Are we dead yet?

I am quite frustrated with corona graphs in the news, since most reporters seem to have skipped math classes back then. For instance, just plotting the number of confirmed infections at the respective dates does not tell you anything due to the different time point of outbreak. So lets fix that first.

The following charts are based on live data from https://github.com/pomber/covid19, which in turn sources jhu.edu.

Countries to compare

Italy; Germany; France; Spain Korea, South; Israel; Austria; Sweden India; EU; US; Brazil

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This is still pretty useless as the countries differ in total population and population density, lets turn to something actually comparable.

Here, confirmed refers to a case being reported in contrast to a case being infected. Therefore, fluctuations are introduced by working days (e.g. less tests performed on weekends & holidays).

Spreading rate measures

The values are smoothed using a moving average over seven days. This numbers actually allow comparing how well the different countries are doing in their corona countermeasurements, regardless of the population size.

An infection rate of 1.0 means no new infections.

However, after the initial outbreak a significant part of populatian has been infected and any new outbreaks are dimished in this metric.

# The same data can be visualized more intuitively as the doubling time, i.e. the time it takes for the confirmed count to double. It is given below for reference.

However, this representation is less numerically stable as it diverges to infinity as the infection rate approaches to 1.0.

# Yet another way to represent the same data is the effective reproduction number R.

Actually, it is very similar what we defined as the infection rate above. However, instead of comparing the the absolute number of confirmed from day to day, the change in confirmed over a period of time is used. Therefore, R becomes 0.0 if there are no new infections.

The number R determines which proportion of the population must be vaccinated to stop the disease. Generally speaking: the higher R, the higher the proportion.

There is a variety of models to estimate R. I went with a rather naive approach (see code), so the actual numbers may vary from official reports.

# Yet another way to represent the same data is the 7-Day incidence.

This measures the number of infected per 100.000 over the last 7-Days. This too, measures the effective reproduction of the virus. But the different unit makes this more understandable I guess.

The population count to compute the incidence is based on data from wikipedia

# However, confirmed does not mean the same between different countries and even in the same country at different time points of the epidemic. This is due to the sampling bias induced by the limited amount of corona test kits. In the early days of the epidemic there are enough kits to test everyone, so many cases that do not yet show symptoms are tested. With ongoing spread, we hit limits on test-kit and health-system capacities and the focus shifts to testing severe cases only. This in turn pushes the fatality rate.

A significant increase of the fatality rate indicates that

the confirmed count is being under-estimated.
the health-system capacites being exhausted.

Conversely, a decrase of the fatality rate indicates that

the confirmed count was previously under-estimated. (e.g. by the exhaustion of the health system and focusing on severe cases)

We are only talking about an estimate of fatality rate here, as we cannot measure the true fatality rate while the epidemic is ongoing. For us the relative rate between countries is sufficient. Therefore we simpliy chose the optimisitic deaths by confirmed ratio here.

# In contrast to the fatality rate, the mortality rate below is shown in dead per million inhabitants. This makes it independant of whether the confirmed count is estimated correctly. In most cases both will be correlated.

However, the mortality rate is a better indicator of the influence of the pandepic on a countries society and economy - especially when the health-system is exhausted.

The population count to compute the mortality is based on data from wikipedia

# To close with something positive, lets look at the absolute number of infections. That is, cases which are neither recovered nor died yet and are potentially infectious. If there are no such cases left, we can assume the epidemic to be stopped.

Notably, when this graph reaches zero you can not assume that the epidemic is stopped due to the stochastic nature of the data. However, a rise of the graph after a decline can indicate that a second wave is coming.