Last week: Covid 7/16: Becoming the Mask
The news continues to be cautiously good.
Positive test rates are likely peaking. Deaths are increasing slower than one would have expected, and could well peak a few weeks from now without having risen much further.
This, in context, is what success looks like.
As Florida and Arizona go now, so goes the rest of the second wave later. If the hardest hit places are turning things around without much underlying regulatory change, and with continued huge testing delays, then that tells us that some combination of herd immunity and voluntary behavioral changes is getting us there already.
It was a quiet week by 2020 standards.
There was plenty of news, most importantly the whole thing where the Federal government graduating from banditry and piracy to kidnapping people off the streets in unmarked vans, which is outrageous and a dire threat to our freedom. That does not seem to be getting the proper level of alarm or attention.
There was also the explorations of GPT-3, which also does not seem to be getting the proper level of alarm or attention. People are literally talking about AI taking jobs away from programmers without stopping to think that maybe that might be burying the lead a little. We like to say There is No Fire Alarm for Artificial General Intelligence but let’s raise the possibility that the alarm is there and it’s working fine and it’s us that are the problem.
If you want the most fun improv experience I’ve ever seen that’s also kind of a harbinger of the end of the world, try the dragon model of AI dungeon here. It’s not as good as the pure prompt version, but it’s available to the public.
Also, Slate Star Codex is back! And there was much rejoicing. Woo-hoo.
In other great news, parents in San Francisco have realized that they can get into groups and hire teachers, and provide better educations in healthier and safer environments while spending less money than schools do, and can do so while hiring more teachers, giving them safer, more interesting and more rewarding jobs, and paying them more. It’s almost like we should have been doing this all along, and might not want to go back after the epidemic ends. I rat on San Francisco a lot, so credit where credit is due.
But none of that is relevant to Covid-19. That’s not what we’re here to do right now.
Instead, let’s run the numbers.
Positive Test Counts
|May 7-May 13||22419||43256||37591||56892|
|May 14-May 20||22725||42762||40343||52982|
|May 21-May 27||23979||39418||42977||37029|
|May 28-June 3||32200||31504||50039||33370|
|June 4-June 10||35487||24674||55731||22693|
|June 11-June 17||41976||22510||75787||17891|
|June 18-June 24||66292||26792||107221||15446|
|June 25-July 1||85761||34974||163472||16303|
|July 2-July 8||103879||40139||202863||18226|
|July 9-July 15||108395||53229||250072||20276|
|July 16-July 22||117506||57797||265221||20917|
|May 7-May 13||1082||2288||1597||5327|
|Apr 30-May 6||775||1723||1290||3008|
|May 28-June 3||875||1666||1387||2557|
|June 4-June 10||743||1297||1230||1936|
|June 11-June 17||778||1040||1207||1495|
|June 18-June 24||831||859||1204||1061|
|June 25-July 1||858||658||1285||818|
|July 2-July 8||894||559||1503||761|
|July 9-July 15||1380||539||2278||650|
|July 16-July 22||1469||674||3106||524|
Positive Test Rates
|Date||USA tests||Positive %||NY tests||Positive %||Cumulative Positives|
|May 21-May 27||2,679,365||5.5%||305,708||3.5%||0.52%|
|May 28-June 3||3,041,311||5.0%||417,929||2.2%||0.57%|
|June 4-June 10||3,171,227||4.4%||438,695||1.4%||0.61%|
|June 11-June 17||3,447,528||4.6%||442,951||1.1%||0.66%|
|June 18-June 24||3,636,525||6.0%||440,833||1.0%||0.72%|
|June 25-July 1||4,326,304||7.0%||419,696||1.2%||0.82%|
|July 2-July 8||4,463,797||8.2%||429,804||1.1%||0.93%|
|July 9-July 15||5,125,361||8.51%||447,073||1.1%||1.06%|
|July 16-July 22||5,499,750||8.51%||450,115||1.1%||1.20%|
This chart added a new column: Cumulative Positives. That is the positive tests as a percentage of the United States population. We have that many confirmed cases overall. Note that half our confirmed cases have been since June 10.
The pattern is clear. Infections are up slightly, but that is due to increased testing rather than more infections. Deaths are rapidly rising in the South, rising a little in the Midwest and West, and continuing to drop in the Northeast.
Exponential Growth Will Continue Until Morale Improves
How can we get the reproduction rate below one? When will it happen?
The hugely positive news last week was that the slowing of the rate of increase in positive test percentages. The previous three weeks, positive test rates had increased by 1%, 1% and 1.2%. A week ago, there was only an increase of 0.3%.
Now we have continued good news, with positive test rates essentially unchanged.
If nothing changes, the nationwide numbers suggest there is every reason to expect the positive test rate to begin to decline. For this to be the second peak.
For a better picture, it seems worthwhile to look wade through the annoying spreadsheet manipulation work and look at a few hot spots for test percentages.
Florida’s positive test rate peaked two weeks ago at 19.06%. Last week it dipped to 18.77%, and this week it fell further to 18.58%. This week, 11,116 positive tests per day versus 11,147 last week.
Those are horrifying numbers, but they’re not increasingly horrifying numbers. Instead they’re very slowly decreasingly horrifying numbers.
Contrast that with the previous two weeks. Three weeks ago Florida had a 16.02% positive rate. Four weeks ago it was 13.42%. It’s a similar pattern to the country overall. Things were getting worse, and that has now stopped.
Arizona has it even worse. They had a 24.7% positive rate this past week versus 24% positive rate last week. Prior to that, they had a 27.4% positive rate two weeks ago, and a 25.2% positive rate three weeks ago. Three weeks ago it was 23%, and four weeks ago it was 17.4%, five weeks ago 14.2%.
We see a steady climb up until two weeks ago, then things seem to at least be leveling off. Again, roughly compatible with the national picture.
Despite being in a crisis situation, Arizona’s test counts have declined somewhat over this period. That’s pretty scary and a massive policy failure.
Texas had previously been in the 13% range for several weeks, then was 15.8% last week and 15.5% this week.
Thus, I am cautiously optimistic that we will not see substantial further increases in positive test rates unless or until something new goes wrong. The real situation with regard to new infections is likely about as bad as it is going to get in this wave. As testing capacity improves, positive test counts likely will continue to increase, but that will only be a reflection of using a counting stat where a rate stat was more appropriate.
The control system did its work. People saw that things were getting bad and they responded.
Also, there’s the matter of herd immunity.
Where are we on that path?
Herd Immunity Ho!
I still believe in the model I introduced in On R0. Events since then have only reinforced that basic framework.
That means: There are many times more cases than are reported. Those who get infected are those most vulnerable to infection and most likely to spread infection, with dynamics that work on power laws. This is true both in terms of a person’s vulnerability to the virus, and to how much they come into contact with others in ways that put themselves and others at risk.
This means that what looks like a little bit of infection goes a long way towards reducing the reproduction rate. Over time, those reductions accrue compound interest, although some of that can be lost to control systems.
This week, the C.D.C. analyzed antibody test results and compared them with positive test results. They concluded that at the peak of the first wave, only one case in twelve was being diagnosed. Things are better now, they say, but we are still finding at most one case in five. In places with a shortage of testing such as Arizona, that number is doubtless remains lower than that.
This creates a lower bound we can use to make a conservative estimate of how far things have progressed. It is also highly plausible that many who are immune are coming up negative on antibody tests but are still effectively immune, because they get sufficient immunity in other ways, but for now let us assume this is not an important effect.
We can create a few basic models.
The most basic model is to use strict SIR using only the confirmed positive tests. If it takes five days for a newly infected person to infect others, how much have existing positive tests reduced the current number of infections? Here we also treat everyone in the country as identical, exposing other citizens of the country completely at random, and that all are equally likely to expose others and equally good at spreading the virus.
That is of course a pile of horse-as-three-meter-sphere nonsense all of which makes herd immunity look less valuable than it is. It is possible that it benefits from fully counting people in New York in July, when they’re not as important to marginal infection rates as others, but that comes after making a severe version of the opposite mistake in April and May. Let’s see what happens.
We get a small but real reduction. Without herd immunity effects, with the weakest possible version of herd immunity, we would have infected 4.16 million Americans rather than 3.94 million. Herd immunity reduces the number of infected so far by 5.5%. Current infection rates are 88.3% as high as they would be without herd immunity, an 11.7% reduction going forward.
If we extend that out 30 days and assume our world has a constant rate of infection during that time (70k/day), then the relative rate will drop to 80.3%, for a 19.7% drop going forward and there would then have been a 8.9% cumulative drop in infection rates. Herd immunity matters.
Now let us modify that by assuming that for every case detected, there are four identical cases that are undetected. The C.D.C. thinks the number is at least that high, which implies a 6% infection rate for the country.
This would mean that herd immunity has reduced infections so far by about 25%, and the current infection rate by 47%. It’s a pretty big game!
Now let’s extend that by trying to model a conservative form of the power law effect. Those who got infected are not a random sample. What is a reasonable ratio of the risks taken by those who have been infected to the risks taken by those who have not been infected?
One approach would be to divide people into a high risk pool and a low risk pool. The low risk pool is doing proper social distancing, the high risk pool is not.
Some in the high risk pool have no choice. They are essential workers, or lack the resources to isolate. Others didn’t take the danger seriously and made a choice. This isn’t about blame or judgment. Some in the low risk pool are taking almost zero risk. Some in the low risk pool are taking moderate risks.
What I know is that by being consciously low risk, even someone who doesn’t understand physical nuance is much, much safer. It’s an order of magnitude or more.
Then that happens again. It’s fractal. The highest risk 10% are much higher risk than the next most risky 10%, and so on. It could hardly be otherwise. And that ratio of how risky someone is being, which includes taking into account geography, directly weighs on how often they get infected.
Further factors, such as different people being differently vulnerable to infection, make these ratios even larger.
If I said that those who did get infected had twice the risk of those not infected, that doesn’t seem like a large enough ratio to be believable. Ten times the risk seems like it might be too high and it might be too low, but I want to be conservative. Let’s say the ratio is three to one.
With a ratio of three to one, what was a 6% infection rate becomes an effective immunity rate of 16.1%. It means herd immunity has reduced our case count so far by 62%, and our current case count is 84% lower than it would have been with zero herd immunity.
Extend that out for thirty days, and herd immunity will have reduced our current infection rate by 95.7% and our cumulative number of infections by 86%.
Herd immunity is already a big, big game.
And remember, I think this is a lower bound estimate of the effect. It’s likely much higher than that.
The only reason it wouldn’t be a big game for infection rates is the control system. If we respond to every reduction in risk by increasing risk elsewhere, then the infection rate isn’t changing much, and all we are doing is allowing slash engaging in proportionally more risky behavior. That’s plausibly a substantial factor.
None of this means that we can use herd immunity to get back to normal. It does mean that it’s making a huge difference. It also means that as herd immunity increases, we should rapidly turn the corner towards things starting to improve. It could scarcely be otherwise.
Yes, Once Again: Immunity Lasts. Shame on Those Saying Otherwise.
Because scaremongers and those looking to look responsible and those who think everything must be doomed and terrible are constantly yelling about antibody counts declining and immunity being bound to fade away Real Soon Now, I have to put this reminder in what seems like every week: If immunity faded substantially on a scale faster than the current length of the epidemic, we would know this. There would be more than the handful of claimed cases we’d see from bad test results or misunderstandings and other errors. Thus, we know there is no substantial reduction in immunity for at least four months, which means we can expect that to last at least an average of eight months before basically anyone loses immunity enough to get infected. It would be much longer than that still before immunity would be reduced enough to change the math substantially. Everyone needs to chill.
The people who keep saying this are preventing us from using immunity passports to let those who have recovered move freely and live normal lives. This has done massive economic damage, and prevented us from transferring risk away from those who can get infected to those who can’t. It is a colossal unforced error that we are never going to correct. I despair of what to do about it.
Don’t Fear the Reaper
The death rate continues to rise. Two weeks ago the seven-day moving average was 553 deaths per day. Last week it as 696. It is now up to 835, with the last two days the first two over 1,000 deaths since May 26.
This rise is slower than I expected. It looks like getting to 1,100 deaths per day is going to take slightly longer than my 50% line of August 1. My current best guess is August 6, with a small but real chance things stabilize just before that happens.
After that, when will deaths start to stabilize? Given the lags we are seeing, probably about three to five weeks after infections stabilize, which means some time in mid to late August. If trends continue, we probably peak somewhere around 1,400 deaths per day. I wouldn’t be too surprised by anything between about 1,000 and 2,000.
Doubtless things will change. They always do, sooner or later. Until then, that’s my best guess.
We Can Still See You
Early news from the data suppression experiment is in. We are so starved for experiments of any kind it feels almost refreshing.
The result is disruption of some data collection, and the taking down of other data previously available, but nothing that substantially interferes with the data I’m using to make decisions, or the data that seems to be driving the narrative or big decisions.
Hopefully it stays that way.
I’ll see everyone next week. I’m also working on some other posts on other topics that I hope are ready soon.