Briefing | Modelling covid-19’s death toll

There have been 7m-13m excess deaths worldwide during the pandemic

The rich world suffered relatively badly, but most of the dying has been elsewhere

OFFICIAL FIGURES say there have been 55,000 covid deaths in South Africa since March 27th last year. That puts the country’s death rate at 92.7 per 100,000 people, the highest in sub-Saharan Africa. It is also a significant underestimate—as, it seems safe to infer, are all the other African data on the disease.

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Over the year to May 8th the country recorded 158,499 excess deaths—that is, deaths above the number that would be expected on past trends, given demographic changes. Public-health officials feel confident that 85-95% of those deaths were caused by SARS-CoV-2, the covid-19 virus, almost three times the official number. The discrepancy is the result of the fact that, for a death to be registered as caused by covid-19, the deceased needs to have had a covid test and been recorded as having died from the disease. Although South Africa does a lot of testing compared with neighbouring countries, its overall rate is still low. And the cause of death is unevenly recorded for those who die at home.

South Africa is not particularly unusual in its levels of testing or in missing deaths outside the medical system. Excess mortality has outstripped deaths officially reported as due to covid-19, at least at some points in the course of the epidemic, in most if not all of the world. According to the most recent data, America’s excess deaths were 7.1% higher than its official covid-19 deaths between early March 2020 and mid-April 2021.

Studies of such mismatches have proved illuminating in some countries. For example, Britain saw excess deaths higher than official covid-19 deaths during its first wave, but lower than the official covid death rates in the second—an effect taken to show that measures to stop the spread of covid had saved lives which in another year would have been lost to other diseases, such as seasonal flu, perhaps. Something similar was seen in France.

But the excess-mortality method has failed to provide useful or robust global figures for the simple reason that most countries, and in particular most poor countries, do not provide excess-mortality statistics in a timely fashion. Global estimates have used the official numbers, despite knowing that the figure—currently 3.3m—surely falls well short of the true total.

To try to put numbers on how much of an underestimate it is—and thus on how great the true burden has been—The Economist has attempted to model the level of excess mortality over the course of the pandemic in countries that do not report it. This work gives a 95% probability that the death toll to date is between 7.1m and 12.7m, with a central estimate of 10.2m. The official numbers represent, at best, a bit less than half the true toll, and at worst only about a quarter of it.

As well as providing a new estimate of the overall size of the pandemic, the modelling sheds light on the distribution of its effects and on its overall course.

Unsurprisingly, most of the deaths caused by covid-19 but not attributed to it are found in low- and middle-income countries. Our figures give a death rate for the mostly rich countries which belong to the OECD of 1.17 times the official number. The estimated death rate for sub-Saharan Africa is 14 times the official number. And the first-and-second-wave structure seen in Europe and the United States is much less visible in the model’s figures for the world as a whole. Overall, the pandemic is increasingly concentrated in developing economies and continuing to grow.

To create these global estimates of total excess deaths during the pandemic, we drew on a wide range of data. Official counts of covid-19 deaths, however imperfect they may be, are available for most countries; they are shown in the top map on this page. So, frequently, are data on the number of covid cases and the share of covid tests that are positive. In general, if lots of tests are coming back positive, it is a fair bet that many more infections are being missed by a testing regime that is looking only at those seeking medical treatment and those near them.

Boosting the gradient

In some places there have been seroprevalence surveys which show how many people have detectable SARS-CoV-2 antibodies, a sign of earlier infection. Other factors we thought might matter included the steps governments have taken to curb the spread of disease—such as closing schools—and the extent to which people moved around.

Demography matters a lot: more younger people typically means lower death rates. So, we inferred, do less obvious factors such as systems of government and the degree of media freedom. To take a specific example, excess deaths in Russia are 5.1 times greater than official covid deaths.

All told we collected data on 121 indicators for more than 200 countries and territories. We next trained a machine-learning model which used a process called gradient boosting to find relationships between these indicators and data on excess deaths in places where they were available. The finished model used those relationships to provide estimates of excess deaths in times and places for which there were no data available. A description of our methodology and the ways in which we tested it, as well as links to replication code and data, are here.

We estimate that, by May 10th, there was a 95% probability that the pandemic had brought about between 2.4m and 7.1m excess deaths in Asia (official covid-19 deaths: 0.6m), 1.5m-1.8m deaths in Latin America and the Caribbean (v 0.6m), 0-2.1m deaths in Africa (v 0.1m), 1.5m-1.6m deaths in Europe (v 1.0m) and 0.6m-0.7m deaths in America and Canada (v 0.6m). In Oceania, with only 1,218 official deaths, the model predicted somewhere between -12,000 and 13,000, the lower bound reflecting the possibility that precautions against covid-19 had reduced deaths from other causes.

The ranges for Africa and Asia are spectacularly wide. So they should be. The data from which to make strong predictions are not available, and in some places do not exist. Yet, wide as they are, they provide a more reliable picture than official tallies. The 50% probability ranges narrow considerably: 3.3m-5.2m for Asia, 0.8m-1.6m for Africa, 8.2m-10.5m for the world.

During 2020 deaths per day rose for 33 of 52 weeks. After a brief lull at the beginning of 2021, they shot up to new highs, driven in large part by the tragedy currently unfolding in India. Our model suggests the country is seeing between 6,000 and 31,000 excess deaths a day, well in excess of official figures around the 4,000 mark. This fits with independent epidemiological estimates of between 8,000 and 32,000 a day. On the basis of the model it would appear that around 1m people may have died of covid-19 in India so far this year. Again, this does not seem out of line with other estimates.

The Indian catastrophe will eventually abate, as lesser spikes have elsewhere. But that does not mean that the global picture will improve. Though the disease rises and falls in waves in any given place—a first wave takes some of the most vulnerable and leads to responses that lower spread, a second wave builds up when those responses are loosened—the waves are not all in sync. That is why, to date, the number of daily deaths worldwide has increased in ten out of 15 months, including some, such as June and July last year, when much of the rich world was between waves.

It is worth noting, though, that despite hitting the poorer parts of the world harder than indicated by data on covid-related deaths, on a per-person basis covid-19 really has been worse in richer countries. For Asia and Africa, the average estimated deaths per million people are about half those of Europe (including Russia). India is comparable to Britain, at least for now.

This might sound surprising to Europeans, who have been in lockdown for the better part of a year. How did people in these mostly poor countries see less death despite frequently lacking interventions to curb the spread of the virus and having less well-funded health care? It seems likely that much of the answer comes down to age. If two populations have the same level of health care, the one with more elderly people will see more deaths. If demography were the only difference, estimates of the way that the risk of dying from covid-19 infection varies with age suggest the disease would be 13 times more deadly in Japan (median age 48) than Uganda (median age 17). Reliable excess-mortality data tend to come from countries with older, more vulnerable populations (see chart).

Low as they are in absolute terms, though, the death rates among poor young populations are much higher than they would be for populations in the rich world with similar age profiles. And for the elderly in poor countries the outlook is clearly grim. South Africa has seen 120,000 excess deaths among those over 60.

The fact that a relative lack of deaths in developing countries seems to be due to age, rather than anything else, has various implications. One is that the virus is spreading easily among younger people—a finding backed by seroprevalence surveys, which find far higher rates of past infection in Afghanistan, India and elsewhere than they do in Europe or America. This suggests lots of non-fatal cases of disease, something which suggests that the problem of “long covid” will be worse in these countries. It also means that the virus is getting plenty of opportunities to mutate.

There is an exception to this story. In some countries in South-East Asia, deaths seem remarkably low, at least so far. This is not an artefact of the model: excess-death data for Malaysia and Thailand have hardly risen at all. It is possible that people there benefit from “cross-immunities”—a level of protection against SARS-CoV-2 conferred by past infection by other viruses circulating in the region. Unfortunately, though, there are signs that the figures are now mounting (see Asia section).

The Economist’s global excess-death-toll estimates are, as far as we know, the first of their kind. They are not the only way to infer the total number of deaths due to covid-19. On May 6th the Institute for Health Metrics and Evaluation (IHME) at the University of Washington published the results of a simpler model which applies fixed multipliers, mostly based on test-positivity rates, to official covid-19 death tolls in different countries and territories. This methodology often provides numbers which fail to match reported excess deaths. For example, IHME estimates that there have been 100,000 covid-19 deaths in Japan, far more than have been reported, but the excess-death figure for the year to March 2021 was -11,000.

However they are made, estimates are no substitute for data, notes Ariel Karlinsky, a statistician at the Kohelet Economic Forum, an Israeli think-tank, who as leader of the World Mortality Dataset project has collected many of the excess-mortality data on which The Economist’s model relies. Only by better tracking of mortality in poor countries can estimates of the death rate be improved. Resources should be put into such measures not just to honour the dead and the truth, but also because, without such basic numbers, estimates of other impacts—economic, educational, cultural or in the health of survivors—are hard to understand, or to compare.

Dig deeper

All our stories relating to the pandemic and the vaccines can be found on our coronavirus hub. You can also listen to The Jab, our podcast on the race between injections and infections, and find trackers showing the global roll-out of vaccines, excess deaths by country and the virus’s spread across Europe and America.

This article appeared in the Briefing section of the print edition under the headline "Counting the dead"

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