Covid-19: We have to push down daily growth below 10 percent

How is Sweden doing in the Covid-19 pandemic? Will we manage without a lockdown, in contrast to many other countries?

The short answer: Possibly yes, IF we continue to slow down the spread of infection.

The long answer: Let’s have a look at what the curves tell us.

Firstly: The number of total confirmed cases does not say much. This number correlates mostly with the number of tests done in a country. Furthermore, it is well accepted that the true number of total infected may be much larger. The number of confirmed cases is the tip of an iceberg.

The number of deaths is a better measure. It is easier to count, although even this number may be too low due to many deaths resulting from the virus infection not being attributed to Covid-19.

The number of deaths is also more relevant to the healthcare system—it seems to be directly proportional to the number of persons in ICU (at least in Italy, by a factor of 1 to 5 or 6) which is the critical number for the hospitals.

Just like the spread of the disease, the number of deaths is growing exponentially, i.e. with an increase by a certain percentage every day. Like interest on interest in the financial world.

Note that a small difference in percentage makes a huge difference in the number of deaths over time. If we have 100 dead today and 20 percent growth, we will have 4,600 dead after three weeks. With 30 percent daily growth we will end up with 25,000 deaths!

Thus, it is very important to keep the growth down.

The graphs above is a mathematical simulation that I have done based on the number of deaths so far, for China, Italy, Spain, and Sweden. The dashed part of the curves is a very uncertain forecast based on the numbers from China.

All the curves initiate on the day of the first death is each country, for easier comparison.

The thin curves on the left represent the daily increase of deaths expressed in percent. They have been declining gradually in China and Italy since the introduction of the lockdown (marked with a round dot). The decline could be due to the lockdown, but possibly also to herd immunity (se remark below).

The fat curves to the right represent the number of deaths per day, per 10 million inhabitants (in the case of China, the population of Wuhan, 11 million, is used).

We can observe that the daily number of deaths stops to increase when the daily growth drops below ten percent. BUT this is only true if the growth of daily deaths continues to decline with the same pace as in China and in Italy (otherwise, a constant daily growth of ten percent obviously leads to increasing deaths per day).

We can also observe the steep increase in daily deaths in Spain, which depends on a slightly higher daily growth. Spain has been slower than China and Italy to push down the daily growth, and it is not yet below ten percent, meaning that the number of daily deaths is still growing fast (the top of the forecast curve is outside the diagram).

Daily growth of deaths is reasonably correlated with the spread of the disease, or in other words with the true number of infected cases.

Now, the question is, will the mild measures in Sweden be enough to push down the spread of the disease, also pushing down the daily growth of deaths below 10 percent?

A number of favourable aspects have already helped us to keep the growth down initially (as we can see on the thin blue growth curve for Sweden):

1. Culturally, Swedish people have a tendency to do what they are asked to do for the common good, and we started relatively early with these behavioural recommendations, warned by Italy: Wash your hands, stay at home when you have symptoms, work from home if it is possible (and in Sweden it often is possible thanks to stable internet connections), avoid social contexts (some would claim that this comes naturally to us in Sweden…), protect the elderly by not meeting them etc.
2. We are reasonably helped by younger demographics compared to Southern Europe, and it probably also helps us that there is less daily contact between generations, traditionally.

BUT will this be enough to keep pushing down the daily growth below ten percent? Or will we need a lockdown too? (We are about 19 days after Italy, so a lockdown at the same point in time would be on March 28, 19 days after Italy’s lockdown on March 9. That is tomorrow).

Only the epidemiologists know this.

What I have shown here is the maths describing the connection between daily growth in percent, and the culmination of daily deaths.

The simple conclusion is that we MUST slow down daily growth further.

We can do it together!

Remarks:

1. For the forecast of the thin curves (the dashed part of the curves) I have used the values from China of daily growth of deaths in percent, starting with a value that is closest to the last observed (real) value of daily growth in each country. The forecast part of the fat curves is a calculated result of the development of the thin curves.
2. The forecasts, especially for Sweden which is very early on the curve, are HIGHLY UNCERTAIN.
3. An important uncertainty in Italy is what will happen when the disease starts spreading more in the southern parts of the country.
4. In China and in Italy, the decline of the growth after the lockdown has been approximately 10 percent per day. NOTE, it is not percentage points per day, but percent per day. E.g. if the growth one day is 20 percent, the next day it will be 18 percent, and the next 16.2 percent and so on.
5. The decline in growth in China and Italy after lockdown seems to be a result of the lockdown. BUT it could also depend on herd immunity—a slowdown in the spread of the disease due to a large part of the population being infected (largely without symptoms) and being immune. Since no one knows the true number of infected, we cannot know this yet. Only when antibody detecting tests have been developed and used broadly we might get an answer. Or, if we can observe that the infection does not tend to start spreading again in the Hubei province (if we can trust data provided by China), we could conclude that there is a fairly high immunity. However, what indicates herd immunity as an explanation is the fact that the decline in growth starts immediately when the lockdown is implemented. If the lockdown would be the main factor for slowing the growth, we would see a delay of at least a week for a decline in daily growth of deaths to show up.
6. Data sources: https://ourworldindata.org/covid-sources-comparison, https://www.worldometers.info/coronavirus/, https://c19.se, https://lab24.ilsole24ore.com/coronavirus/.

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