Yet, as I alluded to in passing in two previous columns, this is a very mathematical time. Why do I say that? Because, fundamentally, it is the extraordinarily swift spread of this virus that makes it a “pandemic" — and that spread is explained by mathematics.
This virus is not infecting people at a constant rate — that is, its growth is not “linear". Instead, it is “exponential". Both those terms are mathematical, and the difference between them explains why this pandemic is such a threat. The steady plod of linear growth at least assures us of time—to care for the sick, to find remedies, to build immunity.
For example: Even if exactly a million more Indians get infected every day from today onward, it will be four years before the virus reaches every last Indian. Time enough to develop a vaccine, at any rate.
In contrast, the explosive nature of exponential growth robs us of that time. In the eight days since our current lockdown began, the number of corona cases in India has been increasing by over 17% every day. Starting with the 2,000 cases we have in India as I write this, if that rate persists, corona will blanket the country in less than 85 days.
Let me say that again: less than 85 days. By late June. That’s the nature of this battle we are in, and it’s mathematics that reveals it to us.
Still, there are also plenty of people working hard to model this virus, or to analyse the data about it, to see if mathematics can offer us hints on how to fight it. In this column, I want to give you a sense of one of those efforts.
Over at the New York Institute of Technology, a team of researchers has been trying to find an explanation for one curious feature of this outbreak. As they wrote only a few days ago: “Covid-19 has spread to most countries in the world. Puzzlingly, the impact of the disease is different in different countries."
Take Japan. Its first reported coronavirus case was on 14 January this year—only Thailand (12 January) and China (10 January) reported cases earlier. Even with that early start, Japan never chose to put in place the “more restrictive social isolation measures" that other countries did. (Like India, now.) And yet the number of infections there has levelled off at just over 2,000, with just 57 deaths. For a large and densely populated country, that’s remarkable. In contrast, there’s Italy, which for weeks now has cut down on the movement of its people, confining them to their homes for the most part. Yet they have had over 100,000 cases and, tragically, the world’s highest mortality rate from covid-19: over 12,000 deaths.
You can comb through the data to find more such differences between countries, too. What explains them? The NYIT team points out that they have been “attributed to differences in cultural norms, mitigation efforts, and health infrastructure." But does that also explain the way the virus has spread through the UK and US, and the way South Korea seems to have slowed it down? Or is there another explanation?
The NYIT scientists think there is. They think they can attribute these differences to very different policies around the world about the childhood Bacillus Calmette–Guérin (BCG) vaccine, the well-known protection against tuberculosis (TB). (Their paper is “Correlation between universal BCG vaccination policy and reduced morbidity and mortality for COVID-19: an epidemiological study", published on 24 March in MedRXIV, not peer-reviewed.)
The BCG vaccine has likely left its mark on many of you reading this—look for it high on your arm, near your shoulder. In several countries, it is administered to all new-born babies, or at any rate, before they are a year old. This includes South Korea, Japan, Thailand, Sri Lanka and others. India has had such a regimen in place since 1948, for example, and Japan since 1947.
Like those, several European countries also used to have universal BCG vaccination policies, at birth or during childhood. But with improved health standards there and the consequent low risk of TB infections, most of them have discontinued BCG vaccinations. Why vaccinate for something which is essentially eradicated from those countries? And Italy, for its part, never even had such a policy.
Struck by these differences, the NYIT team wanted to see if they could establish a “possible correlation" between BCG policies and the covid-19 outbreak. Of course, they needed to account for differing income levels, health and medicare standards, and exclude countries that may have underreported covid-19 data for one reason or another. But with all those caveats addressed, they did find a correlation. Fifty-five countries that have a universal BCG policy have an average mortality rate due to covid-19 of 0.78 deaths per million population. For the five that never had such a policy (Italy, the US, Netherlands, Lebanon and Belgium) that mortality figure is 16.39. (There are statistical caveats to these numbers, but I can ignore them here without losing the point). This difference, the scientists write, “was highly significant." Just as significant as it probably seems to you: a 20-fold difference is hefty indeed.
There’s more. (There always is, with numbers). As we know, covid-19 has been particularly lethal for the elderly. But might it be that countries that established their universal BCG regime earlier have therefore managed to protect more of their older population? Again, the NYIT team found a “positive significant correlation" between the moment when a country established its BCG policy and its mortality rate: the more recently instituted the policy, the higher the mortality there. Iran has a universal BCG policy, but it began only in 1984. This late start “potentially leav[es] anybody over 36 years old unprotected." And if your older residents are unprotected, they are more vulnerable to covid-19. Sure enough: Iran has a much higher mortality rate (19.7 per million) than Japan (0.28), which established its policy decades earlier. Or try this other comparison, in Europe this time. Spain had a universal BCG policy for 16 years till 1981. They have a mortality rate 10 times greater than Denmark, which had the BCG policy for 40 years till 1986.
This deeper analysis really reinforces this one thing we know well about covid-19: the older you are, the more likely you are to both get the disease and die from it. Thus, if a country wants to bring down infections and the death rate, it should focus on its older citizens to the extent possible. Indeed: “the earlier that a country established a BCG vaccination policy, the stronger the reduction in their [mortality rate], consistent with the idea that protecting the elderly population might be crucial in reducing mortality."
But then there’s China. That vast country has had “a universal BCG policy since the 1950s". Yet, famously, China led the world in infections and deaths for several weeks as the outbreak spread. If this correlation is genuine, why did it not apply to China?
They grappled with this question at NYIT. “During the Cultural Revolution (1966 - 1976)," they suggest, “tuberculosis prevention and treatment agencies were disbanded and weakened. We speculate that this could have created a pool of potential hosts that would be affected by and spread covid-19." And even so, infection and mortality rates in China have levelled off in China in recent days.
That apart, are these possible links between covid-19 mortality and widespread BCG vaccination encouraging? Yes, and of course it may be especially encouraging for us in India.
But remember this is just an epidemiological study, meaning it is based on searching through the data for these correlations. Do they speak of something real? Meaning, does the BCG vaccine actually act to stop the virus, and if so how? Those are not questions the NYIT scientists sought to answer; in fact, those are not even questions a mathematical analysis can answer. But the NYIT scientists’ conclusions at least suggest that this correlation is worth examining further.
In a world that’s fumbling frantically for answers to a threat unlike any of us have seen, every lead like this is a sign of hope. It must be explored.
Once a computer scientist, Dilip D’Souza now lives in Mumbai and writes for his dinners. His Twitter handle is @DeathEndsFun