Considering how well different states have dealt with the pandemic, there seem to be two clear success stories and a number of open cases.

China seems to have brought the cumulative number of infections to essentially a standstill. The number of daily new cases is pretty low, the total number of cases hovers around 82000, of which 77000 patients have recovered already. (The rest are mostly dead.) One of the attached pdf files gives the case number as a function of time, together with an exponential fit to the first ten data points and a fit to the solution of a three-parameter logistic equation, suggesting that saturation has been reached. (Of course the fitting function is too simplistic, but it gives a decent approximation.) The time axis is in days, day 1 is 01/02/2020, hence day 30 is March 1st, day 61 April 1st. The axis of ordinates is the cumulative number of infections (active plus inactive). Since a constant level has essentially been reached, I have not continued the fit to the current date.

Another country that has succeeded in obtaining control over the spread of the disease is South Korea. Here the data cannot be fitted by a logistic function, but a slightly modified curve, allowing for a linear increase instead of a final plateau, does the job nicely (with four parameters). I attach the result as well. The fit is up to date until yesterday and I would say it is predictive on time scales of a week or even a month. (That is, I don't need to make a new fit with the data of the next few days and the curve will still produce a decent approximation.)

The time scale between take-off and plateau or switch-over to linear behaviour is about 25 days in the case of China and 20 days in the case of South Korea.

In Europe, the disease started spreading later, and no country so far has succeeded in attaining a plateau or weakly (linearly) increasing number of cumulative cases. As an example, I give Germany. We are at about day 25 to 30 after take-off, and the curve is still rising. The exponential curve was obtained by fitting to the 22 initial data points only (omitting days 0 to 29, where the number of cases was below 100), the intermediate curve is a stretched exponential fitted to the first 28 data points (the rationale being that the lockdown measures might lead to a distribution of exponentials with different growth rates first, the average of which would behave as a stretched exponential). The logistic curve is not yet predictive. It gives almost correct predictions for a day or two, then starts to underestimate growth and a new fit leads to a higher plateau. In the case of Italy, we have predictiveness over a longer period and in the case of Spain, the plateau even decreased in height in one case. All of this is suggestive that the lockdown measures seem to work and we may have a plateau on a time scale of two months instead of one. The US is not faring any better than Europe, in fact their success in diminishing the exponential growth rate seems worse than that in countries such as Italy or Spain (which have been hit most heavily in Europe).

The question is what to do once the plateau has been reached? To keep the lockdown much longer than two or three months would be disastrous for the economy, and we are of course still far from herd immunity at the plateau.

First, it may be useful to consider by what strategies China and South Korea were more successful than Europe. Clearly, the numbers from China have to be taken with caution. They report about 3300 deaths, but I have read rumours that the actual numbers might rather be in the tens of thousands. Also their total number of once-infected persons may be way too small due to counting tricks. (It might well be 300000 rather than 82000.) Nevertheless, there seems to be agreement that they have essentially stopped the disease for now. We probably cannot copy their methods, as China is a dictatorship and they may use brutal measures for enforcing a lockdown. (You could probably be killed by the police, if you disobey the lockdown rules.)

With South Korea, the situation is different. While they did not manage to completely stop the case count, they could drastically reduce its growth rate. And we know how they did it. In principle, we could copy their approach; it does not go beyond the power of authority of a democracy. And it works without a complete lockdown.

In fact, on 19 March, I sent an e-mail to our chancelor (Angela Merkel), discussing how the South Korean approach works, in principle, and that in copying it, Germany should be able to keep its case count similarly low. South Korea had about 9000 cases then and has about 10000 now. Germany had about 15000 cases then and has more than 95000 now. South Korea's population is 51 million, Germany's 82 million, so if Germany had done as well as South Korea, they should have brought growth to a slow-down at 16000 or at most 20000...

Anyway, since I sent the e-mail to Ms. Merkel via an official e-mail address, it was certainly read by some official, who filters the (presumably) large number, and it may in fact never have been read by her. Which would be a pity as she is an intelligent woman and has a PhD in physics, so she would certainly have understood it. (Also the person deciding not to give it to her carries a great responsibility.)

Acting on it is of course a different matter, in particular when you get much advice by other experts, each one focused on a different thing. After all, being a physicist, she must have understood the dangers of nuclear power plants for a long time. But it took the emotional shaking by Fukushima for her to act on that knowledge. (And then she overreacted, resulting in the taxpayer having to reimburse electricity companies for lost gains due to early shutdown of power plants -- which might instead have helped reduce carbon dioxide emissions, if rather some carbon power plants had been shut down a few years earlier.)

In that context, it may be useful to point out that there exists a report addressing the German federal parliament, dated 13 January 2013, in which the government presents a risk analysis, among other things, of a pandemic by the virus "MODI-Sars", which is a fancy name for a virus of the Corona type, producing a modified SARS like disease. The risk analysis starts on page 55 and goes on through page 88 of the report. It comes to the conclusion that Germany will suffer 7.5 million casualties by the disease (assuming a relatively high lethality of 10%). Most assumptions on the disease are similar to the properties of COVID 19. Ideas about the availability of a vaccine are conservative, assuming it will take 3 years to produce. The report concludes that there will be 3 waves of the disease, each one about half a year long and each one overcharging the German health system. A new wave starts when lockdown measures from the old one are relieved. Also, the report assumes that immunity after recovery from the disease will be only for about a year, due to continuing mutations of the virus. All in all, the pandemic will take three years. Details about economic reverberations are murky, but I suppose the world economy cannot sustain three successive lockdowns of half a year each and some milder version of lockdown for the remaining one and a half years.

As far as I can tell, no measures have been taken on that report (that would have been communicated to the public). So Bill Gates is right. We were unprepared for the pandemic. (And that is true not only for Germany. Germany is in fact doing o.k. as far as lethality and availability of hospital capacity is concerned. The situations are worse in the rest of Europe and far worse in the US.)

Here is the basic idea on how to stop the disease without a full lockdown and with continuing economic activity. It is pretty simple and I will first discuss it in the form that was given in my e-mail. Since I have more precise figures in the meantime, I will then show that a somewhat more optimistic view is possible.

What was known to me then was that there was an incubation period between one and two weeks, before symptoms showed up, and so an infected person might infect others even before knowing they were ill. Also the quarantine for patients was two weeks, so one may assume that three to four weeks after infection you are either recovered or dead. I assumed that you become infectious yourself after one or two days and lose that a week or so before recovery. The basic reproduction number R0 (which is the average number of persons infected by one ill person) was supposed to be between 2 and 3. (For measles, that number is about 15!) If you infect two to three persons in three weeks time, you will infect fewer than one on average, if you are identified and put into quarantine within a third of your infectious period, i.e., within a week. So we must do what South Korea did: test extensively (and track the contacts of all positively tested individuals). If we catch everyone who is infected early enough, no other measures are necessary in order to keep the effective basic reproduction number below one, which is sufficient to stop spreading of the disease. With additional measures in place, such as a full or partial lockdown, we may succeed in doing so even when discovering the disease in everyone only within two weeks (on average) after infection. But of course we want to get away from lockdown, to get the economy going again.

The problem with this approach is, of course, the huge testing capacity you need. But South Korea did it, so it should not be impossible. What numbers are possible? Right now, it seems that about 300000 tests are done in Germany per week. But Germany is a highly industrialized country, with some of its industries having little to do now. With an appropriate effort, it should be possible to push that up to 500000 tests per day, even a million. (Testing the whole population once every three months.) If Germany can't do it, China certainly can (and sell the equipment to Germany for a good price...). And they even don't have a lockdown... Billions of Euros are being set aside to save our industries across the period of the lockdown. A few of these billions could be spent for tests (and part of them for breathing masks). At the moment, the importance of tests is emphasized in public speeches as a means to learn more about the disease. This is misinformation. They are much more important as a means to stop the spreading of the pandemic (which requires linking them with quarantine).

In fact, I have learned more accurate numbers about the disease in the meantime. There is a paper by the Robert Koch institute [1], in which they say that infectiosity is present for 10 days, starts around day 2.5 and symptoms are present for 9 days, starting at day 4.5. Duration of the disease is 17.5 days, if there are no complications, otherwise up to 28 days (intensive care starting around day 9.5, taking 10 days, resulting in death on average on day 19 for 50% of the patients in intensive care and recovery for the remaining 50% around day 24; - this may be different in other countries). Moreover, the basic reproduction number has been estimated to be between 2.24 and 3.58 in the Wuhan outbreak [2].

What is important for us is that the period of infectiosity is 9 days, of which only 2 days are before symptoms. It is therefore not actually necessary to test everyone before symptoms. If we catch and test everyone on the first day they have symptoms, that should alone be sufficient to reduce the effective basic reproduction number below one, because we are then on day 3 of 9 infectious days, when fewer than a third of the possible secondary infections have happened. So testing symptom-free persons might be reserved to high-risk or high-multiplicator groups (personnel of hospitals, teachers), and a million tests per day may actually be enough. Of course, the result of a test must be available the same day, within a few hours after testing. (Or else, the tested person must be kept in quarantine precautionarily until the test result is available.)

So the course of action for the near future, after -- hopefully -- getting below an effective basic reproduction number of 1 via lockdown, should be

1) to gradually reduce the lockdown, best only partially at the beginning, masks could be worn in public (once enough are available) which gives a small level of protection, but also contributes to lowering the effective basic reproduction number, and what matters is the overall statistical effect (not whether a particular individual has more or less protection -- older people should try to protect themselves more thoroughly than younger ones, being at a higher general risk)

2) making available fast testing with quick results to everyone having the slightest symptoms and putting those people immediately into quarantine on positive testing

3) testing the contacts of positively tested persons, if those have a smart phone on which the app is installed that registers all smart phones that satisfy certain closeness conditions with the carrier of the infected person (temporary measure, as anonymous as possible, expiring automatically, if not renewed be legislation regularly)

4) testing persons from critical professions (that might have multiplier function) on a regular basis even without any symptoms.

5) Production stops in any economic branch for the purpose of a partial lockdown should be limited to less than a month whenever possible, and not happen too often. The point is that losing certain production capabilities via failures of enterprises will also cost some lives in the end, although this may be less visible than direct losses via a disease.

This requires mass production of reliable testing equipment. The tests must be so standardized that qualified medical personnel (numbers of whom cannot be augmented fast) have to spend only very little time with each single test. (The swab could be made by the patients themselves in many cases -- except if they are helpless.)

What do people think about how to proceed? Are there additional or alternative measures that suggest themselves?

[1] an der Heiden M, Buchholz U: Modellierung von Szenarien der SARS-CoV-2-Epidemie 2020 in Deutschland | DOI 10.25646/6571.2

[2] Shi Zao et al., Preliminary estimation of the basic reproduction number of novel coronavirus (2019-nCoV) in China, from 2019 to 2020: A data-driven analysis in the early phase of the outbreak, Internat. J. Infect. Diseases 92 (2020) 214 - 217