Roadmap
Step 01 · Implemented
Global Death Rate
Do you want to know how many people die in a second worldwide? Let's ask the machine.
The problem is that that's not true. Or not completely true. The truth behind this statement is that for the last couple years we've observed between 60 million to 63 million people died every year, worldwide. A year has 31'536'000 seconds (60 seconds x 60 minutes x 24 hours x 365 days). If we divide the number of deaths in a year by the number of seconds in a year it gives ~2 deaths/second. But that's just on average, on a yearly average.
An annual average of roughly 61.6 million deaths implies λ ≈ 1.95 deaths per second. Each square is one sampled one-second interval; the colour shows how many deaths the Poisson model placed in it. The squares are grouped by block size — 2, 3, 1, 0, 4, then the rare 5+ block last — rather than shown chronologically.
In reality there's a big chance that during any given second nobody dies, because deaths don't happen on a steady rhythm. In fact, if deaths where randomly distributed accross the year at the observed annual average, there would be about a 27% chance that exactly two people died in any given second — and roughly the same chance that exactly one person died in that second.
That 27% figure, and every column in the chart above, comes straight out of the Poisson probability mass function — the standard way to model a count of independent random events (here, deaths) over a fixed window (here, one second) when you only know the average rate. The observed annual average is first converted into a per-second average:
e and k! aren't arbitrary — each falls out of picturing what's actually happening underneath the second. Slice that second into an enormous number of tiny instants, each with its own tiny, independent chance of holding a death. e^-λ is what "none of those instants got a death" collapses to once you compound that tiny miss-chance across all of them — literally the same limiting process that defines Euler's number in the first place. The λ^k half counts the k instants that did land a death, one factor of the rate per hit; dividing by k! then erases the ordering, since we only care that k deaths happened somewhere in the second, not which k of the countless instants they fell on. Run that for each k to get the probabilities represented by the sampled seconds in the chart above; counts of five or more are grouped into one last "5+" block.
So, how many people die on a given second? Our new (better) answer is: if people die randomly around the year, probably somewhere between 0 and 4 (with a ~95% certainty). This dot behaves in this way.
That dot isn't rolling the day-count dice above once and spreading the result out evenly — it needs to know the exact wait until the next death, moment to moment. That's a different (but related) formula: the gap between two consecutive events in a Poisson process follows an exponential distribution, sampled here by inverting its CDF:
Here U is a fresh random number between 0 and 1, and μ (mu) is the mean gap — the average time between deaths, currently ~512ms at the real global rate of ~1.95 deaths/second. Draw a gap, wait that long, blink, draw the next gap, repeat — that's the formula timing every randomly-blinking dot and every randomly-placed map on this page, from here through step 4, each with its own mean gap.
Of course, people dying at a random frequency is a big assumptions, but now that we're at it let's also assume that they die at random places.
Blue dots appear at exponentially random intervals, averaging nearly two events every second (~0.5s between deaths), and at uniformly random points on the Earth's surface. This first layer has no country, density, or seasonality weighting.
Step 02 · Implemented
Death Rate By Country
The timing of when people die might be harder to improve. As to where, it's much easier as many countries report their Crude Death Rate by year —how many defunctions they registered in a year. Not all of them do, and virtually all of them overcount or undercount some deaths.
Luckily the WHO has some very smart people working on it and providing good estimates. Even if imperfect the mortality rates by country will be a huge upgrade from rendering random points wherever, with equal chances of it being in Mexico or Lithuania, Togo or the Antartica, on land or in the middle of the ocean.
Now each country fires deaths at its own real annual rate instead of the flat global average — populous countries pulse far more often than sparse ones.
Each country now fires deaths at its own real rate — populous countries pulse faster — but every death still lands on the same single point: that country's geographic center. Step 3 spreads them out realistically inside each border.
Step 03 · Implemented
Population Density
Not having deads pop up in the middle of the ocean is neat. And seeing the popping dots on the countries they should be is also a greate improvement. But if you look carefully, you'll notice that the dots appear always exactly in the center of a given country. Sometimes that's in an inhabited or even inhabitable part of the country. According to the current simulation, all deaths in Russia happen in Lake Vivi, 400 kilometers away from the closest hospital. But we know, that people tend to die where people tend to be, so let's apply a density map to our calculation. This way, the dots will have bigger chances to appear where there's more people and little chances of appearing at unpopulated areas.
Small problem though: the density map is a grid of ~55 km wide cells (0.5°), it's pixelated, so to speak. But country borders aren't pixelated (colonialism got close but not quite), they often follow rivers, mountains or the sea.
West Africa
Benelux
The way we go around this is by converting every source, every complexity layer to a grid. And we assign each pixel to whichever country has the most population in that specific cell.
This map is cheating a little bit: it uses a logarithmic scale. Otherwise you wouldn't see much. The fact is that the earth, even the land, is mostly empty. _Toggle between log and linear scale to see how empty it is*. On a linear scale you barely see anything else than a dozen megacities and some shading around the Indo-Gangetic Plain (the region south of the Himalayas that's home of one-seventh of the world's population).
Now our dots appear mostly in cities and in very popolous areas.
GPWv4 population counts on the 0.5° grid, equirectangular projection. Brighter cells hold more people. Dots now land on a grid cell chosen in proportion to that cell's population, instead of a country's single geographic center.
Step 04 · Implemented
Death Rate By Region
A single national rate hides enormous internal spread. In Japan, rural Akita dies at nearly twice the rate of Tokyo; in the US, West Virginia runs well above Utah; in Europe, north-west Bulgaria and eastern Germany far exceed Ireland or the Nordic capitals. Most of the gap is age structure — older regions bury more of their people each year — layered over real differences in health, poverty, and access to care.
An illustrative example of how big the age structure of a place is to it's CDR is that of Mexico and Lithuania. In 2000, both countries had life expectancy around 72 years, but Mexico's crude death rate was about 4 per 1,000, while Lithuania's was about 11 per 1,000. Same life expectancy, almost 3× crude death rate difference.
Every first-level region colored by its own crude death rate. Inside a single country the spread is dramatic — Russia's is the widest of all, Pskov running over 5× Ingushetia; rural Akita nearly 2× Tokyo, West Virginia well above Utah, north-west Bulgaria far above Ireland. Countries without regional data (China, most of Africa) are shaded a flat national rate instead.
Loading subnational death rates…
Step 05 · Implemented
Death Rate By Time Of Year
From a timing perspective, we're still at the same place that we were at the beginning. Dots still appear at random moments. This looks definitely better than having regular intervals like a metronome, but it's not closer to reality. Randomness feels more organic, but we're striving for something more than feeling.
Do we have something better than random? Yes, at least for some countries, that provide monthly or even weekly CDR numbers. Mortality rates on a given month in a given country vary from year to year, but not by much. Actually, it is quite easy to draw a curve, showing at which time of the year people die less or more. And the data is not only consistent from year to year but also between countries.
Add or remove any country with a directly-measured curve to compare.
A Cluster Of Similar Curves
In this chart a factor above 1 means deaths fire faster than the annual average, and a factor below 1 means they fire slower. Some countries have flatter curves, others have steeper ones, but they all follow a very similar pattern: winter is significantly more deadly than summer. As the song says Summertime, and the livin’ is easy.
Again, I've done a little trickery here and I've only chosen countries in the northern hemisphere. In the south hemisphere the curve would have been the opposite, as winter and summer are swapped relative to the northern hemisphere. And another thing, I've only chosen countries that are quite far from the tropics. As the further from the equator we get, the less noticeable are the seasons.
These choices on my wording reveal an assumption that, even if quite obvious, could be flawed: that change in rates over a one year are mostly based on climatic seasons. In theory they could reflect something different: think social mechanisms like Ramadan or data artifacts like late reporting of defunctions, default defunctin dates,...
Trying to understanding what causes seasonality is very interesting, but it isn't critical for the countries from which we have observed seasonal data, but what do we do with the other ~100 countries that only provide yearly CDR?
When I'm missing the data I need I always ask the question: are there any proxies to the data I'm looking for, that are easier to get? Are they causes of the phenomenon we study, consequences of it, or do they share a common cause with our subject?
In this case I can think of a couple proxies, each with its own strengths and weaknesses:
GDP per capita
As flawed as GDP is, it is an surprisingly effective predictor of quality-of-life metrics (child mortality, average number of teeth, homicide rates,...) and it's easily available for any year and country. We could apply the average seasonality factor of countries with a similar GDP per capita to a country without its own sub-year data.
Neighbouring countries
Geographic proximity could reflect multiple factors at once, that have an impact on seasonality. Take the Golf countries, an average donnor country there would be rich, of Muslim majority and have a very similar climate. Italy and Switzerland have comparable health infrastructure, similarly developed insitutions and are very close in longitude (same time of sunrise and sunset) and in latitude (same climatic seasons). Some problems: there are also some cases where neighbouring countries have big differences; there are some clusters of countries without any direct neighbour countries with seasonal data.
Climatic Zone
If our assumption is true, this would help us group seasonality by similar climate. Climatic Classifications group regions by similar temperature and humidity values in a simlar periodicity. The data is not trivial to get —there are many different classifications— and apply to our mortality numbers. Furthermore, we have the risk of choosing a classification model zones that are too big, grouping very different countries; or too small, rendering zones with no donor countries (countries with observed seasonal data) from which to take the data from.
Latitude
That was my first intuition, and it is actually a second degree proxy that derives climate from latitude, which is readliy available for every point on earth. Nevertheless, if we take a look at e.g. Lisbon and Beijing —both around the 125° parallel— we can see that extremly different climates can coexist in a single latitude: Lisbon has a mild winter and a moderately dry summer while Beijing registers temperatures of −27 degrees during its very dry winter and has a very hot and humid monsoonal summer.
Share of population over 65
Viral infections have seasonal patterns and older people are more vulnerable to those. In summer, they are more at risk of a heat caused death. We could expect that places with an older population experience stronger seasonality. On the other hand, countries with older populations are often richer and therefore tend to have better health access.
Before committing to one, it's worth seeing what actually tracks the strength of a country's seasonal swing among the countries that already report a curve. Each dot is one of those countries, plotted by its measured amplitude against three candidate signals — latitude, climate zone, GDP, and how old its population is.
Seasonal curves are mostly unimodal, roughly sinusoidal curves. Which means that they peak once a year and rise and fall in a smooth, wave-like pattern. For these kind of curves most differenciating characteristic is amplitude: how far the peak is from the trough. We can look at how the proxies match the observed curves' amplitudes.
The following charts show all the countries for which we have seasonal data. The y-axis shows the amplitude: the higher a dot is, the more difference in mortality there's that country between summer and winter. The x-axis will place countries on each of the proposed proxies.
Latitude Correlation
Here the bottom axis shows the absolute latitude; in other words how far a country or individual region is from the equator. Points at the left of the chart are tropical and points close to the right edge are near the poles. Each country is a solid dot; each measured region is a hollow one. Region curves come from Admin-1 regions in Argentina, Australia, Brazil, Canada, Mexico, Russia, South Africa and the US, plus Buenos Aires province as measured by its own partido registry.
We see an expected pattern: amplitude is the lowest between the tropics, as countries there don't experience astronomical seasons. And an —at least for me— unexpected one: above 35° seasonality decreases, instead of keeping raising because of colder and longer winters. A possible explanation is that above a certain threshold people understand that they should adapt to winter and implement social, behavioral, and housing adaptations. That Spain (with a more temperate climate) shows higher mortality in winter than Sweden would point in this direction. [note: Another factor that could cause this are that most countries closer to the pole happen to be relatively rich countries (Canada, Scandinavia, baltic countries, Russia)]
Amplitude by Climate Zone
Looking at it by climatic zone doesn't change much the picture. We confirm that there's a correlation, that seasonality is lower between the tropics and that climate (just as latitude) best predicts seasonality where seasonality is low.
Amplitude vs. Population 65+
How many older people live in a country seem like a very poor proxy. I just see a cloud of dots here. Possibly because richer countries tend to have older populations and one thing offsets the other. Colouring the countries by GDP per capita confirms this: countries on the left are lighter (poorer) than countries on the right.
Amplitude vs. GDP per Capita
More of the same. There's no visible correlation with how rich a country is (as GDP per capita) and how strong their mortality is affected by the seasons. The cause is probably the same as above, richer countries offset their seasonality with stronger health systems and better adaptations.
Amplitude vs. Neighbouring Countries
How about neighbouring countries? That's better. There's a strong correlation here.
Bordering-neighbour adjacency is the strongest proxy — the lowest median error, the highest correlation, and the only one with positive skill against both the mean-curve floor and latitude. Latitude and climate class land close together just behind, with climate edging latitude on the typical country, and all three clear the mean-curve floor comfortably. For every country or region without its own curve, production applies the highest-quality available donor group after adjusting for history, cadence, climate specificity, coverage and distance.
Bordering Regions, Not Just Bordering Countries
Adjacent regions inside the same country track each other even more tightly than bordering countries do. That agreement is why the nearest-region reconstruction below beats every other region-level proxy.
Two RusSTMF regions (Ingushetia, Chukotka) had unusable raw weekly data — zero-rate weeks or excessive spike noise — and are imputed from the average of their nearest good neighbours rather than shown as-is or dropped.
Amplitude By Country And Region
Every rendered country and region is colored by seasonal amplitude. Observations use their measured curves; targets without observations use the assigned climate, neighbour, or latitude proxy.
Step 06 · Implemented
Ongoing Conflicts
The previous layers capture long term mortality trends, which account for most of the deaths worldwide. But if we want to show current mortality we need to take into account finer grain factors, the biggest one being conflicts. ACLED records every reported political-violence event with a location and a fatality count and provides updates on a daily basis.
For all other layers we multiplied the base Crude Death Rate by a seasonality or density factor. But here we get daily —yesterday's— observed or very short-term estimated numbers of real defunctions, so what's our factor?
We do a recency weighted average to predict today's mortality. Specifically we use a robust exponentially weighted moving average (Robust EWMA). Which means something like use recent days more than older days, but dampen suspiciously extreme values before averaging.
For example:
In the last 7 days, we've got the following numbers:
| Day | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| Fatalities | 20 | 22 | 21 | 90 | 24 | 26 | 28 |
We calculate the 10th and 90th percentiles.
| Percentile | Cap | Meaning |
|---|---|---|
| P10 | 20.6 | About 10% of days have lower numbers than this. |
| P90 | 52.8 | About 90% of days have lower numbers than this. |
Then we update the numbers above and below these caps:
| Day | Original value | Capped value | Change |
|---|---|---|---|
| 1 | 20 | 20.6 | Raised to P10 |
| 2 | 22 | 22 | Unchanged |
| 3 | 21 | 21 | Unchanged |
| 4 | 90 | 52.8 | Lowered to P90 |
| 5 | 24 | 24 | Unchanged |
| 6 | 26 | 26 | Unchanged |
| 7 | 28 | 28 | Unchanged |
To calculate the weights we need to chose a half-life factor (how many days it takes to halve the impact a day has in the final prediction). The best way to calculate an appropriate half-life factor for a given series, is to try different values and see which values better predict past observed events based on previous events. We won't do this. We'll use 4 instead, which I've landed on with some trial and error.
So the weights to halve the impact every 4 days look like this:
| Day | Weight | Note |
|---|---|---|
| 1 | 0.354 | |
| 2 | 0.420 | |
| 3 | 0.500 | |
| 4 | 0.595 | |
| 5 | 0.707 | |
| 6 | 0.841 | |
| 7 | 1.000 | Yesterday / most recent day |
Then we do a weighted average using these weights. Which gives us 28.4.
Robust EWMA — today's conflict deaths
No conflict fatalities have been reported in the trailing 14 days (or the live ACLED layer is unavailable), so there is no recent series for the prediction to run on.
Step 07 · Planned
Ongoing Epidemics
Epidemics raise mortality in specific regions and periods by a measurable amount.
The globe is statistical, not a feed of individual records. A flash and persona should be read as a representative event drawn from public aggregate data, never as an identifiable death.
This is a personal project exploring statistical mortality visualization.
The globe is statistical, not a feed of individual records. A flash and persona should be read as a representative event drawn from public aggregate data, never as an identifiable death.