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%. 

The world in the coronavirus war zone

With every day that passes, the war seems more scary. People will certainly continue to die. The guns… we don’t know yet. The governments around the world assume dictatorial powers to steam the epidemic. In France, the country that defined freedom and democracy, people have to fill an online form when they go out to buy bread, and are fined if they forget. Spain and Italy adopt similar stringent measures with police officers everywhere and measures include extreme prison sentences for leaving certain zones.  In the UK, when all schools finally closed, Boris Johnson attempts to police families by advising grandparents to not spend any time with their grandchildren. Children are not sent to prison as of yet. It would be a great danger if the dictators will remain in power after this is all over. It could turn in revolutions and wars with guns if the measures continue for too long.

Quarantine cannot be a way of life. It will have to end within a month or so to still have manageable economies. Otherwise, supply chains will break in an irretrievable fashion, and there will be more deaths resulting from the measures taken than from the virus itself. While flattening the peak is crucial to making the pandemic manageable, one worries that when the quarantine is effective, not enough of the population is infected to gain immunity to the virus. Then if there is no vaccine that works, the death toll goes up again once the quarantine stops, and it has to be reinstated. It could thus be placing each country in dictatorship in conditions that cannot work over extended periods of time without complete economic collapse, more illnesses and eventually, bloodshed and hunger.

Below is my take on how various countries react to the coronavirus pandemic and the outlook for the future:

Germany

The quarantine works. There is vastly less social contact and less opportunity for the virus to spread. Germany will probably flatten the peak of the COIVID-19 pandemic. It may even be sufficient for the healthcare system to cope to some extent. They have also been successful at keeping people away from hospitals, thus allowing critical patients to be reasonably looked after. 

There are over 13 000 confirmed cases today, 31 deaths and only 2 people in critical condition. The death rate still hovers around 0.2%. Germany introduced the quarantine earlier than Italy, largely because of aggressive testing that allowed a large number of cases to be seen, and before people started to die. 

The Northern Provinces in Italy were quarantined on March 8, when Italy had 366 deaths and 6387 positive tests.  On March 15, when Germany introduced the quarantine, it had only 13 deaths and 5813 confirmed cases.  The deaths in Germany are a much better estimate of the number of active cases than the number of people tested. The dead are less likely to not be counted. 

I think the goal of the German approach is to allow the population to be infected at a high rate, so the length time the economy is shut down is manageable. 

What next? In the near future, we should probably see the testing capacity overwhelmed. That means, only severe cases will be tested. We will stop seeing the mild cases and the apparent mortality will increase. 

Austria

They are testing at a similar pace to Germany. It has a smaller population of only 8 million people, and close to 2000 cases and 5 deaths. As my colleague Werner points out, it is notable that most people who tested positive are under the age of 60, and the death rate is close to Germany's 0.2%. Schools are closed. People are homebound.

China

The Chinese are protecting their claim to success by expelling foreign journalists and, perhaps, soon, they will also bring out the real guns — the sort that shoot bullets.   

If the quarantine did work, there should be a new wave of infections as soon as the quarantine is lifted. Maybe the second wave will be better managed, but it will be there. 

If the quarantine didn’t work, the infection is burning through all of China, albeit at a slower pace then Wuhan. 

A 0.2% mortality rate means China would have to deal with 2 people in every thousand dead due to Covid-19. They would probably be the older and more frail. Maybe, their pre-existing conditions can be listed as the cause of death. The normal death rate is, roughly 0.1% a month. So, China would probably have twice the normal death rate for a few weeks when the disease strikes. I believe it is possible to hide that. The number of new infections and deaths seem to obey Xi’s orders too well. 

Xi has also cemented his position as a dictator through this. 

Russia

Russia is one of a kind. Their response to COVID-19 crisis was to change the constitution to allow Putin two more terms as president. It is certainly a good time to bring about the constitutional changes now, that the world and media is looking away due to the epidemic. 

Romania, Bulgaria, some other Eastern European countries. 

As the Romanian currency loses power, I worry that outside the Eurozone the economic impact will not be cushioned and that the economies will not recover.

Can quarantine be too stringent or start too soon? With 200 000 confirmed cases worldwide, there is no way to avert the epidemic. The quarantine does slow it down, but, if you slow it down too much, you will just postpone the problem. People have to become infected in order for herd immunity to stop the virus. It happens with all the other coronaviruses that cause common colds. 

I think the goal is to allow the population to become infected at a relatively brisk pace, as quarantines can’t be kept in place forever due to economic reasons. 

Is it reasonable to start the quarantine nationwide with under one hundred confirmed cases and, maybe a thousand or two that are not detected? Sure, it is a fast moving pandemic, but is it time wasted? Quarantine is expensive. 

There are some very interesting changes to the Romanian law including very heavy jail sentences for spreading all contagious illnesses. They look very much like the sort of legislation a government would pass in times of war. 

South Korea

Here, I would believe they did stop it. Thus, they should expect a 2nd wave of infections when they return to life as normal. 

Italy

The deaths in Lombardy should stop growing soon. Lombardy has 10 000 000 people and, as of March 17, 1640 deaths. This is close to the 0.2% death rate I would expect in general. Sure, Lombardy has a relatively old population (like the rest of Italy) and they are therefore more susceptible. Furthermore, the hospitals are overwhelmed, and, therefore, a lot of people die in situations that would not have been lethal at other times. 

A statistics of the dead show that 99% of those who died suffered from pervious medical conditions, which include high blood pressure (75%) and diabetes (35%). The average age of those who died is 79.5 and the median age of the infected is 63, which likely means that they do not have the ability to test effectively. So far 17 people under 50 died, and only 3 of those did not suffer from pre-existent conditions. The life expectancy in Italy is around 82, which is close enough to the average age of those who died to still see the coronavirus as a 'natural' vehicle for death.

Using my estimate of a death rate of 0.2%, I would predict nonetheless that the number of daily new deaths in Lombardy should stop growing soon as, probably, about half of the population has been infected.  I don’t believe the deaths can come anywhere near 7% of the population. That would be 700 000 if everyone got infected or 350 000 if only half. 

On an interesting note, Italy seems to have a lot of flu deaths. This may have to do with how people count the dead and how often they test older patients for flu before or after they die. In 2013-17, there were 68 000 flu deaths in Italy during a 4-year period. This would make colds a lot more deadly than usual in Italy than in the rest of the world. For example, the Swine Fu had a mortality of 0.02% worldwide, 10 times less than the 0.2% I expected for Coronavirus.