Yesterday, Tuesday, March 18 at 10 AM, the JHU web site said that there were 6519 cases in the U.S. Today, Wednesday, March 19, at 4 AM, it was showing 9415 cases. That is an increase of roughly 50 percent. That increase in known cases is a combination of two factors: increased testing (an artificial factor), which raises the number of known cases to the number of actual cases; and spreading of actual cases. I don’t know how much is due to each, but if you are looking for evidence that the virus is not spreading exponentially, an increase of 50 percent per day is not a good sign.
Now for some grim math. Let C be the number of known cases, H be the ratio of hospitalizations to known cases, and D be the ratio of deaths to hospitalizations. Then we have:
(1) total deaths = DxHxC
For example, if there are 1000 known cases (C=1000), 5 percent of these are hospitalized, and 20 percent of those who are hospitalized die, then deaths = 1000x.05x.20 = 10. Note that in this particular example, I assumed that no one dies who is not hospitalized. In reality some people will die without being hospitalized, and they will count in D.
Note that in this equation, HxC is the case mortality rate. In the numerical example, it is .05x.20 = .01, or one percent.
Next, we can do a logarithmic derivative approximation to write
(2) g = d + h + c
where g is the growth rate of deaths, d is the growth rate of D, h is the growth rate of H, and c is the growth rate of C. Note that this approximation only works for SMALL values of d, h, and c, not for big numbers like 50.
Suppose that cases grow at a rate of 4 percent (c = .04). Then if the hospitalization rate falls by 4 percent (h = -.04), that would offset the growth rate in cases.
Assume that soon the growth rate of cases will reflect true spreading, and the bump from increased testing will be behind us. Then going forward, there is reason for optimism in all three components of (2). The rate of death of hospitalized patients should fall as we get better treatment protocols and find useful drugs. The rate of hospitalization should fall as we get better at triage and we also find more effective treatment protocols that reduce time in hospital. It also could fall if we get better at protecting high-risk populations, so that more of the people who get the virus do not experience severe symptoms. Finally, the rate of growth of cases should fall as the effects of social distancing kick in.
If the rate of hospitalization does not fall fast enough (h turns sufficiently negative), then as long as c, the growth rate of cases, remains positive, we may at some point run out of facilities to treat seriously ill patients. The limiting factor in facilities might not be space and equipment–it could be the supply of health care workers. In any case, once we exceed capacity, that would cause a spike in d, the growth rate of deaths relative to hospitalizations. The growth rate in deaths would be high in such a scenario.
There are web sites that track total cases, C, and total deaths. What would help in this framework is to have H, the proportion of known cases that are hospitalized. As I searched for that data, at first I found what appears to be misinformation:
Up to 1 in 5 younger adults in the U.S. infected with coronavirus wind up in the hospital, according to a new analysis by the Centers for Disease Control and Prevention.
Baloney sandwich. What the report says is
Among 508 (12%) patients known to have been hospitalized, 9% were aged ≥85 years, 26% were aged 65–84 years, 17% were aged 55–64 years, 18% were 45–54 years, and 20% were aged 20–44 years. Less than 1% of hospitalizations were among persons aged ≤19 years
That is, 20 percent of those hospitalized were in the 20-44 year age group, not that 20 percent of the cases in that age group are hospitalized. Since 508 were hospitalized, that means that about 102 in the 20-44 age group were hospitalized.
As I understand it, at the time the report was run, there were 4226 cases, and 29 percent of these were in the 20-44 age group. That means that there were about 845 cases in that age group. So the rate of hospitalization within that age group was 102/845, or a bit under 12 percent. Still a big number, and an indication that letting this “low-risk” population all get infected soon may not be a good strategy. But see my final note.
Overall, dividing 508/4226 gives a value for H of just over 12 percent. With cases having more than doubled since the report was run, in order to hold steady we would need H to have fallen below 6 percent.
Final note: the value of H in the report is greatly overstated to the extent that people without severe symptoms did not get tested, and hence did not show up as cases. That could be a lot of 20-44 year-olds, which would make their H much lower.
I wish we had a dashboard that provided reliable numbers for H. I wish we were testing a random sample of the population so that we could estimate key numbers with more confidence.
There’s quite a bit of agreement that number of cases isn’t the best measure, because we aren’t testing everyone. Number of deaths is better. Using number of deaths, the US is well behind Italy, although there are many people who tell me we won’t know for sure until we hit 100 or 200 (opinions differ)
Italy’s death count from 1 to 200:
1 2 3 7 11 12 17 21 29 41 52 79 107 148 197
US death count from 1 to 200 (well, we’re not there)
1 6 9 11 12 15 19 22 26 30 38 41 49 57 68 86 109 125
So it took Italy 15 days to get to 200 deaths. It took the US 18 days to get to 125.
US death per active cases is, with the exception of one spike, much lower than Italy’s, and declining. Italy’s is increasing. Given that Italy tests more than we do, that’s encouraging.
This has some figures on hospitalisation rates by age: https://www.imperial.ac.uk/media/imperial-college/medicine/sph/ide/gida-fellowships/Imperial-College-COVID19-NPI-modelling-16-03-2020.pdf
Ideally the numbers need to distinguish between travel cases, close contact cases, and community transmission cases. The best public tracking data that I’ve seen is in Ontario and the values are useless as a predictive tool.
To make the data useful, a single tabular text file (e.g. CSV format) stored in a system like Git with revision history. The backlog, turnaround time, and capacity of both Testing and Contact Tracing systems need to be tracked/published. In Ontario, both of these systems reached capacity last weekend and the numbers no longer reflect meaningful trends. The underlying data needs real datetime information that is decoupled from the overloaded reporting and publishing platforms.
I don’t think “low risk” just means young people in the context of the theory of letting the disease spread. There are several other risk factors besides age (diabetes, heart disease). The hospitalization rate for people without any of the risk factors (including age) is the data we would need for us to say whether an “infect the low risk cases to get herd immunity” strategy has merit.
Another interesting point is that in the two cases I’m aware of where they tested everyone – the Diamond Princess and this town in Italy, both showed 50% of the cases as asymptomatic. That would mean that any rates you compute might need to be halved. And it also probably means that mild symptoms are very, very common. So the number of infected cases in the US could easily be 10x what the official numbers report.
Testing capacity is up: https://twitter.com/COVID2019tests/status/1240296031406915584
Number of tests run is up (this number is probably too low because states aren’t uniformly reporting private testing and negative tests): https://www.calculatedriskblog.com/2020/03/update-covid-19-tests-per-day.html
I think the US is still in the testing catch-up phase, so it is tough to judge our growth rate. About 7-10% of tests are coming back positive, which I think is encouraging. Hopefully that number falls as we can test more and more marginal cases.
The 2nd derivative (growth in cases) has been falling in Italy and Iran, and in Italy I expect the absolute number of new cases to hit a peak in the next 5-7 days and start declining after that, if they’ve actually achieved a slowdown.
Whit Brennan says:
I did a quick calculation of the Ontario numbers since last Friday and the positive test rate is about 2.2% (min 0.3%, max 2.7%). Not indicative of anything but maybe useful as a rough estimate of growth trends (none in ~6 days).
This is why I wish we had even bad numbers for British Columbia (B.C.) as their reported case numbers exceeded Ontario’s for the first time yesterday. B.C., Like Washington State, has confirmed community transmission starting in a long term care facility with both patients and health workers affected.
If I’m not mistaken, Ontario represents the Travel only vector while B.C. is mostly Travel cases with an upsurge of Community transmission. My intuition is that the 7-10% numbers are like B.C. and possibly worse at this stage but intuition is all these numbers are good for at this point.
That article says 3% without symptoms in an Italian town with widespread community transmission. I’m skeptical of that value without seeing exactly how “without symptoms” is defined but it doesn’t change the strategy to focus on symptoms because they occur simultaneously with peak contagiousness, especially when you are playing catchup with testing capacity.
One-tenth is the number I hear. Each year’s seasonal flu is one-tenth as bad as this new virus.
So each year, if we wanted to save one-tenth as many lives, we should sacrifice one-tenth as many businesses bankrupted in this current hoopla. We should throw one-tenth as many people out of work in the fight against the seasonal flu. We should put up with one-tenth as many defaults and bankruptcies and closures.
But obviously we don’t cancel one-tenth as many concerts and plays and recitals. We don’t cancel one-tenth of the tennis and one-tenth of the football. For one-tenth as many lives, we don’t cancel anything.
That’s grim math, but nobody feels grim about it.
Check the S Korea numbers for the best estimates of these parameters. They’ve been testing everyone. That mean some false positives, but they’ve identified lots of younger cases who otherwise would probably not have been tested.
Kling says:
If we are following a suppression strategy, there are two critical factors which are being stressed to capacity and are key to preventing health system meltdown:
1. Virus Testing capacity
2. Case Tracing capacity
Singapore, Taiwan, and South Korea deployed massive Case Tracing capacity. Canada’s Case Tracing capacity failed once non-obvious Travel/Contact cases were introduced.
Coronavirus is a good thing, not a bad thing. That’s because it leads to pneumonia.
Sir William Osler, sometimes called the father of modern medicine, famously called it “friend of the aged” (often rendered as “the old man’s friend”) because it was seen as a swift, relatively painless way to die.
These mostly older people that died from pneumonia, what would they have died from instead? And what would their quality of life been?
Imagine some 90-year old, body racked with pain, in an old folks home with Alzheimer’s and dementia. Maybe gone blind from macular degeneration. One of the “lucky” ones who survived the Coronavirus.
What’s the counterfactual here?
Medical assistance in dying is a simpler solution.