Compared deaths vs time curves
In Fig. 1 we show an interactive chart reporting on data regarding Germany (DE), United States (US), Spain (ES), France (FR), United Kingdom (UK) and Italy (IT). The cumulative deaths number is plotted vs. time. The cells in the control table contain values that can be set by the user by digiting numbers in the appropriate cells. The cells in the “Factor” column allows the user to rescale the vertical axis for each country by the chosen factor, or to completely remove the country from the plot by digiting zero. The cells in the “Shift” column allows the user to apply a positive shift in terms of calendar days. The “Normalize....” cell switches the vertical axis from total deaths per country (“N” option) to deaths per million inhabitants (“Y” option).
What do we learn from this chart?
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 similarities and their differences. Similarly, to confirmed cases in the previous section, Italy has long been the country with most deaths, among the ones considered here, both in absolute (a) and relative (b) terms. Starting from early April, the United States became the country with most deaths in absolute terms, and Spain in relative terms.
By acting on the control table, the user can exploit the remarkable similarities in the shapes to shift and rescale the plots of different countries, until the plots overlap. This allow to make some empirical and prudent estimates about the evolution of the countries that are later in the epidemics based on the ones that started earlier. The comments below should be considered as examples: the user is encouraged to use this tool independently.
Comments about the evolution (typically posted once a week)
May 1st – All the trends outlined in mid April are confirmed. Nevertheless, while the pandemic progresses, countries start differing not only for the starting date and intensity (scaling factor), but also for the overall duration of this first violent initial phase. ES, the country that suffered the highest toll in terms of human lives per million inhabitants, among the countries considered here, seems today able to get to the end of this initial violent phase with a relatively shorter cycle with respect to other countries. This curbing is visually shown in the plot by the large negative second derivative of the curve around the end of March.
May 1st – UK shows now a high risk of paying one of the highest death tolls. The screenshot here compares IT, ES and UK. We grossly align the initial phase of the three countries by shifting IT 15 days forward and ES 6 days forward with respect to IT. The UK curve is completely overlapped by IT by applying to it a Factor 0,9. UK follows therefore the same curve than IT, with about 10% more deaths per million inhabitant (about 20% more in total numbers). The ES curve rocketed at the beginning, overlapping the other two countries with a Factor 0,5 (apparently hinting to a double normalized death rate), but switched later to a much milder curve.
April 14 – the user can check directly that the IT plot, relative to cases per million inhabitants, overlaps the UK plot in a wide range of dates if shifted forward by 16 days and multiplied by a factor 1,05. Use the screenshot here for help. Assuming the UK plot will continue following with two weeks delay the IT plot (a hypothesis that will be checked in the future), UK will have in 16 days about the same number of deaths as Italy has now. Once more, the prediction for UK can be made more robust by comparing the curves with other countries that are also ahead in the development of the epidemic, although no other country is so much ahead as Italy is.
April 14 – the user can check directly that the IT plot, relative to cases per million inhabitants, overlaps the US plot if shifted forward by 18 days and multiplied by a factor 0,5. Use the screenshot here for help. If the US will continue following the IT curve (a hypothesis that, once more, will be monitored in the future) US will have in 18 days half the deaths per million inhabitants that Italy has now. Again, the prediction for US can be made more robust by comparing the curves with other countries that are also ahead in the development of the epidemic. Once more, our compared data for confirmed cases and deaths suggest a mismatch in the diagnosis-to-death delay time in the two countries.
Compared percental daily growth of deaths
In Fig. 2, the percental daily growth of deaths is plotted vs. the total number of deaths. For comparison, the equivalent plot of a country that so far contained the spread and lethality of Covid-19 much more efficiently than all Western countries, South Korea, is shown.
What do we learn from this chart?
We observe once more 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 deaths. Italy, Spain, United Kingdom and France show a remarkably similar trend. In comparison with Western countries, the success of South Korea in containing the number of deaths is even more remarkable than for confirmed cases.
In this section we report our comments regarding the evolution of the plot in Fig. 2, that are typically updated about once a week. Comments are listed in inverted chronological order
– The Italian curve shows an undesired “tail”: its decrease trend seems to have slowed down in last days, especially by comparison with Spain. As a result, the normalized number deaths in Italy is becoming close to the correspondent value in Spain. Italy seems to be bound to sizeably exceed 30.000 total deaths.
– The US curves follows a trend corresponding to about a factor 2 less than IT in terms of deaths normalized to the population, a factor 3 more than IT in absolute terms. The potential risk for US in next weeks is following a curve with a smaller decreasing slope, as a result the relative delay existing between the single States contributing to the total (Federal) deaths count.
– Korea, on the contrary, after a relatively long time of fluctuations (with percental growth of cumulative deaths in the 2-3% range), has started again a visible decrease trend.
– The Korean epidemic is still not terminated and the percental number of new cases seems to fluctuate since almost two weeks around a small but substantially constant value. This should be considered a warning as a possible evolution also for other countries.
– Italy, Spain, United Kingdom and France seem now bound to converge to a neighbourhood of 30.000 deaths, but a fluctuating regime, similar to the Korean one, might set in, shifting the final toll to higher values.
– Germany crossed the 10% daily growth line for a number of deaths about a factor five smaller than the other EU countries. The US seems to be bound to cross the same line for a number of deaths about 2-3 times larger with respect to EU countries. The large state-to-state inhomogeneity within the US makes the prediction of this curve more difficult.
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