Flattening the curve for the Coronavirus

In order to better understand the development of the Coronavirus pandemic, I decided to do my own statistical analysis. I only considered the number of deaths in various countries, as this number is probably more reliable than the number of infections. I then made the assumption that this number grows exponentially, but that the coefficient of growth changes linearly with time:

Simple model for the number of deaths N(t). The exponent α(t) is assumed to change linearly with time.

It is now possible to make a simple fit for each country and to estimate when the curve will flatten and the number of deaths will stop increasing.

I was surprised how well it worked. Below is the result for Italy

Number of deaths from the Coronavirus in Italy

The analogous plot for Switzerland looks as follows

Number of deaths from the Coronavirus in Switzerland

Unfortunately, the United States is not even close to flattening the curve

Number of deaths from the Coronavirus in the United States

It is now possible to compare different countries both in terms of actual deaths

or in terms of the fitted curves

The curves tell us an important message: If strict measures are implemented to stop the spread of the virus, this actually helps. It is the only thing we can do at the moment.

As public service, I have made the Python script for the analysis available. It automatically downloads the data from the Center for Humanitarian Data, performs the analysis and plots the data.


Here is a scientific study of the efficacy of different measures from Imperial College: Estimating the number of infections and the impact of nonpharmaceutical interventions on COVID-19 in 11 European countries.

Here is a useful tool for a more detailed analysis of the disease from the University of Basel: https://neherlab.org/covid19/

BTW, there is a good reason be be wary of exponential growth, as this delightful video shows:

When to Pull the Emergency Brake?

Important announcement: COVID-19 is a deadly and extremely contagious disease, which will kill hundreds of millions of people unless we manage suppress it. Please cooperate with the authorities, follow the instructions from health professionals, and avoid unnecessary contacts with other people. Social distancing is important!

The actions currently being taken worldwide to stop the spread of the coronavirus can best be compared to pulling the emergency brake on the world economy. Interestingly, the same governments that refused to sacrifice even the tiniest amount of economic growth to save the environment, are suddenly prepared to implement a complete lockdown of public life, costing trillions of dollars and causing a global recession. It is important to understand why.

The argument for implementing drastic measures against the coronavirus is compelling: If we fail to stop the spread of the virus early, we will lose control of the situation and there will be nothing left to decide. Even if stepping on the brake now will not necessarily solve the problem, it might at least buy us some time to think about what to do next. Currently, it is not clear whether the spread of the virus can be contained.

The same argument can be made for stopping global warming and environmental destruction. If we wait until the polar caps have melted and a large amount of species have gone extinct, there will be very little left to decide. At that point, we will run out of sensible options and will simply be struggling to survive by reacting to disasters as best as we can. It would make a lot more sense to act now.

One important difference between the coronavirus and global warming is the time scale. People are dying from the virus today and the full extent of the disaster will become obvious within a couple of months. This makes the problem politically relevant. With climate change, most people have the feeling that the problem is not urgent and that we still have plenty of time to act.

Bengt Ekerot and Max von Sydow in The Seventh Seal by Ingmar Bergman

Unfortunately, I believe that there is a more fundamental reason for our different reactions to climate change and the coronavirus: a primeval fear of death. Most people are concerned about the future of their children, but they are simply terrified by the idea of contracting a deadly virus. It is difficult to think rationally in the face of death.

The global pandemic caused by the coronavirus will be over in 1-2 years. Despite the current drop in greenhouse gas emissions, the struggle to stop climate change and to decarbonize society will have to continue. Whether we like it or not, society’s response to Covid-19 offers some important lessons for the future:

  • People a mainly motivated by fear.
  • Drastic political measures are possible in the case of an emergency.
  • If scientific models give you early warning of an impending disaster, it makes sense to act quickly and decisively.
  • Never listen to economists when they talk about global challenges.

Less than two weeks ago, some economists were still warning against spending too much money on fighting Covid-19. Apart from the fact that no economist has ever understood exponential growth, they always seem to overestimate their ability to predict the economic consequences of disruptive developments. It simply does not make sense to extrapolate if the entire society sinks into chaos and anarchy.

Unfortunately, this phenomenon is all too familiar in climate politics. When William Nordhaus claims to be able to predict the economic consequences of 4°C of global warming, he is either mad or almost criminally ignorant. We all know that the uncertainties in such a prediction are large enough to render it meaningless. Nonetheless, it serves as a convenient excuse for inaction.

The economy emerging from the coronavirus pandemic will have to be much more sustainable and resilient than the one we have today. This will not be possible if we only focus on maximizing GDP.


PS: If you really want to understand exponential growth, here is an excellent cartoon.

Leben in Zeiten des Coronavirus – danke liebe Jugend.

Gestern erreichte mich ein Aufruf zur Nachbarschaftshilfe, der mich sehr berührt hat. Da im Moment keine Klimastreiks oder andere Aktionen durchgeführt werden können, überlegen sich die jungen Klimastreikenden, wie sie den Alten und Schwachen der Gesellschaft helfen können. Das Besondere mit dem Coronavirus ist ja, dass es für junge gesunde Menschen praktisch keine Gefahr darstellt. Somit macht es Sinn, wenn sie z. B. die Einkäufe der Alten erledigen.

Ist dies selbstverständlich? Diejenigen, die von der Klimaerwärmung am stärksten betroffen sein werden, zeigen ihre Solidarität mit der Generation, die das Problem verursacht hat. Der Homo oeconomicus würde anders handeln und das Coronavirus als Chance sehen, sich Vorteile zu verschaffen oder die Politik zu erpressen. Die Jungen sind aber nicht zynisch genug, um dies zu tun.

Es gibt eine interessante Parallele zwischen der Klimaerwärmung und der Verbreitung des Coronavirus: Politisches Zögern ist in beiden Fällen tödlich, wie Elizabeth Sawin in einem Tweet schön gezeigt hat.

https://twitter.com/bethsawin/status/1238095987211751425

Der Grund dafür ist, dass beide Prozesse eine Eigendynamik besitzen. Bei der Verbreitung einer Grippe ist die Anzahl Neuansteckungen proportional zur Anzahl der Kranken (exponentielles Wachstum) aber der Wachstumskoeffizient ist davon abhängig, wie viele Menschen noch angesteckt werden können. Wenn eine kranke Person im Durchschnitt 1.3 andere Personen ansteckt, fangen die Fallzahlen dann an zu sinken, wenn 25% der Bevölkerung Immunität entwickelt hat, da 1.3×(1-0.25)<1. Wenn stattdessen im Durchschnitt 2.3 Personen angesteckt werden, müssen zuerst 60% der Bevölkerung krank werden, bevor die Ansteckungskurve abflacht.

Das Problem mit dem Coronavirus ist, dass es viel ansteckender und viel tödlicher ist als das normale Grippevirus. Dies führt dazu, dass mehr Menschen krank werden und viele davon sterben. Wenn zu viele Menschen gleichzeitig krank werden, nimmt die Mortalität zusätzlich zu, da die Spitäler nicht mehr in der Lage sind die Kranken zu behandeln. Dieser Zustand ist in Italien schon eingetreten und es ist wohl nur eine Frage der Zeit, bis andere Länder so weit sind. Dies wäre dann der Kipppunkt (tipping point) der Pandemie: Endliche Ressourcen und exponentielles Wachstum vertragen sich schlecht.

Eine sehr gute Zusammenfassung der Gefahren des Coronavirus ist hier zu finden: Coronavirus: Why You Must Act Now. Den Artikel gibt es auch in deutscher Übersetzung.

Ohne drastische Massnahmen gegen das Coronavirus, werden viele alte Menschen sterben. Wenn wir nichts gegen die Klimaerwärmung unternehmen, werden noch mehr junge Menschen sterben. Worin liegt der Unterschied? Nur darin, dass die Alten mehr politisches Gewicht haben und die katastrophalen Wirkungen des Coronavirus innerhalb einer Legislaturperiode sichtbar werden.

Die Coronapandemie wird wohl in 1-2 Jahren vorbei sein. Es ist zu hoffen, dass der Begriff Solidarität etwas länger in Erinnerung bleibt.


Hier ein interessanter Artikel zu unserem Umgang mit Klimaerwärmung und Coronavirus.

Global Climate Compensation

Deutsche Version (English translation below)

Können wir die Klimakrise bewältigen? Die Antwort lautet ja, und es würde etwa $1.30 pro Kopf und Tag kosten. Dies ist weniger als eine Tasse Kaffee.

Das Problem ist nur, dass sich nicht alle Menschen auf der Welt so viel Geld haben. Die Wohlhabenderen müssen also bereit sein, den Ärmeren zu helfen.

Fast 30 Jahre nach der Unterzeichnung der Klimakonvention der Vereinten Nationen (UNFCCC) gibt es immer noch keinen praktikablen Plan, wie die Erderwärmung auf weniger als +2°C begrenzt werden kann, und die CO2-Konzentration der Atmosphäre steigt immer schneller an. Zusammen mit einigen Kollegen versuche ich deshalb einen Plan auszuarbeiten, um das Problem im Griff zu bekommen. Die Details dazu finden Sie hier: www.global-climate-compensation.org.

Ich meine dies ernst. Das CO2-Budget für +1.5°C Erderwärmung werden wir in weniger als 8 Jahren ausgeschöpft haben. Die Weichenstellung für eine bessere Zukunft muss also in den nächste 1-2 Jahren passieren. Nach COP25 in Paris und der Rede von Donald J. Trump in Davos bin ich der Meinung, dass die Reichen und Mächtigen versagt haben.

Melden Sie sich also bei mir, wenn sie an der Idee der globalen Klimakompensation mitarbeiten wollen. Das Problem können wir nur gemeinsam lösen. Das erste Treffen findet am 31. Januar 2020 in Zürich statt.

English Version

Can we overcome the climate crisis? The answer is yes, and it would cost about $1.30 per person per day. This is less than a cup of coffee.

The only problem is that not everyone in the world has that amount of money. The affluent must be willing to help the poor.

Almost 30 years after the signing of the United Nations Framework Convention on Climate Change (UNFCCC), there is still no workable plan to limit global warming to less than +2°C and the CO2 concentration in the atmosphere is rising faster than ever. Together with some colleagues, I am therefore trying to work out a plan to get the problem under control. You can find the details here: www.global-climate-compensation.org.

I’m serious about this. We will have exhausted the CO2 budget for +1.5°C global warming in less than 8 years. The course for a better future must therefore be set in the next 1-2 years. After COP25 in Madrid and Donald J. Trump’s speech in Davos, I believe that the rich and powerful have failed.

So, get in touch with me if you want to work on the idea of global climate compensation. We can only solve the problem together. The first meeting will be in Zurich on January 31, 2020.

Amusing Themselves to Death in Davos

[…] the commercial always addresses itself to the psychological needs of the viewer. Thus it is not merely therapy. It is instant therapy. Indeed, it puts forward a psychological theory of unique axioms: The commercial asks us to believe that all problems are solvable, that they are solvable fast, and that they are solvable fast through the interventions of technology, techniques and chemistry.

Neil Postman, Amusing Ourselves to Death

Next week, the rich and powerful will again gather to do business at the World Economic Forum in Davos. Such fairs are known since the Middle Ages and have always be accompanied by spectacle, acrobats, artists, and prostitutes. On this level, very little seems to have changed.

To refer to the attendees of the WEF as the “global elite” is clearly unwarranted, since wealth and power are no personal traits. Every idiot born as the heir to the throne is powerful and it does not take brains to inherit a fortune. There is no evidence for the WEF participants being intellectually or ethically superior to the rest of us.

I don’t know many people at the WEF, but I am sure that most of them are nice and would have been perfectly harmless in a normal environment. However, with power and wealth comes responsibility and I would therefore like to offer them some reading advice.

The first book they need to read is The Affluent Society, written by the eminent economist J. K. Galbraith in 1958. His main message is that the capitalist system, which was invented to raise the capital required for industrialization, does not make sense in a society where all material needs have been met. Why increase industrial production, when we already have everything we need? In the affluent society, the manufacturer creates the demand for a product through marketing. It is therefore not surprising, that two of most powerful companies in the world today – Google and Facebook – are advertising companies. Such a situation was clearly not envisioned by Adam Smith. In short, capitalism became obsolete more than 60 years ago.

The second book is Amusing Ourselves to Death by Neil Postman, which deals with the effects modern media has had on our ability to reason and discuss. As the book was written in 1984, his analysis is limited to television, but the invention of the internet and social media has only exacerbated the trend. Anyone brought up on visual media has the feeling that any topic can be treated in less than 60 seconds in an entertaining manner. If the news does not amuse me, I switch to a different channel. Nobody would have listened to Winston Churchill’s speeches, had there been a quiz show running on a different channel. “We will fight on the beaches, but only if we get the chance to win a trip to Las Vegas”.

Finally, you might consider reading The Collapse of Complex Societies by Joseph A. Tainter. He starts from that fact that all complex societies have failed sooner or later. The reason was always the diminishing return on investments in complexity. At one point, the costs of maintaining a complex infrastructure exceeds the income generated by it, which leads to a collapse. Incidentally, Swiss ski resorts are perfect examples of this phenomenon. Despite the fact that global warming will destroy winter tourism, the ski resorts invest increasing amounts of money in equipment for artificial snow. Eventually, the revenue will be insufficient to maintain the expensive infrastructure and there will be no resources left to dismantle it. Thus, ruins are formed.

Which brings us to Davos. The diagram below shows the average temperature in Switzerland for almost 160 years. The WEF was founded in 1971 and has been running for 50 years. If it continues for another 50 years, there will be no snow left in Davos. This is not a political statement, but a simple fact.

The interesting question is whether the WEF has the intellectual flexibility and the courage to face the truth about what is happening to our planet and what needs to be done about it. I am skeptical, since – as Einstein pointed out – it is difficult to solve problems using the same kind of thinking that lead to their creation.

In fact, I believe that the people gathering at the WEF are almost uniquely unqualified to solve the problems facing humanity today. Most of them are marketing experts (including the politicians), who have made a career out of catering to people’s desires for pleasure and fun rather than to their needs. The people who actually understand how the real physical world works, i.e. the climate scientist, the renewable energy expert, the biologist, or even the historian or political scientist, are not welcome. If they do get invited, they are paraded like exotic zoo animals in discussion forums designed not to accomplish anything. In today’s world, the inmates are running the asylum and the arsonists are responsible for fire safety.

The plot below shows the correlation between global energy demand, global carbon emissions, and global GDP during the last 50 years. Unfortunately, economists are not very careful with error estimates, which made it impossible for me to add error bars. Nonetheless, it seems clear that these three quantities are essentially the same.

If we want to lower carbon dioxide emissions by at least 7.6% annually in order to stay below 1.5°C of warming, we also need to reduce energy demand and GDP. It is simply impossible to lower global emissions quickly using new technology, as any investment in renewable energy or energy efficiency has a certain payback time. It takes at least two years for a solar panel to generate the energy needed to produce it. In other words, investments in renewable energy will initially lead to more emissions and not less. This is not an argument against renewable energy, but one cannot ignore basic laws of physics and common logic. Some more unquestionable facts can be found in the public lecture I gave at the ETH in Zurich: You Can’t Have Your Planet And Eat It.

When Galileo was sentenced by the Inquisition in 1633, it was because he threatened the church’s monopoly on The Truth. Likewise, the financial sector and the fossil fuel industry feel threatened by the facts of global warming. To quote Bertrand Russell: “The Inquisition was successful in putting an end to science in Italy, which did not revive there for centuries.” The participants of the WEF seem determined to put an end to humanity. This is very annoying, as the very same people could actually stop climate change.


PS (2020-01-21): Apparently, the current resident of the White House did go to Davos. I wonder why. It is obvious that he has not read any of the books listed above.

BTW, I am not the only one upset with the WEF. Here some other comments: