Complicated Mathematical Models Are Not Substitutes for Common Sense

A man walks along Third avenue in Brooklyn N.Y., March 26, 2020. (Stephen Yang/Reuters)

Uncertainty still reigns, so prepare for the worst. A lockdown would be prudent, not the end of the world.

As of today, half of mankind is confined at home because of the coronavirus pandemic, although the severity of the confinement varies greatly depending on countries and regions. This situation must be all the more disconcerting given that, less than a month ago, many government officials and public-health experts were still claiming that Western countries would be able to weather the storm without any difficulty and encouraging people not to change their behavior because of the virus. On that point, Trump’s handling of this crisis has been atrocious, but as Zeynep Tufekci recently pointed out, he’s hardly the only one to have underestimated the seriousness of the threat.

Although I think people underestimated the seriousness of the threat until recently, many now seem to underestimate how much uncertainty there is about what is going to happen. To be clear: No matter where we are headed exactly, this is no flu. As of March 29 in France, 2,606 people who tested positive for COVID-19 had died in hospitals alone. Perhaps even more worrisome, there were already 4,632 people in intensive-care units, up from approximately 1,500 one week earlier. Between the number of people who left intensive care because they had died and those who left because their condition had improved, it means that probably almost twice as many people have already required admission to intensive care since the beginning of the outbreak in France. By comparison, during the entire 2018–19 season, 490 people who had the flu died in hospitals, and 2,915 people required admission to intensive care. Not only are we already way past that with the COVID-19 pandemic, but, even in the most optimistic scenario that I consider plausible, those figures will be at least 15 times higher.

Although it seems clear now that COVID-19 is putting health-care systems around the world under considerably more stress than the flu does, and although I’m strongly in favor of confinement until we know more, I think there is still much uncertainty about exactly how bad the situation is and that people are wrong to assume that this pandemic will kill millions of people. That apocalyptic prediction found strong support on March 16, after a team of prestigious epidemiologists at Imperial College London published a paper on their simulations of the epidemic. Their simulations undermine the strategy of curve-flattening, which consists of slowing the spread of the pandemic to prevent hospital services from being overwhelmed by the number of cases to be treated without seeking to suppress it completely.

Indeed, according to the results of their simulations, the policies that have been proposed to implement such a strategy would not prevent hospital systems from being overwhelmed even in developed countries: In the best-case scenario, the need for ICU beds would be eight times greater than our capacity. If nothing is done, the death toll would be over 2 million in the United States, and, even in the best-case scenario, policies aimed simply at slowing the pandemic without suppressing it would only halve that figure. The authors of the study therefore conclude that, in order to avoid carnage, trying to mitigate the pandemic would be insufficient and that only a strategy aimed at suppressing it was viable. However, their simulations show that it would then be necessary to remain confined until a vaccine or other pharmaceutical solution became available. That could take more than a year.

The problem is that, as I argue in a very long piece in which I dissected the model in detail, it’s doubtful that we can trust the results of those simulations. In a nutshell, the model used to carry them starts by generating a population of several million individuals (the size varies depending on the country for which we want to simulate the spread of the epidemic) distributed over the territory in such a way as to reproduce the distribution of the population in reality. At each step of the simulation, each corresponding to a period of eight hours in reality, the model calculates the probability that each individual was infected during the period. The probability is based on the people he or she met at work, at home or at school, and in the community and on whether they were infected.

The different policies that can be adopted to fight the epidemic affect the rate of contact between people in each of these environments and, therefore, affect the results of the simulation. The main goal of this exercise was to predict with precision how different combinations of policies would stress the health-care system and affect the eventual death toll. Once a combination of policies has been chosen, one just has to run the simulation for a while to see how the pandemic unfolds over time. The authors of the study ran this simulation several times with different combinations of policies in place to see how each affects the spread of the epidemic. That’s how they arrived at the conclusions I described briefly above.

But as I explain in the piece, it’s unlikely that we can trust the findings of those simulations. Not only could the authors of the study have specified the model in many very different though equally sensible ways, but they also had to make many largely arbitrary assumptions about the value of the model’s parameters. We just don’t know how trying other specifications of the model or how using different values for the parameters would have affected the results. We have no way to know, as the simulations require huge computational resources and are very time-consuming.

For example, the authors of the study make the hypothesis that a policy of confinement would reduce contacts outside the household but increase contacts within the household by 25 percent. But why 25 percent rather than 50 percent or 75 percent? The authors had no reason to choose a value of 25 percent, but they had to choose some value, and, as I have just explained, they could not try every value in the wide range of values that were intuitively plausible. Intellectually I find this kind of model very interesting, but there are far too many degrees of freedom in the specification of the model and in the choice of parameters for this exercise to be really useful for decision-making. In particular, as long as we don’t have the results of a serological study based on a large random sample, which Germany is apparently about to do, it will be hard to know with a reasonable degree of certainty what the infection–fatality rate is and what the ratio of infected people to those who require hospitalization is. The value of those parameters no doubt has a very large influence on the results of this kind of simulation.

As I also explain in my piece, the situation is really very weird. The data we have are difficult to interpret, generally of poor quality and often difficult to reconcile with one another. For example, why do so few people seem to have died of the virus in countries like Germany and Japan, compared with Italy or even Spain and France, when the virus has presumably been circulating in Germany and Japan just as long or even longer? A whole host of theories, some of which I find plausible, have been put forward to explain the inconsistencies, but the truth is that for the moment they remain speculative and we just don’t know. This conclusion, that we are not in a position to know with any degree of certainty what is going on, is consistent with the result of a recent survey of experts, which found that even they didn’t really know what is going to happen.

It’s possible that the number of deaths in countries such as Germany and Japan will soon explode, but it’s also possible that it will stay relatively low. I have no doubt that the coronavirus is intrinsically more dangerous than the flu, but one theory that I personally find quite plausible is that it’s not intrinsically as dangerous as we might have feared — it’s just that we have no vaccine, and so nobody is immune, and that our health systems are more fragile than we might have thought. Consequently, if only a few things go wrong at the beginning of the epidemic, it just takes something a little worse than what we’re used to for the situation to get out of control and turn into a disaster. That would explain why bodies are piling up in Lombardy and in some places in France and Spain, while in many other places the situation seems more or less under control. But this just a theory, and I also wouldn’t be surprised if the virus really were intrinsically much more dangerous than the flu. I think that we will know more in a little while, but for the time being we have to admit this uncertainty.

But this uncertainty is not a reason not to act. The most important point I want to make is that we don’t need complicated mathematical models of dubious epistemic status to prepare for the worst. The economic consequences of locking down everyone are very serious, but if we don’t do it and the worst comes to pass, the consequences will be even more severe, including for the economy. I’m not American, but I think there are enough reasons at this point to fear that something really bad is going to happen unless you take strong measures to prevent it. At the end of a two-week lockdown, you can reevaluate in light of what scientists will have learned by then. If it turns out that the virus is less dangerous than we feared, a lockdown of two weeks will not have been the end of the world, but if the virus really is as dangerous as we fear, you’ll be happy that you did it.

In France, the government waited before making the decision to order a lockdown. Although we also don’t know exactly what is going to happen, I think it’s already clear that we’re going to have to remain confined for longer because we hesitated. The number of people who need to be hospitalized grows faster than linearly, so by waiting to order the lockdown (which presumably will flatten the curve after a while), the government has ensured that, by the time the epidemic reaches a plateau, the hospitals will be fuller than they would otherwise have been. That in turn means that we’ll have to wait longer before it’s safe to relax the lockdown, because, if we do so as soon as a plateau is reached, any influx of patients would immediately overwhelm the hospital system again. I would advise my American friends not to make the same mistake we did.

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