Monsieur Bernoulli would like you to wear a mask
I simply wish that, in a matter which so closely concerns the wellbeing of the human race, no decision shall be made without all the knowledge which a little analysis and calculation can provide — Daniel Bernoulli
While the individual man is an insoluble puzzle, in the aggregate he becomes a mathematical certainty. — Arthur Conan Doyle
It’s the year 1760, and smallpox is still ravaging Europe. It’s been killing people for over ten thousand years. Every civilization it encountered was left pockmarked. Trade and then the Crusades brought this disease into Europe in the 11th Century. And here it was, this demon fever, this speckled monster, still possessing, blinding children, killing women and men eight centuries later.
But just as small-pox had skipped along the trade routes webbing the known world, news of a magical if somewhat macabre cure was also being echoed. The cure involved grinding down dried scabs from a smallpox patient and puncturing the skin with a needle or quill dipped in this powder. It was said that taoist monks in China and itinerant Indian Brahmins had been using this method for centuries to treat the infected. By all accounts the treated seemed to get a mild version of smallpox and recover quickly.
There was a problem, though. This cure didn’t work all the time. It ended up killing one in every hundred people who were variolated, the name given to the treatment after the latin name for the disease. This fatality rate combined with the vividly repulsive process meant there was impassioned resistance
It is inadvertently affirmed in the Christian countries of Europe that the English are fools and madmen. Fools, because they give their children the small-pox to prevent their catching it; and madmen, because they wantonly communicate a certain and dreadful distemper to their children, merely to prevent an uncertain evil.
That’s Voltaire channelling the mood of the world’s first antivaxxers.
How could you convince people that using this treatment, which could literally kill you, was better than not using it at all? And that too when people had the faintest idea of what caused any disease, or why this cure worked, and just so happened to kill people occasionally.
Daniel Bernoulli was already a famous mathematician by the time this problem caught his attention. He had done pioneering work in hydrodynamics and made important advances to probability theory. (He had also been banished from his house by his jealous mathematician father Johann Bernoulli for the audacity of winning the Paris Academy’s Grand Prize, but that’s a story for another day)
Bernoulli was convinced this treatment saved lives and a number of kids in the extended Bernoulli clan had been variolated. Using calculus and a few simplifying assumptions, Bernoulli showed that variolation helped increase life expectancy by up to three years, an astonishing increase when you consider that average life expectancy back then was only 32 years.
And that’s the story of how Bernoulli came up with the world’s first mathematical model for an epidemic. Unsurprisingly, this spectacular mathematical and computational forecast didn’t do much to change public perceptions. One percent fatality is no easy thing to sneeze at. It wasn’t until Edward Jenner discovered and popularized inoculation through cowpox 30 years later that people began adopting the practice of inoculation or vaccination as we now know it, thanks to its cow-ly origins.
Here we are, some 260 years later, facing another pandemic, facing the same kind of public skepticism when asked to adopt new practices to help us all live longer. And unlike that time, where one was asked to inhale some dried scabs, or poke herself with an infected quill, we are being asked to wear masks and avoid hugs and large gatherings.
Why is it so hard for so many of us to take this seriously?
It is partly to do with the way our brains process information. We are storytellers, and stories are how we receive information. It is fundamentally hard to look at the here and now, when there’s hardly anyone sick and conjure up a future, a future that’s merely one month away, where thousands are dead. Our million-year old machinery for processing information wasn’t built to look at graphs and mathematical notation in greek and take them seriously. We need to train ourselves in these unnatural alchemical acts — or we need a different kind of visual storytelling that can show us what the future has in store.
The other reason has to do with our powerful belief in the myth of our individuality and free will. I make my own decisions, and so do others. I am unique, and so are others. How can anyone predict what an entire city or country will do, when you can’t tell what I’ll do tomorrow? But we are bound by the laws of mathematics. As unique as snowflakes as we are, in the aggregate we are surprisingly predictable. 38% of us will have grey hair by the time we turn 35. 43 of us will order a Biryani in the next minute. 98% of us were disappointed by the Game of Thrones finale.
“You can, for example, never foretell what any one man will do, but you can say with precision what an average number will be up to. Individuals vary, but percentages remain constant. ” — as Arthur Conan Doyle had Mr. Holmes ?declare. The point is, we can look into the future when it involves our collective well-being. We just need to be able to communicate this better.
260 years later, calculus hasn’t really changed all that much, but we have a ton more computational power and we can use this to play out what-if scenarios forecast the future, visualize this future. and tell much richer stories. It is now possible to model the interactions of millions of individuals, rather than lump them together into a few differential equations. We still have to make some simplifying assumptions, reducing them to the proverbial spherical cows in a vacuum, but as Mr Holmes astutely observed, the individuals may vary, and in this case entirely artificial, but percentages remain constant. This approach is commonly referred to as agent-based-modeling. Its flexibility makes it possible to model everything from traffic flow, to stock market behavior and the dynamics of innovation diffusion. And, of course, pandemics.
With that long historical preamble out of the way, let’s paint a picture of the future. What might the three-months-from-now look like?
Agent-models can be as arbitrarily sophisticated as your computational horsepower permits. The Imperial College model simulates millions of individuals in cities using high-resolution population data and models interactions within households, in communities, and at work and beyond. We are going to do something much simpler. Our agents are dots living in Squareville, a drab rectangular patch with no households or any dwellings of any sort. They bounce around randomly with the sole purpose, if one can call it that, of potentially infecting others or getting infected. These squareville citizens can exist in one of the following states:
Our goal is to see how life in Squareville pans out, and how many dot-lives are saved, when adopting different practices and policies. We now need realistic estimates of how infectious people, how often they are tested, how many of their contacts are traced. You can read more about this in Part II (coming soon) or go through the code repository. Or you could see this fantastic video by 3Blue1Brown
Since we have dictatorial powers over Squareville, we could subject them to any policy under the sun. Only allow people in even numbered vehicles to step out on odd numbered days? We could try that. But we subjected the dotizens to only what we consider to be reasonable policies, backed by evidence from many quarters.
The videos you’ll see here are from simulations with 5000 agents. Running these with 20K or more gives similar results.The 5000-agent simulations are easier to communicate visually. We also extrapolated the numbers to 18 million, roughly the population of Mumbai to drive home the magnitude of possible case numbers and death counts.
Here are a few results:
(Note: The simulations were done by our team, and the code will be made publicly available here)
The Bolsonaro — Do Nothing, Celebrate Gatherings
Here’s what happens when you just go about life as if everything’s as usual. This results in 568,000 (5.7 lakh) deaths. This do-nothing bravado is impossible in real-life though. Saner folks will self-police, and hopefully once people start hearing about friends and neighbors down their very street falling sick, they wake up to the danger.
Strict Lockdown! … but people get bored
As we all know by now, strict lockdowns are economically ruinous and result in unintended consequences in large complex diverse countries. Who would have thought! (Well, mathematicians, economists, policy makers, but yeah…). What’s more likely is people cheat, whether out of boredom, lack of childcare, or desperation. You cannot expect people to sit at home, not earn and expect benefactors to provide for nine families. People will step out. What would happen in Squareville when you have a strict lockdown, but 20% of the dots cheat. You get 50,000 deaths . While that is less than one-tenths the above, a prolonged strict lockdown is also a recipe for apocalyptic economic devastation. Ideally and theoretically, a strict lockdown for a time just a bit longer than the lifecycle of the virus would help eradicate it. But try getting one billion people to stay put in their homes. We did, and we failed.
Wear Masks And Stay Away From Strangers
Firstly, let’s come up with a more evocative phrase than social distancing. As bad as it is in English, their translations in Indian languages are worse and parroting this does nothing to drive home the message. We again assume that dotizens are flawed like us humans. They get tired, bored, or forget. So you never get every single one to follow the rules. We assume 80% adherence for both. This results in 108,000 deaths. That is 450,000 lives saved, while not flushing the economy down the turkish toilet.
What can we take away from this?
Wearing a mask and staying away from people (when stepping out) could very well save your life
You don’t have to go by these simulations alone.
Of all the things we could do, these two are the easiest. Wear a mask (a cloth mask is fine; it’s more comfortable too) when you know you are going to get close to other people. Keep it on, do not pull it down when talking to people! And stay away from large gatherings. We don’t need to go overboard and wear masks all the time. The risk when you are outdoors and not in close contact with others is minimal
In order to get infected you need to get exposed to an infectious dose of the virus; based on infectious dose studies with other coronaviruses, it appears that only small doses may be needed for infection to take hold. Some experts estimate that as few as 1000 SARS-CoV2 infectious viral particles are all that will be needed (ref 1, ref 2). Please note, this still needs to be determined experimentally, but we can use that number to demonstrate how infection can occur. Infection could occur, through 1000 infectious viral particles you receive in one breath or from one eye-rub, or 100 viral particles inhaled with each breath over 10 breaths, or 10 viral particles with 100 breaths. Each of these situations can lead to an infection.
So, can we all start wearing masks? 260 years of history tells us it is a tough ask. But we can and must lead by example, and ask others to. Talk to people in your apartment, colony, and community. Get shopkeepers to follow this religiously. Take your wallets elsewhere if they don’t agree.
We need to do this.
Part II will go into the technical details of the simulations
If you liked this, you’ll like these
The Speckled Monster by Jennifer Lee Carrell
Nature Special report: The simulations driving the world’s response to COVID-19
