One of the unknowns in the virus crisis is what explains differences in severity. Of the people who have been infected, it seems that more than 95 percent experience low severity. Also, we see wide differences in severity across countries. Is Taiwan doing better than Spain because fewer people have been infected in Taiwan, or the infections are less severe in Taiwan, or both?

It seems to me that the possible explanations for variations in severity include:

1. How you are attacked–how much of the virus you get and how far it goes initially into your respiratory system.
2. How well your individual body defends.
3. How you are treated by the health care system.

The conventional wisdom, as I understand it, is that (2) matters, and I believe this conventional wisdom. That is, we think that young people without underlying conditions defend better once infected than do old people or people with underlying conditions. Of course, it would be better to have knowledge of which underlying conditions affect the ability to defend.

The conventional wisdom, as I understand it, is that (3) matters, but I am skeptical about it. The conventional wisdom is that we need to keep the number of hospital beds and ventilators ahead of the spread of the virus, or otherwise people will die unnecessarily. The conventional wisdom seems consistent with the high death rates in Northern Italy, Spain, and New York City. But there could be other explanations. Perhaps the rate of infection was higher in those areas. Perhaps how you are attacked matters, and people in these areas were more likely to be attacked more severely.

Suppose that more ventilators and hospital beds had been available in these dire regions. Would that have produced more cures, or merely kept some people alive a few more weeks? I am getting the impression that a shortage of ventilators means that victims who are beyond hope might have to be denied a ventilator, but it is less clear that people who could survive if given a ventilator must be denied one. I am by no means committed to this point of view. It is just a guess. Any evidence to the contrary would be sufficient to get me to change my mind.

The conventional wisdom is relatively silent about (1). But I wish we knew more. For example, suppose that strong attacks only come from symptomatic spreaders, while getting the virus from an asymptomatic spreader means that you face a weak attack. That would imply that fears of asymptomatic spreaders are exaggerated, which would have some significant policy implications. It would imply that a focus on identifying and isolating the symptomatic individuals is the key to preventing deaths. It might mean that universal masks and scarves, while not preventing all infections, might do well at preventing severe infections, particularly if symptomatic individuals are identified and isolated.

1. A grim article on what ventilators can or cannot accomplish. (NYT)

2. Today’s figure puts the 3DDRR at 1.64, a further drop from yesterday. The doubling time has no extended from three days to five days. If this keeps up, in another week there will be a ferocious argument over whether it is time to lift the lockdowns.

[corrected at 12:40 PM–bad arithmetic error before. Thanks to David Henderson for spotting it]
Because we have not done random-sample testing, we have no idea of the true number of cases in the United States. Reported numbers are worthless. Below, when I refer to cases I mean the (unknown) true total number of people who have ever been infected, not the reported case numbers.

Suppose that we try to work backward. Suppose that we assume a lag of n days from the time of infection to the time of death. Then the number of cases as of n days ago is equal to the number of deaths as of today, divided by the true (unknown) case fatality rate.

The more cases (meaning actual cases, not reported cases) that it took to generate all of the deaths as of today, the happier we should be. A higher number means that there are more people who have already been infected, so we are closer to the peak of the curve.

For example, as of yesterday, there were 8314 deaths. If we assume a true case fatality rate per 1000 of 20, that means that as of n days ago there were 50 times 8314, or 41,570 415,700 cases. If both cases and deaths has doubled every three days (3DDRR = 2.0), then the number of cases today is 2^(n/3) times 415,700. If n is 9, then that means we had about 3.3 million cases as of yesterday. Is that a lower bound? Or is the cfr higher than 20 per 1000 (higher than 2 percent)?

If we raise n to 15 and keep the cfr at 20 in 1000, then the true number of cases as of yesterday was about 13 million. If we raise n to 15 but assume a cfr of only 2 in 1000, then the true number of cases as of yesterday was about 130 million. Is that the upper bound? If we are anywhere near that, we are close to a peak.

How will we know when and how to exit from the lockdown strategy? I think we need to conduct experiments.

I know this is a pipe dream. The only experiment we will ever see will be “Lift the lockdown and see what happens.”

But I would suggest that we recruit young, healthy people who are uninfected and have never had the virus as experimental subjects for the following experiments. Note that I would be willing to see the one child of mine who qualifies as healthy to participate as an experimental subject, because I think that these experiments would be safe. Note that for these experiments the “infected person” is either asymptomatic or has only very mild symptoms.

1. The doorknob effect. Have the infected person open a door, and have the experimental subjects follow at one-minute intervals and open that same door. Quarantine the experimental subjects for two weeks and meanwhile test them for the virus.

2. The classroom with masks and scarves. Have the infected person sit in a classroom with one hundred experimental subjects. Everyone, including the infected person (whose identity is known only to the investigator, not to the experimental subjects), wears a face covering of some sort. Try this experiment with the infected person having different types of face coverings. Quarantine and test.

3. The virus-in-the-air experiment. Have a person known to have the disease in mild form walk through a hallway. Have experimental subjects follow at one-minute intervals. Repeat this experiment with a different combinations of face covering. One version would have nobody wear face covering. Another version would have both the infected person and the experimental subjects wear face covering. etc. Quarantine and test.

These sorts of experiments would provide a better scientific basis for making decisions regarding modifying or lifting the lockdowns.

The number that I use to track the virus crisis is the Three Day Death Reproduction Rate. It sounds ghoulish, and it is. It also is a lagging indicator. I wish I had some other indicator. But I do not trust case numbers, because testing criteria are undergoing constant revision.

The 3DDRR is calculated using the data from this site, which is updated every day late in the afternoon, eastern time. It gives the total number of deaths as of each date. The 3DDRR for, say, March 29, is the total number of deaths on March 29 (2428) divided by the number on March 26 (1163), which gives 2.09.

We can say that if the 3DDRR stays close to 2, then that is awful. If it stays over 1.1, then that is still pretty bad. If it is just barely over 1, say 1.002, then that is better. Getting below 1 would require resurrections.

So for all the dates from March 20 through today, we have

The trend is in the right direction, but the 3DDRR is still disturbingly high. It would be nice to see, say, 1.5 by April 7, 1.3 by April 10, 1.1 by April 13, and 1.002 from April 16 on. That would raise April 4ths total deaths of 8314 to 17,834 (exactly, right?) on April 13, with slow increases beyond that.

That is a numerical scenario, but it is hard to know what has to happen in the real world to achieve that. Presumably it would require a continued reduction in the spread rate of the disease, along with improvements in triage and treatment.

The problem is that even in such an optimistic scenario, we won’t know how much of the lockdown policy was needed to achieve it. I keep saying that we need experiments in order to better understand the spreading process, but no one listens.

For people who are new to this blog:

1. The tradition here is for respectful, constructive discussion. For five years up until the past week, I probably deleted fewer than 10 comments for violating that tradition.

2. My wife and I began a self-quarantine on March 12, which was before most people were doing so, and before almost any public official recommended it. I became a doubter of the quarantine approach when it occurred to me that a public hygiene approach could be a more cost-effective alternative. By public hygiene, I mean masks and scarves, handwashing, and efforts to frequently sanitize surfaces that are touched by many people. I will not stand for accusations that my motives are selfish.

To summarize this table (pointer from Russ Roberts):

Of 1584 Covid deaths, 25 were people with no underlying conditions, 380 were people with “underlying conditions pending,” which I guess means that they are not sure whether or not the person had an underlying condition, and the other 1179 all had underlying conditions.

Of those with “pending underlying conditions,” 234 were aged 75 and over. So another way to look at the data is that of the 1584 deaths, 1413 either were aged 75 and over or had definite underlying conditions. That is 89 percent.

Perhaps those of us under age 75 and healthy ought to be given more freedom to go out in public, provided that we wear face covering. Also, it would help to sort out which “underlying conditions” really matter, to know who should be considered healthy.