How deadly is the coronavirus? The 0.2% revisited.

Last week, I put forward 0.2% as the most likely value for the mortality of COVID-19. In this post, I will explain my rationale at greater length and look at today's numbers to see how that prediction holds up. 

I should thank my professors Kip Thorne and David Politzer who taught me how to think. I have learned to play with order of magnitude calculations during countless office hours for Physics 1 that I spent at Caltech with David Politzer, sometimes with and sometimes without students. Kip also did this very often in his TAPIR group meetings, which, for a few good years,  were my main source of pizza. 

The situation is as follows: 

We have this new disease that is killing people. 

We don't know 

• how many are infected because we have not been able to test the entire population.
• how many are dead. Sure, countries keep publishing how many dead people have been testing positive. It is, however, true that some people die without being tested.  On the other hand, a death is still an important event. I thus believe a dead man is less likely to go unnoticed and untested than a man who displays cold symptoms. 
• the difference between the daily deaths at this time of the year and how many deaths we see now in each particular region. I would believe this number more readily than the estimates based on counting tests. 

We know we have more infected than confirmed positives. We are certain it's not less. Valeriu Predoi plots all the data from the various countries and nicely fits it to exponentials. From there, one observes some trends. Germany's death toll is much closer to being parallel to the number of cases than Italy's. The effect of the quarantine cannot be seen in the data as of yet. For Italy and for most other western countries, the deaths toll double much faster than the number of cases because they do NOT test enough. Roughly, the more a country tests, the more parallel these lines get. Countries that start testing later like the US have the number of cases doubling faster than the deaths.

The death rate in Italy is showing a hint of slowing down as is that in France and Spain due to the quarantine. It can be seen that the quarantine moves the death toll to a slower exponential, but cannot entirely stop the spread of the virus. Belgium shows a clear effect on the quarantine where the increase in the number of confirmed cases is also slowing down. This can be clearly seen for China, and recently for Ireland, Denmark, Sweden and Finland. Sweden recently decided to test only the cases requiring hospitalization. I am unsure if in the other countries the testing procedures have changed as well or if there is a working quarantine.

We don't have an antibody test as of yet. If we could test for the viral antibody, we could go to Wuhan and see what fraction of the population has developed immunity to the coronavirus. That would be an accurate measure for the number infected. 

Now... to put forward a reasonable guess for the mortality rate. What do we do? 

I thought it's reasonable to look for well-organized countries with a good health care system. Here, dead people are less likely to go untested and uncounted. So, we can believe the dead.

 It takes awhile (about 2 weeks -- because there is an incubation period) for somebody to die of COVID-19.  But how long does it take for someone to get tested? People are certainly not tested the day they get infected. They are actually more likely to get tested the day they die. The disease has an incubation period of a few days, people wait in line to get a test, the results take some time to come back and be posted online. 

I thus assumed that, with all the counting errors and delays, the number tested today is a reasonable indication for how many people were sick some 10 days - 2 weeks ago.  This assumption no longer holds if, for example, the quarantine works and the number of infected people stops growing. It will also not work if the infection has passed its peak and the virus finds it hard to find new people. Or, if the test policies change - say, if the country runs out of tests or the medical system is overwhelmed and testing is being prioritized for special cases (critically ill, politicians, etc). 

Like most order-of-magnitude estimates, it is a reasonable assumption, but, not always true. It is my best guess. 

Thus, I said, a reasonable guess, perhaps a reasonable upper bound even, for the mortality rate of COVID-19 globally is the number of dead people divided by the number of confirmed cases in the countries where tests abound and health care is good. 

The following common situations will make the mortality appear higher 

• Tests running on short supply. Naturally, healthcare authorities will continue testing critically ill patients and stop testing people with light or no symptoms. The critically ill patients are more likely to die, artificially increasing the apparent mortality rate. 
• Political directives against testing. This appears to be the case of  the United States. Only 1 American in 1 million was tested by March 1. 
• diagnosing COVID-19 based on radiological findings because there are no tests. Only the most severe cases will show on a C-T scan. This certainly happened in Wuhan. 

With the above said, let's look at the numbers today and compare to last week. 

Here's the data from March 14, on which I based my 0.2% guess 

Country	Cases	Dead	Mortality %
Germany	5176	9	0.17
Sweeden	992	2	0.20
Denmark	864	2	0.23
Austria	800	1	0.13
Norway	1205	3	0.25
Total	9037	17	0.19

Here's the same data from today (March 19)

Country	Cases 19/3	Dead	Mortality %
Germany	13083	31	0.24
Sweden	1301	10	0.77
Denmark	1132	6	0.53
Austria	1843	5	0.27
Norway	1606	6	0.37
Total	18231	58	0.32

Germany and Austria stay reasonably close to my 0.2% estimate. 

What does that mean?

• the pandemics doesn't appear to be slowing down. 
• the effects of the quarantine, if it does work, don't show in the data. The quarantine prevents new infections, but, it hasn't been long enough for those newly infected people to be tested. 
• I stick to my guns. Now, my estimate is backed by larger numbers in these two countries. Thus, more solid.  The numbers of cases in the other countries are low suggesting large error bars and not enough tests.
• In a few days, once the hospitals get overwhelmed, there won't be enough tests and the apparent mortality will go up. 

Sweden, Denmark and Norway have gone up. I suspect that they are either out of tests or, due to stress in the medical system, there is no time to test mild cases. My own friend Teresia believes she is now sick with Coronavirus in Sweden and she doesn't even try to get tested. She drinks tea at home and doesn't even turn up the heat (even I am critical of that). Sending you best wishes! 

While in Germany and Austria, the number of detected cases has increased by a factor of 2.4 and 2.3,  Sweden, Denmark and Austria only went up by 30%.  The nature of the virus is the same. The population dynamic sufficiently similar. So, it could be that the pandemic is running its course just like in Germany and that they are out of test or that we start to see the effects of the quarantine.  Sweden stopped testing on large scale -- they are now only testing the cases that require hospitalization. Initially, I was hoping it showed the quarantine working, but it does not seem to be the case.

One can combine the data from the tables above into one table:

Country	Cases Mar 19	Cases Mar 14	Deaths	Mortality 19/3%	Cases 14/19
Germany	13083	5176	31	0.24	2.5
Sweden	1302	992	10	0.77	1.3
Denmark	1132	864	6	0.53	1.3
Austria	1843	800	5	0.27	2.3
Norway	1606	1205	6	0.37	1.3
Total	18231	9037	58	0.32	2.0

Now, let's look at the countries that showed high apparent mortality last week.

	Cases 19/3	Deaths	Mortality %
Italy	35713	2978	8.34
Iran	17361	1135	6.54
China	80928	3245	4.01
Spain	14769	638	4.32
France	9134	264	2.89
USA	9464	155	1.64
UK	2626	104	3.96
S Korea	8565	91	1.06
Diamond Princess	712	7	0.98

 Here's what the data looked like last week:

Country	Cases	Deaths	Mortality %
Italy	21157	1441	6.81
Iran	13838	724	5.23
China	80849	3119	3.86
Spain	6821	208	3.05
France	4499	91	2.02
USA	3045	60	1.97
UK	1140	21	1.84
S Korea	8162	75	0.92
Diamond Princess	696	7	1.01

The apparent mortality is essentially unchanged in China, South Korea and on the Diamond Princess boat. Here, the epidemics is over, or at least over for now. If the quarantine is the main reason the infection has stopped, then the quarantine will have to remain in place. A new wave of infection will start as soon as the country returns to life as normal. 

If the majority of the population has been infected because the quarantine has failed to stop the virus (note that the quarantine would still have flattened the peak of the epidemic, allowing the medical system to better serve the patients), then the country can return to life as normal. No significant COVID-19 deaths or new waves are to be expected. 

The apparent mortality has gone down in the US. That is, most likely, because they started to test more and more people with mild symptoms. The apparent mortality has gone up everywhere else, most likely due to strain in the medical system. 

Lombardy will soon be a good place to test this hypothesis. In the next few days, the epidemy there will stop. We will not see many new cases and people will heal. At that point, we will be able to calculate a lower bound for COVID-19 mortality by dividing the number of deaths to the total population. I guess at least half of the population would have been infected by this point, so this lower bound is correct within a factor of 2. Italy, in general, has a higher than usual flu mortality as I mentioned in my previous post. Thus, the COVID-19 mortality will also be higher, perhaps by the same factor.  

In conclusion, I believe the estimate I made last week is correct. The mortality for the coronavirus still hovers around 0.2%.