Corona Chart – Development of Corona Virus 2020 (Covid-19) visualized

Summary statement: Covid-19 in China is under control. Outside China, the infection is in a beginning state and expands exponentially. Assumed Fatality Rate for Covid-19: 0.7%.

Worldwide Development of Infections and Fatalities

Dates on the x-Axis are report dates of Situation reports by the World Health Organisation (WHO Sitreps), compiling the worldwide reports of the preceding 24 hours. The graph caption contains the date of the latest WHO Sitrep which was used to update the data. WHO Sitreps are published every evening.

As China has been successful in controlling the outbreak, the following discussion will focus on the development outside China.

11.03.2020 Infections and Fatalities worldwide excl. China, linear scale

Development outside China shows an accellerated rate.

Putting both data sets on a logarithmic scale will show whether the development is exponential or not.

11.03.2020 Infections and Fatalities worldwide excl. China, semi-log plot

An exponential development would show as a straight line on this semi log plot. The available data is very close to the exponential trendline which was added to the graph. With a little optimism, a hint of slowdown can be interpreted into the infection curver over the past week.

To put this in relation to the development in China, while there are still more infections inside China than outside, this may well be reversed in the near future.

11.03.2020 Infections in China and Outside China on a semi log plot

Conclusion: At this point in time, Covid-19 virus spreads and kills exponentially outside China.

This sounds drastic, and it corresponds to the data, however I would like to add the notion that this virus is not overly deadly.

Case Fatality Rate of COVID-19

I would assume approximately 0.7% as a fatality rate for Covid-19.

This number is an educated guess. It is based on the fatality rate found in South Korea and in Chinese regions away from Wuhan. The assumption is that on average, out of 7 infected cases, only 1 will ever make it into the statistics, because the other 6 have no symptoms and are not considered at risk, or they have symptoms and refuse to get tested, or tests kits are not available. In either case, they will never be registered as an infected person. Yet they develop the antibodies.

• According to the epidemiologic table in Wikipedia as of 11.03.2020, of worldwide registered 126,121 infections, there were 67,064 recoveries and 4,616 deaths, leaving 54,441 still acutely infected. This would mean that from a total of 71,680 infections which were resolved or concluded, 6.4% ended deadly so far (Concluded Case Fatality Rate).
• Multiplied with 0.14 registration ratio (estimate of registered infections to total actual infections): 0.9% fatality rate including assumed unreported cases.
• The same data could also be used with a different calculation: Of worldwide 126,121 infections, there were 4,616 deaths, hence the death rate is 3.7%.
• Multiplied with 0.14 registration ratio (estimate of registered infections to total actual infections): 0.5% fatality rate including assumed unreported cases.

The final value will likely be between these two values.

South Korea is the first country to excessively test people for the virus. They still didn’t test everybody, but apparently they tested a lot of people. As per the WHO sitrep of 14.03.2020, they report 8,086 infections and 72 deaths, showing a fatality rate of 0.89%. China in areas away from Wuhan found 0.7% fatality rate. Wuhan itself had a shortage of test kits and showed a higher fatality rate – probably because they were unable to capture all infections. Italy shows a huge fatality rate, but an Italian counts as infected when a certain institution in Rome certifies that, and they are overworked. So they are unable to capture the true infection rate. Iran shows a huge fatality rate, but their culture and health system may also have a tendency to not capture all infections. The US show a high fatality rate. But in the US, the citizen had to pay for the test (at least until 13.03.2020), and not everybody has insurance. So people didn’t get tested. Therefore, a high mortality rate likely suggests an underreporting of actual infections.

Let’s look at the calculation:

The fatality rate, also called “case fatality rate” or CFR, also called mortality rate or mortality ratio, can be calculated with different formulas. I will explain two formulas here. For better understanding and differentiation in this article they will be called “Concluded Case Fatality Rate” and “Snapshot Fatality Rate”.

$\textbf{Concluded&space;Case&space;Fatality&space;Rate}=\mathrm{\frac{Total\:number\:of\:fatalities}{Total\:number\:of\:concluded,\:cases,\:i.\:e.\:either\:cured\:or\:dead}}$

This formula shows the case fatality rate after the infection is over, giving a representation of the fatality rate for cases where the result is known.

While the epidemy is in progress, this value could still be distorted, if there are is a systematic difference in the time it takes to reach either recovery or death. This seems to be the case for Covid-19: Apparenly it takes longer to officially clear a person as no longer infected, than it takes for the fatal cases to lead to death. This would explain why the Concluded Case Fatality Rate declined continuously over the past week from 7% to below 6%.

$\textbf{Snapshot&space;Fatality&space;Rate}=\mathrm{\frac{Total\:number\:of\:fatalities}{Total\:number\:of\:infections,\:including\:acute\:infections}}$

This formula shows which fraction of infected people have died from the disease, as a snapshot at the moment of reporting. It implies all acutely infected cases as survivors, which is not likely. This values does not give any indication of the fatality rate for the moment of ending the infection, or “survivability”. While the epidemy is in progress, this number is distorted by definition, as all cases with unknown outcome are part of the calculation. The fraction of acute infections is proportional to the uncertainty of the Snapshot Fatality Rate.

• “The case fatality rate is around 2% to 3%.” according to the report “Three Emerging Coronaviruses in Two Decades: The Story of SARS, MERS, and Now COVID-19” by Jeanett Guarner, American Journal of Clinical Pathology, aqaa029, https://doi.org/10.1093/ajcp/aqaa029, 13.02.2020 – however I could not find any clues in their report to how this number was established. Given the available data, I must assume the formular was number of deaths divided by total number of confirmed cases including those still acutely infected. Data from WHO available on 13.02. showed 45,171 infections and 1,115 fatalities, resulting in a 2,47% fatality rate according to above mentioned formula, it would fit their statement.
• “Case-fatality rate 2.3% (1023 of 44 672 confirmed cases)” according to the report “Characteristics of and Important Lessons From the Coronavirus Disease 2019 (COVID-19) Outbreak in China – Summary of a Report of 72 314 Cases From the Chinese Center for Disease Control and Prevention” by Zunyou Wu, MD, PhD and Jennifer M. McGoogan, PhD, https://jamanetwork.com/journals/jama/fullarticle/2762130, 24.02.2020 – however this number is explicitly calculated as the number of deaths at the report date divided by the total number of confirmed cases, including those which were still acutely infected.

• “But a new report on 1,099 cases from many parts of China, published on Friday in The New England Journal of Medicine, finds a lower rate: 1.4 percent.” according to the New York Times in an article dated 29.02.2020. Upon researching the data source, I believe to have found it with the title “Clinical Characteristics of Coronavirus Disease 2019 in China“. And yes, the number of 1.4 percent is stated as death rate. However further below in the report, Table 3 of this same report discloses that at data cutoff, 93.6% of all cases were still hospitalized. In other words, the death rate in this report also calculates the number of deaths divided by the total number of analysed cases, of which the majority was still acutely infected. Only 0.8% of analysed cases had actually recovered in this very study.

All of these reports make use of a “Snapshot Fatality Rate”. In order to establish the likelihood of infected persons to reach death at the end of the infection, fatality numbers must be sampled among those which are no longer acutely infected, because they were cured or they died (Concluded Case Fatality Rate). This has not been performed in above mentioned studies. Given  that all studies were performed at a fairly early stage of the epidemic, with large portions of subjects still acutely infected (up to 93,6%), the “Snapshot Fatality Rate” was very low, and very uncertain.

The Concluded Case Fatality Rate provides an indication about the likelihood of an individual to die from the infection (or so survive it, positively spoken, looking at the inverse value). A Snapshot Fatality Rate has no such meaning for the individual. A practical advantage of the latter value is that it is smaller while the pandemic spreads, and therefore useful in media reporting in order to avoid panic.

Last but not least, all calculations performed here are based on confirmed infections. Because the majority of infections only has very light symptoms, we can assume that particularly light infections will never be reported. Not everybody consults a doctor for a cough. However deaths will always be reported – in the worst case they are attributed to the wrong cause. If there were actually 7 times more cases than the reported ones, of course the death rate based on the overall number of reported and unreported cases would be only 14% of all values which can be derived from reported figures.

Playing with numbers

For global virus spread figures, mostly driven by the development in China, we have seen the first roughly 100 fatalities on an exponential path. After that, development became rather linear, and it is not contained yet. Let´s hope that the trend outside China will also be controlled and eventually contained.

The infection rate will necessarily decline eventually, at the latest when the virus runs out of uninfected hosts. As a theoretical exercise, I have extrapolated the curves into the future, assuming both infection and fatality will spread exponentially. These are very pessimistic assumptions. As I mentioned, this is a purely theoretical exercise.

11.03.2020 Infections and Fatalities worldwide excl. China, semi-log plot, exponentially extrapolated

Putting the curves on the same scale, it becomes obvious that the current rate of fatalities grows at a faster pace than the rate of infection. At a strictly unmitigated exponential rate, the entire world’s population outside China would be infected by mid/end May 2020. However fatalities would exceed infections in the beginning of April, which is impossible. So this extrapolation is clearly unrealistic.

How bad is the corona virus? How does corona compare to other infections?

• It is much worse than SARS 2002/2003, which had a total of 8.098 infections wordwide. The current Corona virus has already infected a multiple of that, and is still in a phase of roughly exponential rise.
• It has not yet reached the magnitude of e.g. Influenza in Germany 2017/2018, a seemingly “normal” infection, with 350.000 infections and an estimated death toll of 25.100 in Germany alone.
• Fatality rate is approx. 0.7%, making it more lethal than Influenza (0.1%) and less than SARS (9.5%) per case.
• Corona may be best compared with the spanish flu 1918, a global Influenza pandemic with around 30 Million fatalities. This was a different virus in very different time, in that sense these two epidemics cannot be compared. However, the spread may be compareable. The particularly aggressive and lethal variant of the Influenza virus spreading in 1918 had a case fatality rate of 2-3%, therefore higher than Covid-19. At the time, a raging world war made health care less effective, and many patients were weakened due to supply problems. International travel was increasing, and troop movement increased the spread. Today, international travel is far more common and practical, making a virus which is difficult to detect but mildly contagious already very effective in spreading across the globe. Today we have better health care and communication. To quote Bill Gates statement in the New England Journal of Medicine from 28.02.2020: “In the past week, Covid-19 has started behaving a lot like the once-in-a-century pathogen we’ve been worried about.”
• It is not the end of the world. Survivability is on the high side. Your leisure activities may well be more lethat than this virus. Stay fit and healthy, take the basic precautions like washing and disinfecting your hands and keep your distance from other people during the later stages of the pandemic, and you will be fine.