Comparing confirmed cases plotted vs. time

In Fig. 1 we show an interactive chart reporting on data for Germany (DE), United States (US), Spain (ES), France (FR), United Kingdom (UK), and Italy (IT). The total cumulative number of confirmed cases for each nation is plotted vs. time.

The cells in the dashboard on the left side of the plot contains values that can be set by the user by digiting numbers in. The “Factor” column allows the user to rescale the vertical axis by the chosen factor, or to completely remove the country from the plot by digiting zero. The “Shift” column allows to apply a positive shift in terms of calendar days. The Y/N cell allows to switch the vertical axis from total cases per country (N) to cases per million inhabitants (Y).

What do we learn from these graphs?

By leaving the default values (i.e. all Factors = 1, all Shifts = 0), the plots allow to observe the trends of different countries, their remarkable overall similarities and their minor but important differences. We observe that Italy has been the country with most confirmed cases among the ones considered here, both in absolute (a) and relative (b) terms, until late March. Since then, the United States became the country with most cases in absolute terms, and Spain in relative terms.

By acting on the dashboard, the user can exploit the remarkable similarities in the shapes to shift and rescale the plots of different countries, until the plots overlap. This allows us to attempt some empirical, prudent estimates about the evolution of the countries that are later in the epidemics, based on what happened to the ones that started earlier.

Comments about the evolution
May 1 – In spite of the remarkable similarities in the shapes of all curves, once rescaled and aligned in time, some small but relevant differences can be observed. By aligning IT, ES and DE as shown here, we observe that the Italian epidemic seems to have a slightly longer duration. Once aligned to Italy with a relative shift shift of 8 days, Spain starts in fact its epidemic a bit later and seems to be going to end it a bit earlier. Germany as well, once aligned to IT with a relative shift of 7 days, overlaps Italy on most part of the curve but shows a faster growth decrease in last days. A possible explanation for this longer duration is a larger region-to-region time delay within Italy than within other countries.
April 14 – As the user can check directly, by selecting the option N (total cases per country) the IT plot overlaps the UK plot in a wide range of dates if shifted forward by 15 days and multiplied by a factor 0,85. Use the screenshot here for help. Assuming the UK plot will continue following with two weeks delay the IT plot, UK will have in 15 days about 80-90% of the confirmed cases Italy has now. This hypothesis so far might be right or wrong, and will be monitored in the future to test if our approach has a predictive value. Such prediction could be further strengthened by comparing the UK curve with other countries that are also ahead in the development of the epidemic and averaging the data. On the other hand, no other country than Italy is ahead enough to allow attempting a two-weeks prediction.
April 14 – As the user can check directly, by selecting the option Y (cases per million inhabitants) the IT plot overlaps the US plot if shifted forward by 15 days and multiplied by a factor 1,05. Use the screenshot here for help. Therefore, if the US plot will continue following the IT plot (a hypothesis, once more, to be monitored in the future) US will have in 15 days almost the same cases per million inhabitants Italy has now. Again, the prediction for US development can be made more robust by comparing the curves with other countries that are also ahead of US in the development and averaging the data.

Comparing confirmed cases resorting to a time-independent plot

In Fig. 2, the percental daily growth of confirmed cases is plotted vs. the total number of confirmed cases. The case of a country that so far contained the spread of Covid-19 much more efficiently than all Western countries, South Korea, is shown for comparison.

What do we learn from this graph?

We first observe that this is not a time-dependent plot: the time variable has been removed. It shows how efficiently different countries succeed to stop their national epidemics (i.e., get to zero daily percental growth) before getting a too large number of cases. Again, while some comments are posted below, the user is encouraged to use this plot following his/her own ideas.

Comments about the evolution (typically posted once a week)

April 27 – The Korean outbreak seems to be under control: the percental daily growth of cumulative cases is now below 0,1%. When normalized to the number of inhabitants, the curves of the Western countries largely overlap. Removing some nations from the plot (by digiting “0” in the Factor cell) helps following more clearly the trend of the others. Under a careful observation, some differences can be observed. Germany is leading the decrease and approached the 1% line. Spain is fluctuating between 2 and 3% since about 10 days. The French data show clear problems in the data collection/reporting, and are therefore the most difficult to interpret. The US curve shows a slightly different shape, with a slightly slower decrease trend. Beside soon exceeding 106 total confirmed cases, the US might exceed most European countries (or possibly all, i.e. including ES), also in terms of cases normalised to the population. We remind that confirmed cases increase under massive testing programs, as well as under an increase of real cases.
April 14 – All EU countries followed similar trends so far, all crossing the daily 10% growth line for a number of cases about an order of magnitude greater than South Korea. We observe that the US follows a descending curve with a further extra factor 3-4 in confirmed cases with respect to Eu countries. The US curve has a peculiar shape, probably affected by the large state-to-state inhomogeneity within the country. It is still therefore unclear whether it will rapidly bend down as happened for other countries, or will exceed the 106 cases.

For comments or questions please contact us at covid19@spin.cnr.it