused by COVID-19.
We know there is a lot more death. We know some of it is caused by a new and deadly virus. We know that normal hospital care is no longer being provided to a large population of people with preexisting conditions, some of which are life-threatening. We know that a lot of people are dying in their homes. We know that the deceased are not always tested for the presence of the virus, even when their deaths are attributed to the virus.
We have all sorts of numbers, none of them clean.
Locke On, great post.
I don’t know how you would express this graphically, but I see a problem with the idea in your main graph that we can push down R0 by spending money. I think that we can do so in the short term. I do not think that we can do so in the long term.
You’d need an animation to demonstrate my point. Start with your graph:
Imagine an animation in which we spend money to push that purple area to the left (and it goes up a bit anyway), and then when we stop spending the money, it wanders back to the right (and up again), and we spend more money to push it to the left (and it goes up a bit anyway), and when we stop it wanders back to the right (and up again) . . . you get the picture.
That darned purple area wants to migrate back to the right, because it reflects the reality of the characteristics of the virus.
A vaccine could potentially solve the problem, if we could develop one (which is uncertain) and if we have the time (which is unlikely).
At least, this is the way it seems to me. Am I missing something?
Jerry, expressing it as “spending money to reduce R0” invites a cost/benefit analysis on how the money is spent.
There’s one big, expensive thing we can do to reduce R0, and that’s to hole up in our homes and not go to work. That’s a huge, devastating way to spend money on reducing the spread.
Almost every other way we can spend money on reducing R0 is, in comparison, almost free: mass produce masks and other protective gear, adopt practical social distancing habits that allow us to be out among others but not in contact as often, put up physical barriers (“sneeze shields”) in stores, litter the country with hand sanitizer dispensers, etc., give early retirement to every worker over 65 who wants it, etc.
The only thing we can’t afford to do is keep the economy shut down.
Hank, I know, though we don’t know how effective any particular measure might be. Also, as Locke On points out, we don’t have a good idea of the value of R0 without precautions, though I think that we have reason to suspect that it varies widely by location (worst for densely populated cities).
Even other, far less expensive measures won’t solve the problem permanently, but will only buy a bit of time. As soon as we relax and return life to normal, the problem will continue, and that darned purple region in Locke On’s graph will drift up and to the right again.
I am not going to live my life in a hazmat suit. I am not giving up my church and my friends. If that’s the price of safety, it’s too darned high. I will not live in fear.
I am not living in fear right now, by the way. I’m going about my business, mask-free, and I’m annoyed that I shoe-bumped my buddy Hector last night instead of hugging him as usual. I will stick with the shoe-bumps for a while.
I better stop, or I’ll be pompously channeling Patrick Henry. If you have to pompously channel someone, he’s a pretty good guy to pick.
I’m not too hung up on measuring the precise cause of death. I suspect that someone with an underlying heart condition and COVID-19 would have died due to the heart condition, but probably not today. We can call that an excess death, on one measure. But the definition of “excess deaths” most relevant to this discussion is the number of people who died because adequate medical resources were not available because of the number of COVID-19 patients. Moving that number to zero, or “flattening the curve,” is what we signed up to do with the shutdown. It looks like we’re will on the way to winning. The hospitals are not overwhelmed, and as soon as we can get non-emergency treatment back up, we won. Without a cure and/or vaccine, the areas under the peaked curve and the flattened curve are the same–that is, the same number of deaths. When we get the information we need, we’ll know if the system would have been overwhelmed. By that time, we’ll also know a whole lot more about all of the costs of spreading out those deaths. And if by then we know that besides lying about what they knew, the Chinese limited internal travel to and from Wuhan, but not the rest of the world, there needs to be a reckoning.
I have to say that since the data on COVID is not much different than the shifting sands at the Indiana dunes, who knows anything?
I did appreciate Peter Robinson’s initial interview with Dr Jay, as that good doctor acknowledged that no one really knows anything.
But Dr Jay does understand that it is an absolute necessity to have adequate numbers of people tested before going off on some tangent that COVID is a 1918 killer Spanish flu style of disease.
It is also important to ensure that the testing that is done is accurate for the purpose of distinguishing this specific version of COVID 19 from other corona viruses.
Hearing from individuals on social media that in some parts of the nation, anyone who dies from almost any condition but who had not yet been tested for COVID can be lumped into the COVID death statistics.
It would probably help here to have an overlay of the current situation compared to past high-end winter viral outbreak years, particularly the 2009-10 H1N1 cycle, in order to have a comparison of where the U.S. and the world were in those years versus where we are now. COVID-19 is more widespread, but for certain areas of the globe, like China’s neighbors, it was virulent enough to make them more proactive to the current problem, and many of those countries already are into the next phase, where they’re trying to balance reopenings against renewed increases in contaminations.
The looming battle is obviously going to be at what level reduction of the death line becomes acceptable in the trade off for reopening some parts of the economy — having a way to track what was acceptable 10-11 years ago and in other time frames would at least give people an idea of what society did accept in the past. Whether or not that would be acceptable to society in 2020, as levels of risk tolerance have gotten lower and lower over the years, is another question (and of course is compounded by the current election cycle, where because reopening the economy carries with it the risks of increasing infections and deaths, people’s willingness to accept the trade-off might be based less on their own personal safety concerns than on how it might affect vote totals 6 1/2 months from now).
Problem with any graph is that it requires reality to conform to your assumptions. And it tends not to. Here is an interesting take on this phenomenon through history:
https://issuesinsights.com/2020/04/18/after-repeated-failures-its-time-to-permanently-dump-epidemic-models/
I find the thread of Know-Nothing-ism on the right to be regrettable.
The problem with the models is that even those with decent science behind them won’t work if you don’t know have knowledge of the most sensitive parameters driving them. This whole exercise was to point out that we do not know, even after several months, and we desperately need to if we’re to reopen in a sane fashion. Unless you are willing to throw open the doors and take our chances with ‘herd immunity’ without any predictive ability of what’s going to happen. I’m not, and this is also an exhibition of why not.
Further to the OP’s point that the pandemic doesn’t respect averages, see this article about NYC’s impact on the US statistics. Between crowding, subways, and incompetent leadership, New York has become the poster child for lock-downs. The rest of the country is not NYC, though several other cities are working at it.
I’m divided on this.
To some degree, a lack of detailed knowledge is “the problem.” To some degree, complexity is the problem. And those are two different problems. I don’t know to what degree complexity enters into it when you’re talking about 330,000,000 people in 50 states, every one of those people making independent choices about which risks he will accept and which he will avoid, and adjusting as he sees and hears more information (accurate or otherwise).
There’s an alternative to mid-term models and projections, and that’s short-term feedback and correction. The two aren’t mutually exclusive, but they’re distinct, and adopting a more dynamic approach based on close monitoring seems more sensible to me when there are so many unknowns.
In my opinion, the moment we think we can monitor a locality sufficiently well to avoid overwhelming the local health care system, we should cautiously relax constraints in that environment. I think most of the country is either already at that point, or is very close.
I believe we’re in agreement for the most part. It isn’t “know-nothingism,” it’s recognition of the limits of our knowledge. Where we disagree is with respect to the idea that we need full knowledge in order to reopen, or that this knowledge is even available… Or, lastly, that we will agree on what to do with that information if it ever comes.
I agree with most of this. One error at the beginning was trying to use the Imperial College model for forecasting, with extremely little knowledge of critical parameters. It might be useful in the long run (not even mid-term) when we have enough data to try to predict results of easing off some constraints. We don’t yet, again that’s part of the point of the OP.
The IHME modelers did better, because it’s completely empirical. All they did is take the actual experience from locations that suffered the virus earlier and reapply that to those that came later. Their death forecast were decently close, the predictions of resource usage not so much because they had to SWAG the course of the illness in the American clinical setting at the start.
Yes. And we should be carefully choosing some localities that have both testing and research resources to become test cases for particular removals of constraints, and figure out the cost-effective ways of reducing R. And I note that your statement is more or less what Trump’s policies of a couple days ago are saying.
One of the things that I find most frustrating about the current situation is that it purports to be a cost/benefit analysis, but it looks only at one side of the equation. We have the same lack of knowledge about the eventual economic impact as we do about the epidemiological impact. But we don’t have a frightening IHME model attempting to show a impact, over the next year or two, of the economic carnage. Absent that, it’s difficult to make anything akin to a sensible risk assessment.
One thing I think we can assume is that, while the virus will essentially follow one or another bell curve whatever we do, the economic destruction will continue to increase until we re-open the country.