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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