We can read and rethink everything through the Covid crisis: our institutions, our economic dynamics, our ecological and social policies. We can also read contributions from almost all sciences. Much has been said about the role of certain mathematical applications linked to artificial intelligence or tracking. There are also less publicized topics, such as the statistical modelling of epidemic dynamics. Why does this discipline play a decisive role in this crisis today, despite its uncertainties?
When, at theParliamentary Science Officewe embarked on the Covid-19 epidemic, our first task was to analyse and comment on the evolution of the epidemic. Like so many observers around the world, every morning we added a point to the case and death count curves from a panel of countries and observed them. Exponential growth or not? At that time, even among the most recognized health experts in France, there was no consensus as to whether the French curve would follow that of Italy.
The Parliamentary Science Office deals with issues at the interface between science and politics, to help parliamentarians in their choices. The universally recognised quality of its reports, both in France and abroad, has never been a source of significant political and public weight, alas: the same is true of all the French institutions linked to the Scientific Council. One example among others: France's remarkable mask doctrine - remarkable, but not followed over the years - had been elaborated in an OPECST report some fifteen years ago. I have been working for three years to restructure and increase the weight of OPECST: much remains to be done.
At the beginning of our efforts, to illustrate our notes, like others, we had to produce two graphs: one with the Italian curve and one without the Italian curve. The Italian curve hovered so far above the others that, in comparison, the other curves were barely discernible from the abscissa axis; the zoom was a way to distinguish between them. But after a week, there was no need for a separate graph: exponential curves evolve so fast! The European countries other than Italy had taken off, and it had become clear that the French curve followed the Italian curve impeccably, with 8 to 10 days of delay.
To better visualize exponentials, it is a good idea to switch to logarithmic coordinates: on the axis, a displacement of one unit will correspond to a multiplication by 10 (say). We can thus adjust the exponentials in straight lines, whose slopes can be compared.
How do we know we're going to beat VID- 19. minutephysics. You can activate French subtitles via the "settings" button.
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If there is one thing that strikes us, it is, hidden behind the apparent anxiety-provoking deluge of figures, the universal nature of the epidemic's propagation curve. I myself was amazed to see it appear so clearly and visually. Whether in Seoul or Tehran, despite the differences in customs, cultures, housing and medical systems, the epidemic is spreading in exactly the same way. So there would be a model and a mathematical equation that reflects the reality of the epidemic.
Epidemiologists know how to use differential equations for this purpose, such as the famous "compartmentalized models", from the simple SIR model with 3 compartments, up to those used today for the fight against Covid-19, which include a dozen, with a number of parameters to measure interactions and contaminations between individuals, and the famous R₀ parameter, or reproduction parameter - the number of people that an infected individual contaminates, on average. This number is close to 19 for measles, and 3 for COVID... it determines a great deal of information: the dynamics of the epidemic, exponential growth (R₀>1) or extinction (R₀<1), the number of contaminated individuals in the end, the quantity to be vaccinated, and much more. In short, all kinds of questions related to the quantity of infected individuals can be asked and studied.
What is the current contamination rate of the population? For Covid-19, no one knows exactly, but it is thought to be less than 10% in France; research work even suggests that in the highly contaminated area of the Ile-de-France, it would be only 6%. The studies are ongoing and require reliable serological tests, good statistical sampling, rigorous methodology and strong coordination between jurisdictions. Like everything else in this epidemic, this requires a delicate dosage.
When a mathematical parameter becomes a health issue
If herd immunity is not present, and as long as a vaccine is not available, control of the epidemic requires a decrease in the reproduction coefficient R₀, from the natural value (say 3) to a modified value, which we wish to maintain below 1 (epidemic control). Below 1 does not mean that the virus no longer exists, or that contamination is impossible: it means that if a new outbreak occurs, the dynamics of contamination and healing will lead to the disappearance of the outbreak.
And this is how a mathematical parameter becomes a life or death issue for our collective health care system. Until two months ago, world leaders were making fun of this coefficient R₀, but today it is their daily obsession. It has even been made explicit in press conferences by Angela Merkel and Édouard Philippe. On the value of the coefficient depends the growth of the number of cases, and the possible saturation of the system... and it is very sensitive!
"With a coefficient of 1.1 the German health system explodes in October; with a coefficient of 1.2 in July. "(Angela Merkel)
Yes, the value of the coefficient is important... but its measurement is very delicate, and can only be a sort of average value over several days. Estimated between 0.7 and 0.9 last week, it would have fallen between 0.5 and 0.6 in the last few days. But what is at stake is not so much its value during the time of containment as its value after the start of deconfinement. In order to contain R₀, binding measures will have to be maintained.
We must not think that we can get away with it lightly: the universality of the spread, in countries where we kiss easily as well as in countries where we keep more distance, shows that it is not a simple adaptation of behaviour that can do something about it; it is only with real constraints that we can hope to change things!
Sophisticated epidemiological models have a lot of unknowns, which does not scare computers, but also come with a lot of parameters to set. Some of these parameters represent the interactions between individuals, others the probabilities of contamination... It is a great difficulty to fix them, to estimate them, according to experiments, epidemiological studies, technical devices... Do the masks lower R hardly, or a lot? What can be said about isolation procedures, by estimating the proportion that can be identified? What proportion of the measures will be applied in practice? It is a puzzle to decide on all these issues. The best experts will be reluctant to comment on the quantitative value of masks in these equations. Each element comes with its own uncertainty.
Here we are faced with a problem with multiple sources of uncertainty. Frustrating... Of course, different teams have different analyses: it's normal, all scientists know how controversial science is. But it's hopeless for a politician who is looking for a solution to the problem. the a recipe in the scientists' predictions. And yet these efforts are undoubtedly worthwhile. To reduce below 1 a coefficient that has invaded all our lives and is costing us, on a national scale alone, 2 billion euros per day, we must explore all avenues, seize all the tools that will make it possible to predict the evolution of the curve, confront the points of view, and it is impossible to ignore epidemiology.
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We can go further in the diagnosis: at the end of the day, if we agreed, collectively, to shut down the entire economy, it was to preserve the capacity of our health care system, which was at risk of explosion. This does mean that the major indicator that should enable us to judge health policy is the number of people in intensive care. Epidemiology, the only science capable of making predictions about this number, must have the final say in any scientific analysis of the situation. Heavy responsibility, when one understands all the difficulties it encounters...
The dance of epidemiologists
Between containment and decontainment, the objectives are different. The editorialist Tomas Pueyo hit the nail on the head with the image of "hammering" and "dancing". First, to avoid the collapse of the health system, the epidemic is given a huge hammer blow, the containment, to bring the R coefficient down suddenly to well below 1, and get time to recover. Then, once all the tools are in place, we release the containment to bring the coefficient to around 1, just below, even if it means playing trial and error, to stem the epidemic while sacrificing as little as possible on our way of life.
And to prepare for this "dance" phase, it is up to the epidemiologists to have the final look, integrating the entire medical arsenal into their reflections. But it is indeed up to politics to have the last word: in the face of the abundance of parameters to be regulated, with repercussions on our lifestyles and economy, science should only present possibilities and leave politics to arbitrate. Thomas Pielke put it very well in his book The Honest Broker Informed choice is that which is decided by the politician, possibly through citizen debate, from among the coherent and acceptable options provided by the scientist.
We've seen it over the last few weeks: that's not how it happened. All of the epidemiologists' scenarios made assumptions that have since been beaten to a pulp: school closures for several months, and prolonged confinement of at-risk categories. On prolonged confinement, the policy began by following the scientists' recommendation: we saw this in the statements by President Macron, President Van der Leyen, the Chairman of the Scientific Council, etc.
But the very bad public debate that followed, with senior citizens furious at being infantilized, forced the authorities to back down. Seniors, the choice is yours, titled Le Parisien on the cover. Choose between what and what? No one really knows, and no one could have known until acceptable options were defined. On the opening of the schools, the politician chose to ignore the scientists' warning, and the scientists took note of this decision (report of the President's Scientific Council). In the end, what do epidemiologists predict with this new data? Just nothing: let's wait for the experts' new simulations. And let us remember that in the end, what we need is a global solidarity plan, which will make it possible to limit the spread of the epidemic below the level of hospital saturation.
Fortunately, epidemiology does not only work on differential equations; it also learns a lot from the experimental method, and from comparisons - especially cross-country comparisons. Let's look again at the epidemic spread curves, as discussed above. So far, apart from China, two groups of countries have managed to contain the epidemic, and this is clearly visible on the curves. First, South Korea and Hong Kong (which can be considered here as one country). In these two cases, no generalized containment, but a discipline of mask wearing and a very rigorous policy of tracing, testing and treatment (DTC) aimed at vigorously isolating contagious people from the rest of the population. The second group is made up of Western countries, Western Europe and the United States, which at first found themselves overwhelmed by exponential growth, forced into generalized confinement to avoid disruption of their health care systems. Here again, the parallelism of the curves is impressive. It is also impressive to see these gigantic efforts summed up as the decrease or increase of a mathematical parameter...
I was talking earlier about the universality of the epidemiological curve profile. For me it not only reflects the power of mathematical models: it also illustrates how we are all connected in this crisis - all in the same boat. There is a political vision behind it.
In this case, it was a sin of pride on the part of many countries to believe that they would be able to escape the common fate. As late as March 12, some of our best experts were betting that France, thanks to more efficient medical management than Italy, would escape confinement. Four days later, our country was trapped by the exponential, like the others, and confined like the others. It is also worth reminding those who see the closure of national borders as a call for nationalist retreats: what the surprise confinement demonstrated was not that we should close ourselves off from others, but that we should not think we are better than others, that we should coordinate with others, learn from their experiences. And it is together that we must come out of the crisis, in a coordinated way, because we are all linked; by sharing results, analyses, experiences, know-how, care.
Shall we go on our way? The fact that countries are deciding on their deconfinement strategy in a piecemeal fashion, competing for scarce resources, and unexpectedly pulling out of large collaborative projects such as trials or software, makes it doubtful. At the very least, scientists, beyond their healthy controversies, will take it upon themselves to compare the experiences of different countries and learn from them. Careful to remain faithful, in all situations, to the humanist and universalist ideal that underlies all science.
At a time when international tensions are rising rapidly, when authoritarian regimes are growing stronger, when supranational organisations are crumbling, when Europe is incapable of defining its policy, when international cooperation is struggling, it is our duty, more than ever, to support these values in politics. For the survival of us all.
Cédric VillaniMathematician, Professor of the Claude Bernard University, Lyon University