COVID-19: Time series analysis

Here, I analyse the time course of major characteristics of the epidemic in different countries. Data are based on the Johns Hopkins repository. See below for possible systematic errors in the data base.


Results for four European countries (last update May 19, 2021)

Europe

Fig. 3. Outbreak dynamics in different countries in Europe (Germany, Italy, Spain, and France). Top row) Number of detected active cases (prevalence) as a function of time. Middle row) Number of detected active cases (stars) on a semi-logarithmic scale. Bottom row) Corresponding growth rates, r, (obtained by local regression through a moving window of 5 days) as function of time. Doubling times can be calculated as T=log(2)/r. The time shown in days, starting in each country from the point where the epidemics takes off.

Results for four Asian countries (last update May 19, 2021)

Europe

Results for four small European countries (last update May 19, 2021)

Europe

Results for four small European countries (last update May 19, 2021)

Europe

Results for four other countries (last update May 19, 2021)

Europe

Results for four other countries (last update May 19, 2021)

Europe

Results for four countries in East Europe (last update May 19, 2021)

Europe

Results for four countries in South America (last update May 19, 2021)

Results for four countries in Africa (last update May 19, 2021)

Sources of error

Note, that there many uncertainties and sources of error in the currently available data on COVID-19. This in unavoidable, given the actual rapid developments. Hopefully, with ongoing time data quality will improve. Most notable, data only give the detected prevalence, that is, the cases of SARS-CoV2 virus that have been detected. In all likelihood, the real number of cases will be much larger. Not much is known about the reporting rates, but first estimates indicate that a substantial fraction (possible 86%) of infections go undetected. Furthermore, reporting rates might not stay constant, but change in time with the awareness of national health institutions and available detection capabilities. At the begin of the epidemic (small awareness) probably many infections are not detected. Detection rates probably increase during the epidemic, and might decay again during the epidemic peak when incidence rates are too large for complete coverage of the population.

Problems with JHU data and France

Additionally, there are unfortunately some inconsistencies in the Johns Hopkins University data. Most notably, the data on confirmed cases in France was changed in April 14th, after which they included probable cases (from nursing homes). Probably, for such cases data on recovered never enter the data base, which might mess-up with my calculation of active cases. Note, that different data repositories treat this differently. For example, worldometer does the same, other repositories (WHO, ECDC) don't.

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Bernd Blasius
Professor for Mathematical Modelling

I am interested in the theoretical description of complex living systems at the interface of theoretical ecology and applied mathematics

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