key: cord-0486079-7q2rjasv authors: Kreuz, Thomas title: Comparative visualization of epidemiological data during various stages of a pandemic date: 2021-02-22 journal: nan DOI: nan sha: b9ba07407b9c0cb9ff1aa61b17fc0242e73e8b5e doc_id: 486079 cord_uid: 7q2rjasv After COVID-19 was first reported in China at the end of 2019, it took only a few months for this local crisis to turn into a global pandemic with unprecedented disruptions of everyday life. However, at any moment in time the situation in different parts of the world is far from uniform and each country follows its own epidemiological trajectory. In order to keep track of the course of the pandemic in many different places at the same time, it is vital to develop comparative visualizations that facilitate the recognition of common trends and divergent behaviors. Similarly, it is important to always focus on the information that is most relevant at any given point in time. In this study we look at exactly one year of daily numbers of new cases and deaths and present data visualizations that compare many different countries and are adapted to the overall stage of the pandemic. During the early stage when cases and deaths still rise we focus on the time lag relative to the current epicenter of the pandemic and the doubling times. Later we monitor the rise and fall of the daily numbers via wave detection plots. The transition between these two stages takes place when the daily numbers stop rising for the first time. Human cases of COVID-19, the disease caused by the novel coronavirus Severe Acute Respiratory Syndrome Corona-Virus 2 (SARS-CoV-2), were first reported in Wuhan City, China, in December 2019 [1] . After initial transmissions were restricted to Central China's Hubei province, already by January 2020 first cases had been reported not only in other Asian countries (starting with Taiwan, South Korea and Japan) but also in Australia, the US and several European countries [2] . Similarly to what had happened before in China [3, 4] , within February 2020 first cases turned into first deaths [5] and South Korea, Iran and increasingly Italy emerged as early hotspots outside of China where the epidemic now seemed to be under control [6] . On March 11, 2020 , the Director General of the World Health Organisation (WHO) declared the novel coronavirus outbreak a worldwide pandemic [7] . A few days later Italy became the clear global epicenter as the first country to surpass China in number of deaths [8] . Since then the coronavirus has spread across the globe with an unprecedented impact on healthcare [9] , economy [10] , finances [11] , science [12, 13] , education [14] , travel [15] , sports [16] , mental health [17] and basically all other sectors of society. Already on January 22, 2020, the Center for Systems Science and Engineering (CSSE) at John Hopkins University (Baltimore, MD, USA) started publishing a freely available COVID-19 Data Repository that was updated daily [18] . Once global datasets like this one became publicly available, the scientific community sprang into action and within a short time a host of studies appeared that focused to a large extent on modeling the data and using these models to predict the future course of the * Electronic address: thomas.kreuz@cnr.it pandemic (e.g., [19] [20] [21] [22] ). While modelling the Covid-19 pandemic has already yielded some important results and policy recommendations [23] [24] [25] and much work still remains to be done [26, 27] , extrapolation based on often incomplete, inaccurate or unreliable data does also have its limitations and pitfalls [28] . In this article we refrain from making inferences about the future but rather restrict ourselves to pure visualization of past and present data [29] . The aim, in a nutshell, is to develop a simple and consistent comparative data visualization framework that is general and adapted to the various stages of a pandemic, thereby summarizing in one sweep the dynamic and heterogeneous situation worldwide. First, we focus on visualizations that allow a meaningful comparison of the course of the pandemic for many different countries (or on smaller spatial scales: states, regions etc.) at the same time. This is in contrast to the commonly used histograms in which the temporal profile of the data is plotted for one country at a time. Second, we argue that the most relevant information to be found in the data changes between the early and the later stages of a pandemic and accordingly we present two different kind of data visualizations. In the early stage (as long as cases and deaths continue to rise) it is most important to monitor both the time lag compared to the current epicenter (typically the country where the epidemic first took hold but later this can shift) and the severity of the spread of the disease (usually expressed by means of the doubling time). Both of these quantities provide very useful information about the urgency of the situation [30] and can help with general decision making in order to find the right moment for the implementation of preventive measures [31, 32] . On the other hand, the later stages are more about monitoring the course of the pandemic in each country in terms of peaks, valleys and plateaus. This is when there is often a back and forth between imposing, tightening and relaxing of contact restrictions depending on the tra-jectory of the epidemiological dynamics in the population at that point in time [33, 34] . The transition between these two stages takes place when the daily numbers of cases and deaths stop rising for the first time [35] . The remainder of this article is organized as follows: First in Section II we describe the dataset and the preprocessing performed. The two Method Sections III A and III B illustrate the quantities, graphs and sorting criteria we will use to visualize the data in the early and the later stages of the pandemic, respectively. In Sections IV A and IV B we show the data plots for 42 selected countries from all over the world as well as two more local examples, the US states and the regions of Italy. Finally, in Section V we summarize and conclude. Dataset: We illustrate our data visualizations using the freely available dataset from the COVID-19 Data Repository by the Center for Systems Science and Engineering (CSSE) at Johns Hopkins University (Github Webpage: https://github.com/ CSSEGISandData/COVID-19) [18] . We here use the daily cumulative data for both cases and deaths right from its first publication on January 22, 2020, until January 21, 2021, thus covering exactly one year of data. We selected 42 representative countries focusing on Europe and larger countries in other parts of the world. The data for the US states were available within the same repository. The data for the Italian regions can be found on the webpage https://github.com/pcm-dpc/COVID-19. The data from Liguria were not available and this region was thus not included. The population sizes used in the normalization were taken from the webpage https: //www.worldometers.info/coronavirus/ (data as of January 21st, 2021). Preprocessing: Datasets of both the overall number of cases and deaths up to a certain date can be expected to increase monotonically with time, but not strictly monotonously since there might be days without any new cases or deaths. However, occasionally some of the datasets do contain negative jumps from one day to the next, typically due to elimination of double counting or other kinds of retrospective reevaluations such as fundamental changes in the way cases and deaths were defined (see the COVID-19 Data Repository [18] for details). To clean the data and eliminate these negative jumps we follow the reasonable assumption that later data are more correct than earlier data (after all that is what corrections are for) and each time decrease all the spuriously high early data points to the corrected later value. As a positive side effect this smoothing also eliminates most of the plateaus that were created due to the aforementioned corrections, and this helps in the later calculations of the doubling times. Finally, we apply a moving average of order 7 days in order to smooth out weekday variations such as the tow-day dips that often occur due to reporting delays on weekends [36] . The cumulative absolute (not normalized by population) number of deaths and cases for the selected 42 countries and the year from January 22, 2020, to January 21, 2021, obtained in this way are shown in Fig. 1a and Fig. 1b , respectively. In the Method Section we illustrate the various data visualization plots using the number of deaths as an example. Deaths tend to be more reliable [37] since they are not affected by the number of tests performed which itself depends on a variety of factors, not only the number of either symptomatic or essential people (compare, e.g., [38, 39] ) but also healthcare system capacities and political decisions [29] . However, for completeness, in the Results Section IV we also show two plots based on the number of cases. In the early stages when cases and deaths are still in their first rising phase, it is important to monitor the initial spread of the pandemic [31, 32] : How far behind are different countries compared to the country where the epidemic started and how fast is the current spread in each country? The most relevant quantities are the time lag with respect to the current epicenter of the pandemic and the doubling time. In Fig. 2 we show the course of the number of deaths for three selected countries (Italy, Spain and the US) during the initial period of the pandemic, from the first reported death in any of these three countries to the end of March. For better comparability the numbers were normalized to the overall population of the respective country. Italy was the country in the Western hemisphere with the earliest onset of an epidemic [40, 41] and also the first Western country with an officially recorded COVID-19 fatality which, as the graph shows, occurred on February 23, 2020, eight days earlier than in the US and eleven days earlier than Spain. In order to compare the course of the epidemic in different countries it thus makes sense to use Italy as the reference country. The first important information to know is by how many days your country lags behind Italy's curve or, at a later stage, after a potential reversal of fortune, by how many days it is ahead in its epidemic course. To this aim, we define the time lag of a country with respect to Italy as follows: 2. Do vice versa in case Italy is behind. In Fig. 2 this is illustrated for three different countries, using the end of March (marked as thick dashed vertical line 2) as an example. By construction the time lag of Italy to itself is always 0. Spain reached 129 deaths per one million inhabitants three days later than Italy. Accordingly, the time lag is −3. The US reached 9 deaths per one million inhabitants 19 days later than Italy. So here the time lag is −19. Note that the time lag defined this way is a timedependent variable. Instead of extracting via some kind of double fitting one value for the pair of two entire curves it is estimated such that it can change day by day. In our example from Fig. 2 in the particular interval from March 11, 2020 (marked as thin vertical line 1) to March 31, 2020 (again line 2) the time lag between Spain and Italy decreased from −9 days to −3 days (Spain was catching up), while the time lag between the US and Italy increased from −17 days to −19 days (at that time the US was falling further behind). The second variable of importance is the doubling time, the characteristic unit for exponential growth. It is the time it takes for the number of deaths (or cases) to double. The lower its value the faster the spread of the epidemic. The first step in calculating this number is to determine the percentage growth rate p(t) from one day to the next: Here d(t) refers to the cumulative number of deaths until day t. From the percentage growth the doubling time T d is calculated as: . Like the time lag the doubling time is also a time-local quantity that changes day by day. In Fig. 3 we depict the course of the doubling times for the same three countries and during the same time interval that was already used in Fig. 2 . In the beginning of the pandemic in each country the doubling time exhibits quite large fluctuations due to the low absolute numbers, but after a few weeks when the numbers rise this tends to stabilize into a more smooth course. Articles that have applied the doubling time in the context of the Covid19-pandemic include [42, 43] . In the next step we combine these two time-local quantities, time lag and doubling time, in one large overview graph that allows for an easy comparison of the current state of the epidemic in many different countries. In Fig. 4 we plot the doubling time for deaths versus the time lag with respect to Italy for ten countries (including the ones from Figs. 2 and 3). The countries that are compared with Italy were selected as follows: Four of them (Russia, South Korea, China and Spain) were at that moment in time closest to one of the four corners in the plot. The remaining five countries were on different stages of a rather typical curve of a country on this graph [44] . In this plot we use the brightness of the background to indicate the preferred order of the corners from Bright Basically all countries start on the lower left of the graph. There it is still early days, presumably the virus has started to spread within the country not that long ago so the time lag to the epicenter is typically quite big (depending on how long it took for the virus to reach the country, the later a country enters the plot the bigger the time lag). The initial doubling times are rather low so the spreading advances quickly but the numbers are still such that it might appear as if there is not yet that much to worry about. However, this is actually the time where measures should be taken as soon as possible in order to make a big difference later. At the end of March 2020 the closest country to this corner A was Russia which had just entered the plot with its first registered deaths. B -Large relative time lag, high doubling time. If a country is close to corner B it means that it has basically contained the virus in its earliest days and the doubling times are so high that one can hardly speak of an epidemic. On this day no country had really gotten there yet, but among the countries selected here South Korea was the one that was slowly getting closer. This means that for the moment the worst is over but also that it was very bad. Eventually all countries tend to go up towards larger doubling times but of course it is much better to do it earlier rather than later. On the 31st of March 2020 China was the country closest to this corner but since less and less new deaths were reported it was actually moving towards corner B. D -Relative time lag close to zero, low doubling time. This is the situation to avoid at all costs (literally). Here countries are already right in the middle of an epidemic but the doubling times are still very low. This can be very bad because of the characteristics of unabated epidemic spread. At A it might take a few days to double the number of cases from 100 to 200 but at D it would take exactly the same time to double from 10.000 to 20.000 or even from 100.000 to 200.000 (depending on the overall stage of the epidemic). At the end of March 2020 the country closest to this situation was Spain (apart from the reference country Italy) and in fact it was right on its way of catching up with Italy. The remaining countries were at that point in time positioned somewhere between A and C. Like Spain, the US and the UK were moving closer to Italy. France was basically time-locked with Italy which means that its death curve was following Italy's with a constant time lag. By contrast, Germany and Canada were moving further away from Italy. In Fig. 4 we show the position of all the countries in this two-dimensional plot at the end of March 2020 but to each country we also append a tail that depicts the development over the previous seven days. The direction of the movement over that week is captured in the trend which can be found as the very last entry in the legend: A -towards lower doubling times but larger time lags with respect to Italy ← -no change in doubling time but towards larger time lags B -towards higher doubling times and larger time lags (best possible course) ↑ -towards higher doubling times, no change in time lag C -towards higher doubling times but shorter time lags → -no change in doubling time but towards shorter time lags D -towards lower doubling times and shorter time lags (worst possible course) ↓ -towards lower doubling times but no change in time lag • -no change in either direction Over this week, apart from Russia and Canada, the doubling time of most of these countries had increased. Fig. 4 and for the year from January 22, 2020 to January 21, 2021. Each row represents one country and colours are normalised from 0 (white) to 1 (black) by the maximum number of deaths of that country over the whole interval. The last row depicts the sum over all these countries together. Local maxima are marked by white bullet points and the ordinal number of the wave peak. On the left we indicate the absolute number of deaths on the last day and on the right the trend over the last week ('+','-','o' for upwards, downwards, constant, respectively). Finally, the histogram plot on the right shows for each country the number of deaths per one million inhabitants over the whole year. In order to provide information on the relative overall impact of the epidemic in different countries we here use this number as the criterion for the sorting of rows. Regarding the time lag, there were three groups: for the countries on the right (Spain, the US and the UK) it had increased, for the countries on the left (Germany, South Korea, Canada and Russia) it had decreased and for the two countries in the middle (UK and France) it had remained constant. Accordingly, overall the trends were dominated by B, ↑ and C with only two countries on a downward trend towards A. While the plots for the earlier stages are designed to provide a comparative overview of the initial rise, in the later stages the focus shifts to monitoring the course of the pandemic in each country in terms of peaks, valleys and plateaus in order to be able to react accordingly [34] . The transition between these two stages takes place around the time the daily numbers of cases and deaths stop rising for the first time [35] . The left side of Fig. 5 shows a 2D color plot of the number of new deaths per day for the same ten countries already depicted in Fig. 4 and for one year starting on January 22, 2020. Each row is normalized individually in order to provide an overview of the course of the epidemics for each country separately. This means that for each country the color scale ranges from zero daily deaths (white) to the maximum daily number of deaths over the whole interval (black). As a consequence the course of the pandemic even in countries with numbers of different orders of magnitude can be compared in the same plot. It also becomes immediately apparent whether a country is already over its peak and whether there are new waves; the brighter the colors on the last day, the further away a given country is from its peak value. We also use the color plot as a wave detector by identifying for each country all the local maxima that fulfill the following two criteria: -Minimum prominence P min The prominence P is defined as the smaller of the largest decrease in value on both side of the local maximum before encountering the next local maximum. For any given sequence of daily increases D the largest possible prominence is P max = max(D) − min(D). The separation S is defined in units of sample points (here days). For a given S > 0, we select the largest local maximum and ignore all other local maximum within S units of it. This process is repeated until no more local maxima are detected. There is no unique and unambiguous definition of a wave peak, so varying these two parameter values will lead to different detections. Here we set the minimum prominence to P min = 0.5 and the minimum separation to S min = 10 days. This selection eliminates all minor bumps and maintains only the large-scale peaks that appear to be significant. We also added trend indicators right next to the value of the current day that show whether the numbers from the last day are more than 5% higher than they were the week before ('+', upward trend), whether they are within 5% of that value ('o', plateau) or whether they are more than 5% lower ('-', downward trend). The individual normalization used in the color plot facilitates tracking the course of the pandemic within each country and allows to infer relative time lags of peaks and valleys between different countries. However, it does not provide any information about the overall severity of the situation in each country. To rectify this we add a histogram (right) with the overall numbers for every country normalized by population size. Finally, depending on which information should be stressed, countries can be sorted in various ways: -The value of the histogram on the right hand side sorts countries by the overall severity of the situation (e.g., deaths per one million inhabitants). This sorting was used in Fig. 5 and will also be used in Figs. 7a and 7b for both worldwide deaths and worldwide cases. -The value of normalized new number of deaths/cases on the last day allows a comparison of the current state of the pandemic compared to the peak value of each country. Which countries are currently at their absolute peak and for which countries the worst is behind? This sorting will be used in Fig. 8 to compare the situation for all the US states. -The occurrence of the first death/case or the position of the peak of the first wave provides information about the gradual or sudden spatio-temporal propagation of the pandemic. Where did the pandemic start and where did it arrive last? In Fig. 9 we will use the sorting based on first cases to trace the initial spread of the virus in the Italian regions. -The similarity of the daily new deaths/cases profiles. We use a straightforward combination of correlation coefficient analysis and single linkage algorithm to cluster countries according to the similarity of their temporal profiles. From the resulting hierarchical dendrogram we obtain an order that starts with the countries that are most similar to each other and ends with those that are least similar to any of the other countries. This sorting will be used in Fig. 10 for the worldwide data. In the early stages cases and deaths are still on their first rise and typically there is an early epicenter which becomes a very useful reference to which to compare the state of the pandemic in any given country. The most important indicator of this state is the doubling time. Thus, the two relevant quantities are the time lag with respect to that epicenter (here, Italy) and the doubling time and in Fig. 6 we plot one against the other. First, in Fig. 6a we look at deaths numbers for all the 42 countries on April 30, 2020 which was around the time the first worldwide peak in deaths had just passed [45] . Fig. 6a is accompanied by Supplementary Movie 1 which contains the development from the day Italy reported its second death up to the end of April (such that the final frame of the movie corresponds to this Fig. 6a) . At this moment in time countries could basically be divided into three different groups. The most severe situation was found in the US which actually had already surpassed Italy as the front runner of the pandemic and even at that advanced stage had a rather low doubling time of 20 days and was thus continuing its course towards higher positive time lags. The other members of that group were the European countries Italy, the UK, Spain and France which were all more or less phase-locked with Italy, i.e. the time lags remained quite constant. The second and by far largest group of countries was showing a trend towards increasing negative time lags and higher doubling times, thus getting closer to corner B (compare last entries in the legend). Typically this meant that for those countries the initial rise was already flattening considerably. This group included Iran, Germany and Belgium, which were all closest to Italy but still moving away. The third and last group consisted of Taiwan, Iceland, and China which had all basically stopped reporting any new deaths. At least for that specific moment in time these five countries had brought the pandemic under control. Fig. 6b depicts the same kind of plot as Fig. 6a , but now for cases instead of deaths. As before, Supplementary Movie 2 shows the whole history of this plot from the beginning of February (first reported cases in Italy) to the end of April. Overall, both the groupings and trends for cases are very similar to the ones seen for deaths. One notable difference is that for cases the separation between the three groups is much less pronounced. Once the initial rising phase of a pandemic has been passed, it becomes more important to monitor the rise and fall of deaths and cases via the characteristic peaks, valleys and plateaus in the profile of each country. Accordingly, we continue with Fig. 7a which follows Fig. 5 in showing the number of reported daily new deaths from the beginning of the dataset up to a year later, but it does so for all 42 countries. Similar to before, Fig. 7a is the last frame of Supplementary Movie 3, which tracks the development of the number of deaths over the whole year. After this one year, the countries hit the hardest were predominantly in Europe, but also countries like the US, Peru and Mexico had suffered very high numbers of deaths. On the other hand, many countries in Asia and Oceania had fared quite will. Among these countries were Taiwan, South Korea, Japan as well as New Zealand and Australia. At this specific point in time there was almost equal division among upwards, constant and downwards trends, but there were just a few more countries trending downwards rather than upwards. So most countries were either plateauing on an unprecedented high level or had just started to slightly decrease (for confirmation just refer to the data for all countries together in the last row). The relatively highest peaks on that day were obtained for the US and Mexico, whereas a few countries (Taiwan, New Zealand, Singapore, Australia and Iceland) were reporting no deaths at all. Fig. 7b shows the reported number of daily cases for the same countries and the same time interval. The overall situation was quite similar to the one reported for deaths (Fig. 7a) . Also here half the countries were peaking or close to peaking and again only a handful of countries (Taiwan, China, New Zealand, Australia, and Iceland) reported almost no new cases at all. Fig. 7b corresponds to the last frame of the final Supplementary Movie 4. When comparing the relative positions of the countries in the two graphs for deaths (Fig. 7a) and cases (Fig. 7b) we find a rather high correlation coefficient of 0.84, which means that typically countries that rank high in deaths also rank high in cases. The two most notable exceptions are Israel (which ranked much higher in cases than in deaths) and Mexico (the other way around, it ranked much higher in deaths than in cases). So far we looked at global plots containing a comparison of different countries from all over the world. The last two plots depict the same kind of data but now for smaller regions within a country -first the US states and then the regions of Italy -and each time using a new kind of sorting criterion. First, in Fig. 8 we visualize the data of the US states (plus the country as a whole), again over the same first year of data availability. In this graph we sort the states according to the number of deaths on the very last day (in this case January 21, 2021) normalized to the maximum value obtained for each state so far. This gives us a good idea of the relative severity of the situation on that day since it sorts states according to how close countries are to their absolute peak. The states that are currently peaking can be found at the top whereas the states that have passed their peak(s) appear at the bottom. On this very day in the US mostly southern states like South Carolina, Oklahoma, Kentucky, Texas, and Georgia were still peaking in deaths, while the state furthest away from its own past peak was New York (followed by Colorado and Nebraska). On the other hand, as the histogram on the right shows, the highest overall numbers of deaths had been obtained in north-eastern states such as New Jersey, New York, Massachusetts and Rhode Island. Fig. 9 depicts the regions of Italy sorted by the time of their first reported death. It started with Lombardy in the North which became the early epicenter and then gradually reached the whole country with Basilicata being the last region to report a death. This plot also shows quite nicely how the severity of the situation in each region can vary for different waves. Marche and Lombardia, two of the regions that were hit early and hard during the first wave (in fact were among the first places in Europe to report Corona-related deaths), were relatively speaking spared during the the second wave of the next winter, 2020/2021. On the other hand, regions such as Basilicata, Molise and Toscana had much worse trajectories the second time around. Finally, in Fig. 10 we return to the worldwide data and combine a correlation coefficient analysis (Fig. 10a) with the single linkage algorithm to arrange the countries in a hierarchical cluster tree (dendrogram, Fig. 10b ) according to the similarity of their daily new deaths profiles (from Fig. 7a ). Note that during this mapping from the pairwise distance matrix to a one-dimensional order important information gets lost. Vicinity in the ordered list does not correspond to a direct measure of distance. However, what hold is that countries that are most similar to each other appear on the left and countries with the most unique profiles can be found on the right (as reflected my the monotonous increase of the distances from left to right). Using the resulting order from the dendrogram we get a new wave plot (Fig. 10c ). Now we have on top the countries closest to each other which seem to be those with a rather weak first wave (spring 2020) but a very strong second wave (winter 2020/21). The next group contains the countries with two rather strong waves. Both of these groups are predominantly European and North American. They are followed by countries with a wave in summer 2020. This might be due to a later arrival time of the virus but there are also many countries from the Southern hemisphere which also points to an explanation in terms of anti-phase seasonal variations between the two hemispheres [46] . The last group include those that apart from a few sporadic eruptions had brought the pandemic mostly under control and ends which China with its very Fig. 7a. (b) Hierarchical cluster tree (dendrogram) obtained from (a) via the single linkage clustering algorithm. Countries that are most similar to each other (lowest distances between them) are on the left, countries that are more unique (higher distances) are on the right. (c) Same data as in the wave plot of Fig. 7a but with the countries sorted according to the similarity criterion. For clarity the same sorting was already used in (a). Note that the three colors in (b) and the corresponding separating lines in (a) and (c) are just visual aids, they are not based on any strict criteria. early outbreak followed by a consistent flattening of the curve. We presented visualizations of epidemiological data (such as the number of deaths and cases) that take into account many countries (states, regions, etc.) at the same time and are tailored to the specific stage of the epidemic. During the initial rising phase we focus on time lag with respect to the current epicenter and doubling time since this combination can inform about the timeliness and the urgency of interventions needed to curb the spread. In contrast, during the later stages we monitor the state of the pandemic by following the wavelike profile of daily new death or case numbers with regard to peaks, valleys and plateaus. This, together with other epidemiological quantities such as attack rate [47] or basic reproduction number [48] [49] [50] , can help to decide about appropriate counter measures, i.e. whether to impose, tighten or relax contact restrictions in the population [51, 52] . The visualizations used here are universal and can easily be applied to other kinds of epidemiological data. The spatial scale is flexible as well. While we focused on countries, states and regions, it would of course also work with smaller areas. Moreover, in the two-dimensional plots designed for the initial stages of an epidemic (Figs. 4 and 6) we use a country of reference, namely Italy, the early European epicenter of the pandemic [40, 41] . However, this is certainly a matter of choice. Different countries could be chosen, e.g., in order to test different hypotheses. Or you could select your own country and then the plot can basically be seen from your countries' point of view and provide more detailed information about its relative position in the pandemic. Finally, our methodology based on time lags and doubling times was only applied to the rising phase of the first wave (and indeed there it is most useful), but of course in cases where the individual waves are separate enough (e.g., due to seasonal variations [46] ) it would also be possible to look at second, third or even later waves. The color-coded wave detection plots used during the later stages can easily be modified to be sensitive to several other traits in the data. Here we used four different sorting criterions (Figs. 7, 8, 9 and 10c) but also the normalization of the color scale could be altered to stress certain other aspects of the data. Similarly, one could adapt the wave detection parameters in order to focus on specific time scales and resolutions. Note that the current study itself is not concerned with drawing specific conclusions from the data, rather we focus on efficient and informative ways of presenting the data to then be in a better position to actually draw specific conclusions. We restrict ourselves to examinations of the past up to the present day, but there is no extrapolation into the future based on any kind of model, assumption or parameter selections. This way we avoid any pitfalls caused by potential deficiencies in either completeness or accuracy of the data [28] . However, given reliable data these visualizations could be used to, e.g., correlate the data with different containment strategies [43] , or to perform other more extended analyses [29, 53] . We would like to close with the following appeal: Please always be aware of the tragic real-life consequences behind these numbers and do whatever you can to keep them low or bring them down again. Matlab source codes will be available at this webpage: http://wwwold.fi.isc.cnr.it/users/thomas. kreuz/Source-Code/Corona.html Since the worsening of the pandemic in Italy (March 2020) regular updates based on the data analysis methods described in this article have been posted on this Facebook page: https://www.facebook.com/tk.corona.updates/ This will continue as long as the pandemic causes significant damage all over the world. Regular updates show data for the same 42 selected countries used here. On demand the data from the regions/provinces of some individual countries with publicly available data (specifically the US, Italy, Germany, Spain, the UK, and Canada) are displayed as well. For now this is mostly the US, the only major country with continuously elevated numbers and strong regional diversity. Caption Supplementary Movie 1 (https://youtu.be/2BMZw5PHmK0): The first supplementary movie depicts the doubling time for deaths versus the time lag with respect to Italy for all 42 countries from February 21, 2020 (the day Italy reported its second death) to April 30, 2020. The layout is identical to the one used in Fig. 6a , in fact, it ends with Fig. 6 , the state of the pandemic at the end of April 2020. Over the course of time most countries tend to slowly move towards corner B (larger time lags with respect to Italy, higher doubling times). But there are a few exceptions, notably Spain, France, the UK, and in particular the US which during April can be seen to slowly overtake Italy. Caption Supplementary Movie 2 (https://youtu.be/vAsSQfWvJwQ): The second supplementary movie is similar to the first but depicts cases instead of deaths. It runs from February 2020 (the day Italy reported its second case) to April 30, 2020. Its last frame is identical to Fig World Health Organization: Coronavirus disease 2019 (COVID-19) Situation Report 11 World Health Organization: Coronavirus disease 2019 (COVID-19) Situation Report 40 World Health Organization: Coronavirus disease 2019 (COVID-19) Situation Report 51 World Health Organization: Coronavirus disease 2019 (COVID-19) Situation Report 60 Diabetes & Metabolic Syndrome The Lancet Infectious Diseases The Lancet. Infectious Diseases mSystems 5 World Health Organization: Coronavirus disease 2019 (COVID-19) Situation Report 72 Coronavirus disease 2019 (COVID-19) Situation Report T.K. would like to thank Alban Levy for useful discussions, his thorough reading of the manuscript as well as his very early efforts in rising awareness about the upcoming pandemic. T.K. would also like to thank Don MacLeod, Kaare Bjarke Mikkelsen, and Sabine Raphael for feedback on the data analysis and Benedetta Moschitta for many inspiring discussions. The third supplementary movie shows the course of the pandemic for all 42 countries over one year, from January 22, 2020 to January 21, 2021, in terms of number of reported new deaths per day. The layout is identical to the one used in Fig. 7a . Countries are again sorted by the relative number of deaths over the whole year (histogram on the right) which makes it easier to follow the overall impact of the epidemic for different regions. During the initial stages China, Italy, South Korea, Iran and Spain were the epicenters of the pandemic, at the later stages Belgium, Czechia, Peru, the UK and the US were among those countries that exhibited the highest relative numbers of deaths.Caption Supplementary Movie 4 (https://youtu.be/WCyhIEQJc7Q):The fourth supplementary movie is similar to the third but instead of deaths it depicts cases for all 42 countries over one year. Its last frame corresponds to Fig. 7b .This movie shows even more clearly how the pandemic spread from China and its neighboring countries all over the world.Further movies (various combinations of deaths/cases with/without normalization and different kinds of sortings for the 42 selected countries, the US states, and the Italian regions can be found on the tk.corona.updates Youtube channel:https://www.youtube.com/channel/ UCASTaaV9CKZEpsFRhnYF-EQThe first four movies on the channel correspond to the Supplementary Movies 1-4 of this article.