“It’s about money and life!”
Interview with Prof. Anita Schöbel
When major decisions have to be made on the basis of complicated data, that’s when mathematics comes into its own. Prof. Anita Schöbel, director of the Fraunhofer Institute for Industrial Mathematics ITWM, is delighted about the growing popularity of her subject. We talked to her about the power of math and its limitations.
How can mathematics help us make informed decisions in times of crisis?
Schöbel: Math is a helpful tool, particularly when you’re dealing with a lot of unknowns. First of all, we analyze which data and information is uncertain and how big an influence this uncertainty has on our methods. Then we use models based on either robust or stochastic optimization in order to calculate the best and the worst case. This helps us specify complex problems to a much finer degree. It gives you a much clearer picture of the consequences and a more solid basis for planning. In a pandemic, the number of unknown cases has a substantial influence on the further spread of the disease. We were able to calculate that even with a very high number of unknown cases, it would take between two and three years to achieve herd immunity on the basis of a controlled spread of infection. It would therefore be a very bad option to wait until then. Instead, rapid and rigorous containment is the best option.
How reliable are such predictions?
A model is only ever as good as the assumptions used to calculate it. Besides, something unforeseen always happens: a new medical discovery, or basic immunity turns out to be higher than originally assumed, or a vaccine or new drug is developed. You can only ever say that the predictions are reliable under the current assumptions. In applied mathematics, we try to estimate missing parameters in such a way that they conform to events so far. There’s a real art to modeling. It’s about creating mathematical models of a real problem. Unfortunately, it’s not taught nearly enough at university. There, you only learn how to calculate with a given model and you assume that the model is correct.
From a mathematical perspective, would you say that the right measures have been applied?
The measures were sensible and appropriate. They came at the right time and, happily, weren’t as strict as in other countries. The problem is, once you’ve prevented the worst, people don’t appreciate the effort behind it. They just think it was all a big fuss about nothing. It’s difficult for people to imagine what exponential growth actually means. It can happen alarmingly quickly, so that all of a sudden there are not enough intensive-care beds.
To what extent is it possible to calculate the influence of political decisions within complex systems – for example, their impact on the economy?
That’s what we’re discussing right now at the institute and with economists as well. Unfortunately, it’s not that easy to juxtapose epidemiological and economic modeling, as there are a lot of factors that are extremely difficult to gauge. For example, how do restrictions of differing type and degree effect the continued performance of the economy? What effect do relaxations have on different sectors of the economy – and on the reproduction factor, which then has to be coupled with economic factors? There are many aspects to this problem. These currently make it difficult to produce a robust calculation.
Can you calculate the moment at which a measure has a greater negative impact than that which it is intended to prevent?
There are mathematical disciplines for this. In the field of multiple criteria optimization, for example, we simultaneously observe a range of objective functions and find the best compromise. That gives you concrete help with decision-making. At Fraunhofer ITWM, we’ve developed some visualization tools with which you can actually to see the relationships between different factors. A good example of this – in a completely different context – is the use of radiation therapy for cancer. We can precisely calculate the radiation dosage required to destroy a tumor without substantially compromising the surrounding organs.
How can multiple criteria optimization help in the current situation?
Things get difficult once you have a number of complex systems – such as heath care, the economy and the social system – interacting with each other. That’s even more so when we lack data – as we do here, since we’ve never had such a lockdown. But we can learn a lot for future crises. In public debate, it’s often presented as if there were two options – making money or preserving life – and these are in opposition to one another. They’re not! It also benefits the economy if we can contain the epidemic as quickly as possible, rather than trying to minimize the reproduction factor for years on end with a variety of measures. In other words, it’s about money and life! Our strategy aims to find the best compromise between protecting public health and safeguarding the economy.
What kind of data should we be collecting so as to learn how to deal with future challenges?
From an epidemiological point of view, we need to learn which measures help prevent the spread of a virus and how effectively they do this. We also need to analyze the impact on economic factors such as productivity or unemployment. And it’s useful to evaluate movement data and contact data so as to learn how and in what way specific measures modify patterns of movement. In the future, this will help us prevent the spread of infection more efficiently.
Which kind of areas are going to become more important than previously?
We’re going to have to rethink supply chains and inventories, so that in the future we’re not dependent on other countries. Right now, we need more face masks, but in the next crisis we’ll maybe need different products altogether. We need to be thinking on a more general level. Also, there’s bound to be a review of reporting chains so as to ensure that key information is handed on more quickly. Workforce planning, for example, at health authorities will have to become more flexible. And we’ll be more aware about the need to travel, especially on business, because what the crisis has shown is that it’s possible to discuss a lot of things digitally.