Two reasons to do this.
1. I messed up the arithmetic the first time. Now corrected.
2. Let’s check this approach against New York information. New York is at 4159 deaths. Lower bound estimate for cases would be 4159 times 50 times 8 = 1.64 million cases. Upper bound estimate would be 4159 times 500 times 32 = 64 million cases, which is more than the population of the state. So I think we can rule that out. Probably because the true case fatality rate is significantly higher than 0.2 percent. If you believe that the case fatality rate is that low, then I think you have to believe that the number of cases stopped doubling every three days in NY at least a week ago, which is another plausible scenario.
Please check my arithmetic!
In the film “Apollo 13” Tom Hanks radios somebody on the ground to check his arithmetic. If the calculation is wrong the vessel will either burn or skip irretrievably into space. Checking is good.
According to Robin Hanson, “conventional wisdom” holds that the true case fatality rate is 0.5%:
https://twitter.com/robinhanson/status/1246832586154037249
What answer (i.e., what number of cases yesterday) would your formula yield, if the true case fatality rate is 0.5 (whilst we have adequate hospital capacity), and if we conjecture that, 15 days ago, cases in NY were doubling every 4 days?
4,189 times 200 times
… Need the missing third term.
Using the most current data for NY here:
https://covidtracking.com/data/state/new-york#historical
Cumulative deaths on April 4th = 3,565
Cumulative deaths on April 1st = 1,941
3DDRR, April 4th/April 1st, = 3,565/1,941 = 1.84
Assume, per “conventional wisdom,” that IFR (what Dr. Kling calls “true case fatality rate”) = 0.005 (i.e. 0.5%)
Assume n = 15 (average number of days from infection to death).
Assume that, 15 days ago, the underlying number of cases in NY was doubling every 4 days.
Then would estimation of the underlying number of cases on April 4th go as follows?:
(3,565/0.005)(1.84^(15/4)) = approx. 7 million cases in NY
You should stick with one rate, since the growth rate of deaths today was the growth in cases back then.
The daily rate is the 3DDRR^(1/3), so, in this case, 1.84^(1/3) = 22.5% growth per day.
Cases now = (deaths now/IFR)*(daily rate)^n
So, (3565/.005)*(1.225)^15 = 15 Million people, so, if all that were in the ballpark, herd immunity would have already been achieved.
By “true CFR” do you mean IFR? CFR is pretty easy to determine, since it means death after diagnosis, and both diagnosis and deaths are reported.
First daily drop on NYC virus cases today.
I would beware a weekend effect here.
I just point it out because I have been fooled previously with countries in Europe reporting a plateau/drop, only find that by Tuesday, the increase picks up again and makes up for the plateau/drop.
I suggest that even these working backward models have much too great a dependency on homogeneity.
In particular, I suggest that the real infection fatality rate is a function of:
a. Immune system decline from perfect function of a typical 18 year old – age is a surrogate for this. The perfectly functioning immune system of the 18yo scores 0, the nearly failed immune system of a 90yo scores 0.9. But it would appear all sorts of things may accelerate this decline other than age.
b. Underlying health problems, known or unknown. [I knew a man who died of sudden cardiac failure on a golf course – and it was a shock to everyone. NO medical exam had revealed any risk of this.] Suppose great real health is 0 and very poor basic health is 1. But also suppose that for many people it’s really quite poor (say 0.7) but this not observed.
c. Characteristics of exposure. Meaning how many virus particles, over what period of time. Suppose 0 is 0 virus particles, and 1 is a huge swarm of them striking in 1 second.
And so real infection fatality rate is something like a*b*c with various modifiers I’ve left out because I don’t know what they are.
It’s not a constant. It’s not close to a constant.
I further conjecture that the infection rate itself is some knarly function of how much time is spent sharing air with how many people in how confined a space.
All of this suggests that *maybe* what we’ll see this week is the peak of death rates in the Bronx, in nursing homes around Seattle metro, and so forth. That peak doesn’t really tell us what will happen later.
I further conjecture that the infection rate itself is some knarly function of how much time is spent sharing air with how many people in how confined a space.
—
The transmission rate of a virus particle at various temp and humidity and densities is well known. It is a fairly stable constant, and will not vary much except via temp and humidity (live in hot wet climes). It is measured for corona style viruses. We have natural experiments, well controlled that verify the numbers.
Here we have Saudi Arabia measuring people density over time, fairly accurately. The health ministry there has read reports of ex post testing after mass meetings (human experiments).
So we have the constant. It is a matter of breaking up the Saudi economy into units of the basic constant and extracting current transmission rates then update your accumulating model.
https://www.arabnews.com/node/1653766/saudi-arabia
JEDDAH: The Saudi Health Ministry has described the results of a Google Maps COVID-19 Community Mobility Report as “very concerning” — as it shows people’s mobility rate in Saudi Arabia remains above 40 percent.
“Unfortunately, there is still more than 40 percent of mobility, shopping and outdoor activities; this is a very alarming percentage,” Dr. Mohammed Al-Abd Al-Aly, the Health Ministry spokesman, said on Sunday.
“We are all in this boat together; those who risk their own lives by going out for no urgent need are risking everybody else’s lives too,” he said.
The report, published a few days ago, showed that visits to grocery markets, food warehouses and pharmacies dropped by 24 percent in Saudi Arabia compared to a baseline of data calculated during the five weeks from Jan. 3 to Feb. 6.
It also showed that mobility trends related to shopping and entertainment dropped by 54 percent and by 45 percent in workplaces, while it increased by 23 percent in residential places.
Sure – but the singing practice and the 1st cruise ship illustrate that “lab transmission rates” only apply in lab like contexts.
The question is, in detail, what human associations produce the high transmission contexts? (Choir practice seems a proven case. One suspects that closing down large crowd events like concerts and sports events had a huge effect.)
Thought you’d be interested in this
Lives vs. Livelihoods? Lessons from the Ebola Epidemic https://econofact.org/lives-vs-livelihoods-lessons-from-the-ebola-epidemic
I think you mean 0.02 and equivalently 2%.
I approve of your embrace of macro modeling! I think you’re using it as it should be too – as a check on both messy empirical data and less-messy micro models.
The PSST complement to these very simple models would emphasize that there’s probably no ‘real macro’ infection rate, incubation period, or rate of asymptotic infection because those probably depend on the specific people involved and the specific details of their ‘temporal contact graph’ with others, as well as the mitigation efforts each of those people engage in (and how well they follow the relevant ‘protocols’).
A pertinent xkcd comic posted yesterday:
xkcd: Scenario 4
From the hover-text of the comic:
I think that’s incomplete: some models (e.g. those used in particle physics) can also be ‘for’ making (incredibly) precise predictions.
I think PSST is a wonderful theory and that it’d be great to model it – and in a myriad of ways, e.g. combinations of various elements or components of the overall theory.
I’m with you, in terms of PSST versus ‘mainstream macro’, on PSST being underrated. I also don’t think the existing computer models are of much greater value than possibly simpler models. My (possibly poor) understanding is that a lot of models – not just in macroeconomics – are ‘complex’ (or complicated) because the mathematical models can’t be solved ‘analytically’ and that computers are needed to solve them approximately. I think simpler computer models are probably sufficient, but it’s still necessary to use computers because some important dynamics are consequences of ‘large’ systems, e.g. systems with lots of elements or agents, and it’s not feasible to explore or test models with these dynamics ‘by hand’.
Based on random readings on the internet, I would apply your model with the following inputs.
Tomas Pueyo updated on March 19 that the CFR can be 0.5% (South Korea) or 0.9% (China excluding Hubei) or 3% to 5% (overwhelmed health care system). An expert podcasted by Sam Harris on March 11 says it will be between 0.1% and 0.6% and I think he was referring to the U.S..
I’m going to use 3% which is the low end of an overwhelmed country.
Observablehq.com says time from infection to death is 23 days.
If U.S. total deaths now is 9504 then true infections is 64 million now.
2 dead from coronavirus, 45 ill after March choir rehearsal
https://www.cnn.com/2020/04/01/us/washington-choir-practice-coronavirus-deaths/index.html
430,000 People Have Traveled From China to U.S. Since Coronavirus Surfaced
https://www.nytimes.com/2020/04/04/us/coronavirus-china-travel-restrictions.html
How the Virus Got Out
https://www.nytimes.com/interactive/2020/03/22/world/coronavirus-spread.html
1.26MM+ Confirmed Cases
https://www.arcgis.com/apps/opsdashboard/index.html#/85320e2ea5424dfaaa75ae62e5c06e61
1. Infection Rate between 20%+ (Diamond Princess) and 75%+ (Choir Rehearsal)
2. 430,000 people traveled from China to US since CV19 surfaced
3. Millions of people left Wuhan between the time the virus surfaced and travel was restricted
4. Worldwide confirmed cases of 1.26MM+
Millions left Wuhan and 400K+ came to the US. They traveled unrestricted at their final destination for more than a month. It’s hard to imagine the number of current cases and previously infected and recovered is not 100x+ more than current confirmed cases.
Relevant 538 article:
https://fivethirtyeight.com/features/coronavirus-case-counts-are-meaningless/
He assumes a 15 day lag between infection and *positive test results report* and of course the lag from infection to death is likely to be significantly longer than the lag from infection to reported positive test.
Your arithmetic is impeccable. NYC death is probably between 1%-2%. I am not sure that this can be extrapolated. NYC is densely populated, had significant daily influx of non-residents, and was told that the virus was no big deal in Feb. when it got started. The illegality of prescribing hydro… hasn’t helped.
Given the uncertainty about cause of death in an elderly population with comorbidities, one wonders if there is anyway to look at actual excess mortality? Like after the hurricane hit PR and 16 people were killed but the experts assured us that the excess mortality was actually 3,000+. Is anyone able to track it in anything approaching real time? How many deaths occurred in the USA in 2019 as of April 1 versus 2020? Dr Roy Spencer took a look at the Euro MOMO (monitoring of excess mortality) on his blog on March 29th. But I am unable to find anything comparable on the CDC web site despite their $6 billion + budget. And Anthony Watts suggests today that excess mortality might have advantages over deaths attributed to the novel virus: https://wattsupwiththat.com/2020/04/05/how-to-analyze-and-not-analyze-coronavirus-deaths/
Korea had a big increase in cases early on, since then apparently has managed to contain it, has done lots of testing, tracked contacts of people with covid19..
As of the latest figures reported by WHO:
10,300 cases, 190 deaths. CFR = 1.8%
Go back 4 weeks:
7,380 cases, 51 deaths. CFR = 0.7%
I can’t come up with a scenario where the IFR (infection fatality rate) is under 0.5%, at least for the subsection of the population affected (it can be very different for different ages, underlying medical conditions, etc). If that was the case we would be seeing confirmed cases still shooting up as more of the population got tested and we found the actual cases we didn’t know about.
Maybe someone *can* come up with this scenario from the figures, I haven’t tried to create a model.