The Worst Model in History: How the Curve was not Flattened

"Flattening the Curve" was an incredibly successful meme during the early stages of the Covid epidemic. Unfortunately, it was based on a model that we can describe as the worst ever proposed in history (or maybe the second worst, after the one that assured Napoleon that invading Russia in Winter was a good idea). Here, I explain why the model was so bad, and I also include a discussion on whether climate change models might suffer from the same problems.  

You may have heard the quote, "all models are wrong, but some can be useful." It is true. But it is also true that wrong models can be misleading, and some can be lethal. In history, some of these lethal models were fully believed ("let's invade Russia, what could go wrong?), while the lethal consequences of following some current models are still not understood by everyone ("economic growth can continue forever, why not?"). Other models are telling us of the lethal consequences of not following them; it is the case with climate models. There are many kinds of models, but you can't deny that they are important in determining human actions. 

In this post, I'll discuss the model that gave rise to the concept of "Flattening the Curve" at the beginning of the Covid-19 epidemic. It was based on the idea that "non-pharmaceutical measures" (NPIs) would slow down the diffusion of the virus and avoid overloading the healthcare system. It was one of those models that looked good at the beginning, but that turned out to be a disaster. Among other things, it gives us a chance for a critical examination of climate models: could they suffer from the same problems? 

About the "Flattening the Curve" story, this idea of slowing down the diffusion of a viral infection was not wrong in itself. For millennia, people had noted that many illnesses were transmitted from person to person and that staying away from sick people could reduce the chances of infection. But country-wide lockdowns, universal masking, and the like had never been tried before. So how would you know that they could have a significant effect? 

Indeed, before the great Covid scare, the general opinion among practitioners and experts was that quarantines and other drastic measures were counter-productive, if not completely useless. Then, in early 2020, a new concept burst into the scene and took the memesphere by storm: "Flattening the Curve." It was expressed in the form of a graph that appeared over and over on the media in slightly different forms, but always showing the same concept. Here is an example among the many.

Image from "The New York Times," 2020,

Let's start by noting that the model is based on the typical shape of the curves describing an epidemic cycle. It occurs when something grows (e.g., a virus) by exploiting a resource (e.g., human beings). If the resource is limited, as is the case for the number of people that can be infected, then the growth of the infection will start slowing down, reach a maximum, and then decline. The result will be a "bell-shaped" curve, a behavior that has been known from the time of the Great Plague of London in the mid-17th century. (note, incidentally, that epidemic curves do not normally show the "Seneca Effect," that a faster decline in comparison to growth. It is because the system is relatively simple, and viruses are not affected by "pollution"). 

So, the "Flattening the Curve" model was based on something real; nevertheless, it had enormous problems. Take a careful look at the figure above. The model implies no less than two separate miracles. The first is that the "zero" of the x-axis is supposed to coincide with the "first case." It implies that, miraculously, the government would be so farsighted to decide to lock down a whole country on the basis of a single observed case or just a few. Such a government never existed, and you may argue that it cannot exist in the real world. In practice, NPIs were mandated only when the epidemic was well on its way and fast growing. Note also how the "Protective Measures" curve touches exactly the limit of the healthcare system's capacity without overcoming it. How the measures could be calibrated so precisely is another miracle. 

The need for two miracles is bad enough for a single model, but there is a much worse problem with it: the model shows two curves with the same shape; they differ only in scale, a parameter that cannot be reliably determined in the early phases of an epidemic cycle. Then, of course, in the real world, the epidemic will follow only one of the two curves, and how do you know which one? In other words, how do you know if the measures are having any effect? Remarkably, the question was almost never publicly asked during the epidemic. The "flattening the curve" model soon became a political issue and, in politics, there are questions that you are not allowed to ask. 

So, let me try to step out of politics and use science to ask a forbidden question: how would the curve react to the "measures" applied while the curve has already started to grow? Everybody expected an effect, of course, and, obviously, a strong effect if it had to be worth the effort. Tomas Pueyo correctly used the term "the hammer" to describe the expected effects of NPIs (one of the very few correct observations he ever made). And if you hit something with a hammer,  you do expect some immediate effect. But what kind of effect, exactly? 

In a previous post, I described a simple SIR (sane, infected, removed) epidemic model, not a sophisticated model but several steps higher on the scientific scale than a purely qualitative two-curve diagram. The model can be easily tweaked to show the effects of a sudden reduction in the transmission factor (Rt) of the infection as a result of NPIs (note that it doesn't apply to vaccines, which can only be introduced gradually). Below, you see a typical result of my calculations. 

The vertical axis is the infected fraction of the population (the "prevalence"), which should be proportional to the number of measured positive cases. The horizontal scale is the time; a typical epidemic cycle lasts a few months. The graph is roughly modeled on the Italian case in early 2020, and it assumes that the "measures" are mandated on the 20th day of the start of an infection cycle that lasts a few months. The model assumes that the NPIs reduce the infectivity (Rt) of the virus by 50% (as it was commonly expected to happen). 

The result is that the slope of the prevalence curve changes when the NPIs are put in place. You can play with the parameters in different ways, but, for a significant decrease in the virus transmission rate, you will always see a discontinuity in the curves in correspondence to the start of the measures. NOte also that there is a certain latency time before a contact with an infected person will lead to a positive result to a PCR test, but for Covid this latency is estimated as of a few days, no more than five. The effect of the latency time will be to smooth the transition, but the change of slope should remain detectable. Overall, this is what the real "flattening the curve" should look like.

Of course, there exist much more sophisticated epidemiological models, but good modelers know (or should know) that complicated models are not necessarily better than simple ones. Here I don't want to enter into the academic debate on the effect of NPIs (it never reached policymakers and the public, anyway). Just as a quick note, you may wish to take a look at this 2020 paper. It was published by the group led by Neil Ferguson at the Imperial College in London, who was one of the main proponents of lockdowns. The authors argue that lockdowns were effective, but, if you examine the paper carefully, for instance, looking at fig. 2 of the extended results, you'll see that their own results do not support their conclusions. (and I am not the only one who noted the problem).

But rather than going into the details of complicated models, let's just use common sense. The NPIs are a sudden change in the parameters of the system. When the government orders people to stay locked at home, most of them do that immediately. So, you do expect an immediate effect on the shape of the epidemic curve. The problem is that you don't see anything like that in real-world data. Below, the case of Italy in 2020. NPIs were enacted on March 9th, when the curve had reached about 25% of the peak. The curve continued to grow along the same trajectory for 19 days more. 

Italy is just one case. Maybe, if you are a real first-class sleuth, you might find some cases where you can evidence a discontinuity in an epidemic curve in correspondence with the NPIs being enacted. But we have hundreds, probably thousands, of examples, and they are almost always smooth, except for the unavoidable random noise. The conclusion can only be that if the NPIs had an effect, it was very small. Incidentally, these observations are consistent with the recent Cochrane Review that used different methods to examine the effectiveness of face masks and other NPIs in slowing down the diffusion of viruses. No detectable effects were found. 

In the end, more than two years of "measures" were imposed on citizens on the basis of a model that implied miracles and didn't include methods to verify the effect of the recommended actions. The damage done to society was enormous in psychological, economic, and human terms, all for effects that turned out to be so small not to be measurable. We are still reeling from the disaster, and it may take several more years before we completely recover -- if we'll ever recover. 

The question, then, becomes how it could be that almost everyone in the world was completely overtaken by such a bad model -- possibly the worst one ever developed in history? It is a story related to the military implications of epidemics as bioweapons, but I'll tell it in a future post. 

The Age of Exterminations: How to Kill a Few Billion People

Bill Gates has been accused of having publicly declared (*) his intention to exterminate billions of people in order to reduce overpopulation. It is not true; Gates never said anything like that. Unfortunately, though, that doesn't mean we can rule out that some powerful elites are actually planning mass exterminations. It has already happened in the past, there is no reason to think that it won't happen again. The problem is not with overpopulation itself, but with the concept of "utilitarianism" that empowers the elites to take action without being bound to moral principles. We saw it happening with the Covid pandemic. We must rethink our implicit assumptions if we want to avoid even worse disasters in the future. 

With 8 billion people alive on Earth, it is reasonable to believe that the planet is becoming a little crowded and that life would be better for everyone if there weren't so many people around. But we should not neglect the opposite opinion: that we have resources and technologies sufficient to keep 8 billion people alive and reasonably happy, and perhaps even more. Neither position can be proven, nor disproven. The future will tell us who was right but, in the meantime, it is perfectly legitimate to discuss this subject.

The problem is that we don't have a discussion on population: we have a clash of absolutes. The position that sees overpopulation as a problem has been thoroughly demonized over the past decades and, still today, you cannot even mention the subject without being immediately branded as a would-be exterminator. It happened to Bill Gates, to the Club of Rome, and to many others who dared mention the forbidden term "overpopulation." 

The demonization is, of course, a knee-jerk reaction: the people who propose population planning would be simply horrified at being accused of supporting mass exterminations. But note that there is a real problem, here. Exterminations DID happen in the recent past, and they were carried out largely on the basis of a perceived overpopulation problem. During the Nazi era in Germany, the idea that Europe was overpopulated was common and it was widely believed that the "Lebensraum, the "living space," available was insufficient for the German people. The result was a series of exterminations correctly considered the most heinous crimes in human history. 

How was that possible? The Germans of that time were the grandfathers of the Germans of today, who are horrified at thinking of what their grandparents did or at least did not oppose. But, for the Germans of those times, killing the Untermenschen, the inferior races, seemed to be the right thing to do, given the vision of the world that was proposed to them and that they had accepted. The Germans fell into a trap called "utilitarianism." It is one of those principles that are so embedded in our way of thinking that we don't even realize that it exists. But it does, and it causes enormous damage. 

In principle, utilitarianism wouldn't seem to be such a bad idea. It is a rational calculation of the consequences of taking or not taking a certain action based on generating the maximum good for the maximum number of people. So defined, it looks both sensible and harmless. But that's the theory. What we have is a good illustration of the age-old principle that "in theory, theory and practice are the same thing. In practice, they are not." 

For a good illustration of the problems with utilitarianism in our current society, you can read an excellent post by Simon Sheridan. A typical example of the basic feature of utilitarianism is the diagram in the figure. 

In this case, the choice looks obvious. You act on the lever to direct the trolley to the track where it causes a smaller number of victims. Easy? Not at all. The example is misleading because it assumes you know the future with absolute certainty. In the real world, there is no such thing as certainty. There exists such a thing as a "fog of life," akin to the "fog of war." Just like no battle plan survives contact with the enemy, no Gannt chart survives contact with a real calendar. And, if you made a mistake in your evaluation, you may direct the trolley along the wrong path.

A good example of the damage caused by utilitarianism is the recent Covid pandemic. To refresh your memory, take a look at this 2020 post by Tomas Pueyo, which was one of the starting points of the disastrous ideas of "flattening the curve" and "Covid zero." On the basis of models that predicted millions of victims caused by the virus, a series of measures were proposed and then implemented. They were supposed to be both short-lived and harmless, at most a minor inconvenience: lockdowns, social distancing, face masks, and the like.  

I don't have to tell you that all the assumptions at the basis of these ideas turned out to be wildly off the mark. The pandemic was much less deadly than the models said it would be. The "flattening of the curve" just didn't happen despite the measures lasting more than two years instead of two weeks. "Covid zero" turned out to be not just a dream but a nightmare. Finally, the measures were far from harmless (for instance face masks positively harm health). The psychological damage was immense, especially to children, with people deprived of their jobs, their social life, and even the possibility of comforting their sick relatives. And people died as a result of depression and lack of proper medical care. Just as an example, Sheridan reports that "two infants in South Australia needed to be flown interstate for life saving surgery but were denied because the borders were closed due to covid. They died." This was real damage done to avoid possible damage. A classic case of misfiring utilitarianism: the trolley was directed along the wrong path. 

Now, back to overpopulation, we are in a similar situation but more dramatic. We have models telling us that a combination of resource depletion and pollution (especially in the form of climate change) could lead not just to millions of victims, but billions. If the models are right, what do we do? Unfortunately, if you really believe that billions are going to die if nothing is done, then you could make the case that killing a few billion people now would save more billions later. It is the same logic of the trolley dilemma, aka, "we had to destroy the village in order to save it."

Would you bet that, today, nobody in the higher spheres of power is thinking about something like that? That is, can you rule out that someone is planning to exterminate a few billion people in order to "save humankind?" Go back to the history of the exterminations planned and carried out by the German Nazi government and you'll see that this idea is not so farfetched. During the pandemic, the "anti-vaxxers" were singled out, insulted, isolated, demonized, fired from their jobs, and more. Just like the German Jews in the 1930s. Fortunately, the animosity against the anti-vaxxers seems to have fizzled out before it could evolve into a mass extermination. But it was clearly heading in that direction, and we don't know whether it could pick up steam again in the future. 

The problem is not whether the models are right or wrong. Models can be extremely useful if you understand their limitations. But if you use models as oracles, then doom is guaranteed. That's exactly what happened with the Covid pandemic. Is it the same for the world models that predict humankind's doom. Are they right or wrong? The answer is simply "we cannot be sure." They might be completely wrong or perfectly right, or even too optimistic. But you should never ignore the models. They are not oracles, they are maps of the future. A good map tells you about the roads that lead you where you want to go, but it is up to you to choose the one to follow.

So, how do you avoid misusing the models? You need to approach them differently. There is an alternative to utilitarianism. It is called "personalism." It is both a religious and a philosophic stance that sees the human person as sacred, the basic value, not exchangeable with anything else. It is the principle of "First do no Harm" ("primum, non nocere") that we derive from the Hippocratic Oath. 

Personalism doesn't mean that you can do nothing against emergencies, but blind faith in science must be tempered with moral sense and the capability of understanding the value of the human person. If you are in a condition of uncertainty, then try at least not to worsen the situation by taking hurried and unproven measures. It is a point forcefully made by Dr. Malcolm Kendrick in a post titled, "Don't just do something, stand there!" His point is that physicians are often overtreating their patients in their hurry to "do something." And they may do more harm than good. 

In his post, Kendrick proposes to apply to medicine the OODA principle: Observe, Orient, Decide, Act. It is not philosophy. it is "a practical concept designed to function as the foundation of rational thinking in confusing or chaotic situations". It was developed by the Air Force Colonel, John Boyd. It means that you refrain from acting until you have at least a certain degree of understanding of what happens. It is the military equivalent of the medical principle "do no harm." OODA is a good idea, but it can be interpreted in various ways. It is the same problem we have with the "Precautionary Principle" -- it may be interpreted in terms of avoiding rash decisions, but also in the opposite way (**). Personalism, instead, has a deeper relevance and is less ambiguous. If you say that life is sacred, then it is. 

Applied to the Covid pandemic,  the approach based on personalism (and maybe on OODA as well) would have avoided drastic and harmful actions taken in a moment of great uncertainty. Sick people would have been cured, but those who were not sick would have been left in peace. Vaccination would have been recommended, but not made mandatory. It was done in Sweden, which didn't suffer more damage from the virus than countries that, instead, took a drastic approach to the pandemic. 

How about climate change? In this case, the risk is not just millions of victims, it is truly "existential." That is, the climate tipping points might well kill us all. Even without tipping points, we have plenty of negative effects ongoing. Droughts, sea acidification, seawater rise, melting ice, extreme weather, and more. This said, it is also clear that the system we are modeling is hugely complex and hard to predict. We have no idea of when, where, and how fast, a climate tipping point could manifest itself, despite the dull certainty of people who define themselves as believers of the "near-term extinction" concept. Humans may well go extinct in a non-remote future, but there is no reason to hurry up in that direction.

In a personalistic framework, we deal with climate change by applying the "do no harm" principle. It means first of all avoiding panic. There are hasty actions against climate change whose consequences are unknown and could cause more harm than good. Apart from mass exterminations (obviously!), geoengineering or CO2 capture and storage are good examples of potentially disastrous "solutions" which might not be such. Then, "do no harm" does not mean "do nothing." It means taking actions that we believe are effective, but also that we are reasonably sure are not harmful. 

For instance, assuming (as it is very probable) that fossil fuels are an important factor causing climate change, we should make sure that phasing them out doesn't harm people. A lot of people, everywhere, are living at the edge of survival, and forcing them to stop using fossil fuels without offering substitutes is tantamount to killing them. They need alternatives: efficiency, PV panels, wind turbines, and the like. Think also of "degrowth," is it a good idea? Not for those living at the edge of survival: asking them to degrow means, again, killing them. (***)

So, should we also do something to reduce population growth? Why not, as long as we don't harm anyone? The Chinese government did that with the "one-child" policy. You may argue that it was not a good idea, and also that it didn't work. But it is also true that nobody was killed and nobody was harmed. The policy may have been the main factor that contained the Chinese population to manageable levels. (I told the story in some detail in a previous post). Population planning at the world level could be a good way to stunt the action of those evil people who may be planning to obtain the same results by means of mass exterminations. 

Unfortunately, given the way the pandemic was managed, it is perfectly possible that we will soon go into "panic mode" about climate change. That may well lead humankind to make truly horrible mistakes. But this is the way humans are. Maybe one day we will learn, but that will take time.  

______________________________________________________________________ 

An excerpt from Sheridan's post about utilitarianism and its disasters. Read the whole post on his blog.

Many people could recite the most basic formula of Utilitarianism: the greatest good for the greatest number. Utilitarianism is a form of what is sometimes called consequentialism which just means that the ethical value of actions should be judged by their consequences. If you, purely by accident, blundered your way into creating the greatest good for the greatest number, your action is deemed of higher value than if, with the best of intentions, you failed to create anything good.

Now, of course, Utilitarianism is a big topic and there are numerous sub-variants which are attempts to answer the objections made to the doctrine. Probably the main objection has always been that Utilitarianism implies that killing an innocent is justified if it saves the lives of others. This is one of those classic arguments that always seems confined to university faculties at universities and can usually be counted on to draw the cynical response that it’s “just semantics” and “nobody would ever have to make that decision in real life.”

Well, during the last three years, exactly these kinds of decisions were made. To take just one of the more egregious examples, here in Australia two infants in South Australia needed to be flown interstate for life saving surgery but were denied because the borders were closed due to covid. They died. The justification given, not just by politicians but by everyday people on social media, was the utilitarian one: we couldn’t risk the lives of multiple other people who might get infected with a virus. The greatest good for the greatest number.

(This raises the other main objection to Utilitarianism which is that it must rely on speculative reasoning. We can only predict more people will die based on some model. But we can never know for sure because, despite what many people apparently believe, we are not God and we do not control the future).

The death of those children was a low point even for the corona hysteria and is, in my opinion, one of the lowest points in this nation’s history. Combined with the countless other episodes of people being denied urgent medical care, the elderly residents of nursing homes left without care for days because one of the staff tested positive and all the staff were placed in quarantine, the people unable to be at the side of loved ones who were on their death bed, the daily cases of police brutality, or any of the other innumerable indignities and absurdities, for the first time ever I found myself being ashamed to call myself an Australian.

(*) Publicly expressing one's evil plans is a typical trope of modern fiction. It is called the "badass boast." It shouldn't be needed to say that this is not something that happens in the real world but, strangely, many people seem to believe that it does. For instance, Osama bin Laden is commonly believed to have confessed his role in the 9/11 attacks in New York in a videotape.

(**) About how the precautionary principle could have been correctly applied to the Covid pandemic, there is an interesting paper by Vianna Franco et al. -- highly suggested.  

(***) That degrowth or "zero-growth" is not a good idea was clearly understood by Aurelio Peccei, the founder of the Club of Rome, already in the 1970s, See this post on the subject on "Cassandra's Legacy."

The Seneca Effect: why decline is faster than growth

__________________________________________________________________________________________________________

Originally published on "Cassandra's Legacy" on Aug 28 2011

"It would be some consolation for the feebleness of our selves and our works if all things should perish as slowly as they come into being; but as it is, increases are of sluggish growth, but the way to ruin is rapid." Lucius Anneaus Seneca, Letters to Lucilius, n. 91

Don't you stumble, sometimes, into something that seems to make a lot of sense, but you can't say exactly why? For a long time, I had in mind the idea that when things start going bad, they tend to go bad fast. We might call this tendency the "Seneca effect" or the "Seneca cliff," from Lucius Annaeus Seneca who wrote that "increases are of sluggish growth, but the way to ruin is rapid."

Could it be that the Seneca cliff is what we are facing, right now? If that is the case, then we are in trouble. With oil production peaking or set to peak soon, it is hard to think that we are going to see a gentle downward slope of the economy. Rather, we may see a decline so fast that we can only call it "collapse." The symptoms are all there, but how to prove that it is what is really in store for us? It is not enough to quote a Roman philosopher who lived two thousand years ago. We need to understand what factors might lead us to fall much faster than we have been growing so far. For that, we need to make a model and see how the various elements of the economic system may interact with each other to generate collapse.

I have been working on this idea for quite a while and now I think I can make such a model. This is what the rest of this post will be about. We'll see that a Seneca cliff may indeed be part of our future if we keep acting as we have been acting so far (and as we probably will). But let's go into the details.