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The mathematics of contagion

Chess, exponentiality, and the failure of political imagination

· Covid-19

Prime Ministers, Presidents, and The Great Mughal of India

It baffles me that our government believes it can outwit the maths of contagion. Well, even the Great #Mughal thought so too when rewarding the inventor of the game of #chess.

I’m relatively innumerate, but I’ve always held this simple parable of ruination at the forefront of my mind. I’ve used it with friends and family to describe Moore’s Law, or how the #Covid-19 pandemic might overwhelm by force of numbers:

“The scholar who invented chess prostrates himself before the Great Mughal, to whom he has presented his brilliant invention.

Asked by The Great Mughal what he desires, the emperor is taken aback by the scholar’s reply:

Your Highness, I desire just this single grain of rice, placed on the first square of my board, then doubled on each succeeding square, and the accumulated proceeds from each square.

Laughing at such eccentricity, the emperor grants the scholar’s wish instantly, believing that his gift is worth nothing more than a small bag of rice.

But bound by his promise, that summer the entire rice harvest of the empire is given to the scholar, and the Great Mughal is ruined.”

That parable describes very neatly the exponential curve. As you double your squares of rice up to 32nd square of the 64 squares of a chessboard, you’re in the small brown bag of rice territory.

As soon as you cross the threshold into the other half of the board, you’re in ruination territory, and warehouses overflowing with rice. The numbers run amok.

Now apply this to people moving around, instead of rice on a static chessboard.

On the first day, an infected person infects one other person. On the second day, they both infect one other person. On the third day, each person infects one person. By the tenth day, more than 1,000 people have been infected, and by the 20th day, more than 1 million (still a sack of rice).

I've used the example of my great Aunt Peggy and her contagion party, or my sister’s contraction of the ‘flu at a soiree for Tom Hanks to indicate the fact that by the time you’re acting on the 20th day, it’s way too late. The scourge is widespread. The wise course is to assume you have it already.

Flattening the curve is about stopping the doubling every day. It’s about giving away a bag of rice, rather than losing an entire empire.

This parable is bracketed by all sorts of considerations of course:

  1. How easy is it to infect people? The evidence so far is that Covid-19 can be transmitted by touching the same surface as an infected person, and by air. It’s easy, and likely that a contagious person will infect more than one person in the course of a day. It’s also known that many more people carry the infection than fall ill, some with mild symptoms, and some with none at all. Right now, an air of normality and manageability reigns in Australia, because we don’t yet feel the effect of this early doubling. I'm as guilt as anybody of complacency.
  2. How long will the curve of the contagion last? We don’t know, because it is impossible to know at this stage. It might last six months through one season, or last the year, or mutate and return with different qualities in 2021. We don’t know whether the human herd will build sufficient immunity during this time to resist multiple waves.
  3. How serious is the infection? Judging by early studies of the morbidity and mortality rate, or the estimate by the U.S. Covid-19 Czar, Anthony Fauci, Covid-19 is "at least" ten times as deadly as seasonal ‘flu, and possibly thirty times more deadly. Best predictions are that it will infect between 20-80% of a population over the course of the contagion.
  4. How can we know how many people are currently carrying the virus in Australia, who will either sicken, or continue to contaminate others? We can’t know. If we were in Singapore, Taiwan, or Hong Kong, we’d probably have a good idea because the authorities there moved to stop the doubling of the rice at around the 5th square of the chessboard. They locked down, tested at a massive scale, and their health surveillance system apparently located every piece of rice. Whether or not Australia moved swiftly enough is an open question as the contagion continues to be spread throughout the community.
  5. Why does this matter in a country with one of the world’s best health systems, with a generally healthy population, and with a very different geography? No health system in the world can cope with the second half of the chessboard. Australia has around 4 beds per thousand people (a generous estimate). Three out of four of those beds are probably used in the ordinary course of our health load (scheduled operations, emergencies, serious cases of seasonal ‘flu). That leaves one bed per thousand to spare (25,000 beds). If just 20% of Australia’s population sickens (5 million), and just 5% of those are so seriously ill they must be treated (250,000 people), and you spread that evenly over the course of ten months, that’s just about manageable (assuming that a severely ill patient with pneumonia is treated for an average of a week). If the number doubles, or if those numbers occur at one time (the dreaded epidemiological tsunami curve), then the health system is quickly overrun.

I don’t have the very best information at my fingertips, a Mughal’s court of advisors, strategists, bankers, and agronomists. I must go by instinct, the wisdom of years, and a healthy suspicion of political leadership, given the past two decades of our embroilment in the follies of Iraq and Afghanistan.

Beyond just squares on a board, chess is a game of strategy, but fighting Covid-19 is a game where the rules are not yet known.

Contagion has no friends, and it’s own hidden logic that will only be revealed at the end of the chess board.

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