Corona confusion: How to make sense of the numbers and terminology | Science| In-depth reporting on science and technology | DW | 20.03.2020
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Corona confusion: How to make sense of the numbers and terminology

For three months, Covid-19 has been keeping the world in suspense. It's hard to keep track of all the different figures and the technical terms. What do they mean and why are they helpful?

The "basic reproduction number" actually refers to the spreading potential of a virus. It tells us how many people, on average, an infected person will in turn infect. If this number is bigger than one, each infected person transmits the disease to at least one other person. If the number is less than one, infected people have a low chance of passing on the infection, so fewer and fewer people become infected and the disease typically dies out. 

Infographic explaining meaning of basic reproductive number

To contain the spread of a virus, its reproduction number must become less than one.

Germany's federal public health organization that monitors infectious diseases, the Robert Koch Institute, estimates that the basic reproduction number of SARS-CoV-2 is between 2.4 and 3.3. 

Each infected person therefore infects about two to three other people.

That means, in order to bring the epidemic under control, about two-thirds of all transmissions must be prevented.

As there are no vaccines available and no reliable protection against the virus as of yet, it's expected that 60% to 70% of the population will become infected. Only then will the virus be unable to spread further, as it will then start to encounter more infected people than uninfected.

Infographic explaining meaning of incubation period

On average, the incubation period for SARS-CoV-2 lasts five to six days, but can vary from one to 14 days.

Infographic explaining meaning of contagious period

But this is just an estimation at this stage. At the moment, it's assumed an infected person can pass on the virus 24 to 48 hours before symptoms appear. Research from the Chinese metropolis of Shenzhen suggests that a quarter of all infections are transmitted by people who have not yet shown symptoms.

Once an infected person shows symptoms, they're likely to be contagious for seven to 12 days if the disease is mild, and for more than two weeks if it is severe. The virus is transmitted by droplets. The deeper they come from in the lungs, the longer the virus remains active — you can think of it as mucus being more powerful than saliva. As far as we know, transmitting the virus via excretions is unlikely.

Infographic explaining meaning of case fatality rate

The case fatality ratio indicates the risk of death for a person infected with SARS-CoV-2. However, it's difficult to calculate this risk for the current pandemic, and there's several reasons why.

First of all, the casualty rate always depends on the context, time and place of occurrence. Across the world, SARS-CoV-2 impacts countries differently, depending on how their healthcare systems are equipped, the age of their populations, how people cohabitate and the prevalence of pre-existing medical conditions.

All these factors (and more) determine how vulnerable a population is. That makes it almost impossible to make sweeping worldwide generalizations.

The numbers used as a basis for calculating the proportion of casualties also have a great influence. If, for example, on day one of the epidemic the number of all those who died was divided by the number of all those who fell ill, the number of those who fell ill would be very high, while the number of those who died would be relatively small. The proportion of deaths to illnesses would therefore be — erroneously — very small. We saw this at the beginning of the pandemic in China.

On the other hand, it can be assumed that many cases are not known or not recorded. In this case, the proportion of those who have died compared to all those who have fallen ill is again disproportionately high. This was the case in Iran, for example.

Mathematician and epidemiologist Adam Kucharski, from the London School of Hygiene and Tropical Medicine, assumes that the two effects will cancel each other out in the course of the pandemic. He estimates that the real casualty rate is 0.5 to 2%, i.e. one or two people die for every 100 people who are infected.

Infographic explaining meaning of estimated number of unknown cases

The true number of infected people is, in short, unknown. Although the World Health Organization (WHO), Johns Hopkins University and the Robert Koch Institute (RKI) monitor and publish the numbers of currently confirmed corona cases, these are only confirmed cases. These can only give us an indication of the number of actual cases and how quickly the virus spreads. It depends on how many people get tested at all or how many tests are available in a country.

Based on current death rates, one can make assumptions about what the actual number of people infected might be. Extrapolating from the death figures, mathematician Tomas Götz from the University of Koblenz and Landau in Germany, estimates that there must have been 40,000 cases in Italy at the end of February. This would be a factor of 50 above the reported number of 800 cases.

However, this calculation can't be transferred to Germany, "as the current comparatively extremely low number of deaths does not fit in with the international comparison," Götz said. Data on the number of cases treated in hospitals in Germany is also missing.

If you do not see the interactive map above, click on this direct link to John Hopkins University.


Infographic showing exponential growth of a virus

It's hard for us humans to understand growth that isn't linear. When we grow, we intuitively think something is going to keep growing: one today, two tomorrow, seven in one week. But viruses don't grow in a linear way, they grow exponentially. An infected person infects another person. These two, in turn, infect two more, and four infected persons infect four more people and so on.

Filling a chessboard with grains of rice illustrates this growth. Let us imagine that we do this, starting with A1 and adding rice every day. If we had linear growth, the chessboard would be filled with 64 grains after 64 days. If we had exponential growth, after 64 days there would be an incredible 9,223,372,036,854,775,808 grains of rice on the chessboard.

It's sometimes tempting to compare the absolute case numbers in different countries. But this isn't enough because the numbers are growing very fast and tomorrow they will look very different from today. In order to track the spread of a virus, one must look at its doubling speed. At the moment, the virus needs less and less time to double. As soon as the doubling speed decreases again, humans will still be infected, but the virus is on the retreat.

World map made of rice grains

Viruses don't reproduce linearly, but exponentially — which is difficult to grasp

Adam Kucharski is working on mathematical models of infectious diseases to better understand their course. This understanding can help politicians and health experts to make political decisions to contain the spread of a virus.

In the past, Kucharski has already done this for diseases such as Ebola, SARS and influenza, and is now researching Covid-19. In his book "The Rules of Contagion: Why Things Spread - and Why They Stop", he identifies four parameters that describe the contagion potential of a disease. In English, they begin with the initial letters D-O-T-S (dots).

  • Duration: corresponds to the duration of infectivity. The longer a person is ill, the longer they can infect other people. The sooner a person who is infected is isolated from others, the less chance they have of transmitting the virus to others.
  • Opportunity: how much chance does the virus have of getting from one person to another? This variable virtually maps our social behavior. According to Kucharski, under normal circumstances each person has physical contact with other people about five times a day. This number can be reduced if we increase the social distance, for example by not exchanging physical greetings.
  • Transmission probability: how likely is it that the virus is actually transmitted from one person to another when two people meet? Kucharski and his team assume that this happens on every third occasion.
  • Susceptibility: if the virus has been transmitted, how likely is a person to get it? Since there are currently no protective mechanisms, no vaccination, no assured immunity, this figure is close to 100%.

The rest is mathematics: multiplied, D, O, T and S give the reproduction number. All four parameters are adjustment criteria to stop the spread of the virus. Normally, vaccinations are particularly effective for this purpose. Since these don't exist at the moment, we can only work with D, O and T — that means, isolating the sick, avoiding social contact, coughing and sneezing into our elbows, and washing our hands.

The aim of the measures is currently "to flatten the curve." The number of sick cases should not exceed the capacities of health care systems, so that doctors don't have to decide which patients to treat. And which not to treat.

But why does the proportion of deaths differ so dramatically between countries? Why is Italy, for example, overwhelmed, while the case numbers in Germany are similar, but the death rates are much lower?

This question was investigated by economists Moritz Kuhn and Christian Bayer, based in Bonn, Germany. Clinical figures show that mortality increases the older a person with the disease is. The economists assume that people are mainly exposed to infection in working life, which means that a country's working population is particularly at risk.

Infographic showing transfer of viruses between different countries

Now there are various models of how societies can be structured. Generations can either live separately as in country A , or close together as in country B (pictured in the infographic).

Economists have found that the proportion of casualties increases when there is a higher number of working people living with their parents because this entails more contact between the generations. If their theory is correct, the countries most at risk are India, Taiwan and Thailand, and, in Europe, Serbia and Poland.

Infographic: Percentage of generations living together

But in Asian countries this trend wasn't observed. Bayer suspects that this could be due to differences in cleanliness standards and the way people live together physically.

So what should we be doing?

Kuhn says, first and foremost, we should be reducing contact between the old and young populations. But he goes one step further, saying if we want to successfully combat COVID19, we need to "rethink our social networks" — older people should also avoid contact with each other, and workers should return to the single earner model.

"We're currently traveling at 180 km/h towards a traffic jam. The only thing that can be done is to hit the brakes. And then we'll see if we can pull over in time, or at least not crash into it."