Bram Nauta is a professor of IC design at the University of Twente.

29 October 2020

I find it incredible how politicians and administrators lack even basic technical and mathematical insights. They use the term “exponential growth” in relation to the virus outbreak, but probably have no clue what it means. For them, it probably means: so much growth, I may not get re-elected. But even a student interviewed on a street in Delft commented on national TV: “I’m a technical student, so I know what exponential growth means: if you plot something in a logarithmic X-axis and logarithmic Y-axis and you get a straight line, then it’s exponential!” The journalist, who was even more unaware of what exponential growth is, nodded with interest. “Hmm, aha, that makes sense.”

As engineers, we of course understand exponential growth. It’s a property of even a very basic linear first-order system. First-year undergrad stuff. Real-world systems, including our virus outbreak, are more complex than just first order: the system has feedback in the form of measures taken to suppress/release the virus and the system also has significant latency, which consists of, for example, the incubation time.

We all know that control systems with latency are hard to make stable. Just imagine standing under your shower and turning the knobs to tune the water temperature. If the shower hose was 100 meters long, you’d have to be extremely careful.

But the failures we see in managing this crisis would occur even if the corona system wasn’t as complex as it is. Even if the virus wasn’t spreading exponentially, the measures taken would still fail. Let’s have a look.

The first example illustrates both a total denial of exponential growth and a lack of elementary-school mathematics skills. At the start of the epidemic, the focus was on ‘herd immunity.’ The assumption was that when a large majority of the people would have caught the virus, society as a whole would be protected. With a very optimistic fraction of only 0.5 percent (1 in 200) of the infected getting really sick and ending up at the intensive care, we only needed to take care that our intensive care capacity of 2,000 beds wouldn’t be exceeded.

Time for a simple calculation. Assume each victim stays about 20 days in intensive care, so there’s a maximum influx of 2,000 / 20 = 100 people per day. With the aforementioned 0.5 percent assumption, this means that 200 x 100 = 20,000 infections per day is the maximum we can handle. Note that this is a flat rate: no growth allowed at all. If we would be able to do this, it would take 17,000,000 / 20,000 = 850 days to have all 17 million inhabitants infected in a controlled way. That’s 2.3 years.

Another simple calculation is the estimation of the number of tests we need per day. More testing means less latency in the control system, so this is crucial. At the moment of writing, the official target was 30,000 tests per day. This may sound like a lot, but it’s orders of magnitude away from what we need. If we want to test each inhabitant of the Netherlands, then with 30,000 per day, that would take 17,000,000 / 30,000 = 567 days. That means: every inhabitant can be tested only once per 1.5 years. Talk about latency!

So, I’m afraid we’re stuck with this virus for a while.

Basic mathematical and technological insight appears to be important in managing these difficult times. It would be good if those who turn the knobs of our society would possess these insights.

The good thing is that there are people who understand complex control systems and managing exponential growth. That’s us! We created computers, communication means, the internet, smartphones, tablets, webcams and much more to come. Almost everything can be done online now. Imagine this virus had come 30 years earlier, how would we have survived? Without the continuous exponential growth via Moore’s law, we’d be in panic sending faxes to each other!