The Soap Boiler and the Coronavirus

"Once upon a time, there was a man who was a soap-boiler..." - that's how the story I want to tell starts. It is, frankly, not a real fairytale, because it is also about numbers and how they depict the spread of the corona pandemic. But since this is for many people a book with seven seals, here comes:

The bitter story of the imperious soap-boiler Exsder and his friend the box builder.

Leader:

We are in a small German town in the country-side. The good citizens usually adhere to the new distance rules. Schools and most shops are closed, some companies are still working. Only the coronavirus is busy jumping from person to person wherever it can. Most people stay healthy. A few become bitterly ill and die miserably.

And here comes the story of the soap-boiler.

It should help to illustrate how the coronavirus works, I hope:

Once upon a time, there was a soap-boiler, called Lisder. When this story begins, he has  100 pieces of soap in stock. Every day he produces ten new pieces, which he brings to his warehouse to sell at the big spring markets in May.

How will its stock change in the next ten days? On the first, second, third ... tenth day? It will grow 110, 120, 130 pieces up to 200. After 20, 30, 40, 50 days, he owns 300, 400, 500, 600 pieces. In May, he had several hundred pieces to sell. That is linear growth!

The case of the imperious soap-boiler, called Exsder, is different. He also produces soap. But he generates 10 percent of the stock from the previous day every day. On the day the story begins, he starts with 100 pieces of soap in the warehouse. On the first day, he has in the evening 110, on 2nd day 121, on the 3rd day 133. Then, 146, 161, 177, 195, 214, 236 and 259 pieces of soap. If he continues like this, then after 20, 30, 40, 50 days he will have 673, 1,745, 4,526, and finally 11,739 pieces of soap in his warehouse.

It is obvious: after a brief time, Exsder, the imperious soap-boiler, will be many times more successful than his colleague Lisder. In the first few days, the difference is hardly significant. There are only a few pieces of soap more than Exsder produces. But then:  The production is picking up. The number of soap pieces is soaring! Every seven days Exsder's goods double, while the tranquil Lisder will have produced only 70 extra pieces of soap.

However, both soap boilers have a problem at the door: where to go with all the goods? Luckily, the sap-boilers have friends who produce boxes to store pieces of soap. Usually, a box builder can build a box for 100 pieces every day.

That suits the friendly soap-boiler well:  every ten days he gets his box and knows his goods well stored. The two, Lisder and his box builder, work perfectly together. One makes his soaps, the other the boxes, and both are satisfied. No soap lies around unwrapped.  In May, the friendly soap-boiler can travel to the spring markets with five or six boxes of soap. And if they have not died, they still work and live today.

The imperious soap maker’s case is developing differently. The box builder will deliver his first box on day 1. His second box is needed already on day 7, three days earlier, when the friendly soap-boiler needs his second box.

Then it goes stroke by stroke. The next boxes are needed on day 11, 14 and 17. From day 19 to 25, the box builder has to produce a box every day. He only works for the imperious soap boiler. Then that it becomes demanding: to produce two boxes a day, from day 36, there are already three boxes a day needed, from day 40 four boxes a day. From day 50 the imperious soap boiler needs ten boxes per day.

It is not possible! The box builder does not know what to do, burnout, illness... and worse. From day 25, the box builder can no longer do the job, the pieces of soap pile up unpacked everywhere – and every day, there are more and more... The world is choking on the soap!

And so it is with this new infectious disease, the coronavirus.

The number of infected people grows like the soap mountain of the imperious soap-boiler Exsder. At the beginning it's leisurely: Exsder has only produced every day a few pieces of soap more than his colleague Lisder. Translated from fairy tale into reality, this means that at first only a few people are infected. But soon it's all about!

And that's not a fairy tale.

It is a simple calculation:

Trailer:

It is 29th March 2020 in the small town from which I report. On this day, 18 people are known in the small town who are infected with the coronavirus. That sounds comparatively harmless since the town has at least 20,000 inhabitants. In percentage terms, this ratio is currently German normality. If the number of 18 sick people in the small town were to be calculated and per 100,000 inhabitants, 90 people would be affected. But even that would still be within the framework. By way of comparison, in other regions, there are currently 300-400 cases per 100,000 people. However, the number of people who are infected but do not show symptoms is probably much higher in our case. That is a peculiarity of the coronavirus disease.

Three observations can still be recorded:

1.                    In terms of population, the cases of the disease are minimal. That also means that there are still a great many people who can become infected.

2.                    The virus spreads irregularly. That means that there are still many white spots on the map of infections where the virus may still appear.

3.                    The number of cases in the affected areas can grow very sharply.

The third observation conceals the phenomenon of exponential growth. The first and second observations describe the conditions under which exponential growth can occur.

Exponential growth is typical of the growth of a large number of reproducers – such as a population of viruses, an algal bloom, or "humanity." Contagious diseases are just one example.

What does this mean in terms of corona infections? Why are the figures that describe them so hard to grasp? Because our everyday experiences with growth have little to do with exponential growth. We usually experience linear growth. Who is already following the development of an algal bloom in a pond?

From soap boiling to the spread of the coronavirus.

If there are 100 infected people in a population and the infection rate is 10 percent, these 100 people will infect in 10, 20, 30, 40 and 50 days 259, 673, 1,745, 4,526 and 11,739 others. But how should they be treated by a doctor? How many hospital beds are available to them?

This problem of reality corresponds in the fairy tale to the problem of Exsder's box builder:  You can't get along!

On the current situation, in Italy, the growth rates of people newly infected every day are 10 percent. Every seven days, the number of people infected there is currently doubling. In Germany, this is faster: it doubled in our case every five days until 29th March.

The growth rate in the region where our small town is located is closer to 13 percent than 10 percent. It has been stable for a few days. It is a simple prognosis.  Given the case that on 17th March would be 100 infected people and the expected growth would be 10 percent, then the spreading of the infection would have to be as follows (The actual figures are in brackets):

18th March 110 (134), 19. March 121 (157), 20 March 133 (179), 21 March 146 (202), 22 March 161 (219), 23 March 177 (224), 24 March 195 (254), 25 March 214 (277), 26 March 236 (315) 27 March 259 (335).

But the growth rate is higher than 10 percent, closer to 13 percent. With a growth rate of 13 percent, about 1/1000 of the population in the region were infected on 27th March. On day 50, the 6th May one in seven people will be ill: 58,277 people. If the growth rate remained at 10 percent from 18th March to 6th May, it would be "only" 11,739 people sick. That's 46,538 fewer people than the 13 percent forecast.

At the time of writing, the fate of the 356 people, which are identified as infected in my county, is as follows:  About 85 have overcome the infection. One person died. Hence, the fate of about 25 percent of the people is known. About 10 percent of sufferers have to go to the hospital. Of these, one fifth is in intensive care.  Today, the region's hospitals can provide for the people. However, if the current growth rate of coronavirus infections is maintained, the possibilities of intensive care in our region will be fully exploited in a few days.   Then it gets tight. These are not fairy tales; this is mathematics.

Conclusion: The growth rate of infections must be reduced. Fewer people have to fall ill than in recent weeks. That is why we need 'social distancing' with all its measures. They reduce the likelihood that an infected person will be able to infect other people without any visible symptoms.

Uncontrollably, the virus behaves like Exsder, the imperious soap-boiler. It is becoming impossible to provide the necessary supplies.

Measures such as quarantine and social distancing, as well as increased hygiene, slow down the spread and are therefore so important for the sick people to be taken care of.

End of story.

Please stay at home!

p.s. At date of 5th April, the number of infected persons was 481; it works!

© Ukko  El'Hob 29th March 2020