Double, double, toil and trouble!
-- Shakespeare
COVID-19: Why Nobody Likes Math
(Or at least, Mathematicians)
Um. The majority of people I speak with are busy making business-as-usual plans through summer.
COVID-19's global reach is doubling every 4 to 6 days resulting in explosive exponential growth. There's a lot of finicky issues in calculating these numbers... let's be optimistic and say it's only doubling every 10 days.
That is to say, the total number of people who have been infected with the virus doubles in every 10 day period. Let's roundly say that each month has three 10 day periods, so it will double three times every month. The total at the beginning of any month will grow by a multiple of 2... 4... 8 times by the end of that month.
As I write, today's global total is 300,000 who have been infected.
How many months ahead do you want to plan? Each month, the total grows by a factor of 8. Here's a convenient little planner:
- Mid-April ... 8 x 300,000 = 2,400,000
- Mid-May ... 64 x 300,000 = 19,000,000
- Mid-June ... 512 x 3000,000 = 153,600,000
- Mid-July ... 4,096 x 3000,000 = 1,228,800,000
- Mid-August ... 32,768 x 300,000 = OOPS...
... exceeds human population. - >>> Here there be Monsters <<<
- As I write, this is the earliest we might hope for a vaccine.
Things not cool today? So many months from now, the first number is how many times worse it will be at the present doubling rate. The math spotlights the urgency.
If you can think in terms of doubling time (rather than days, weeks and months) it will help you with vital decisions.
*****
At the rates we used, the spread will peak sometime between four and five months out if it hasn't been flattened. That's the July? August? the President mentioned.
While the CDC knows all this (their data, after all), they are coy about being specific. They urge, for example, that we have supplies on hand for "a period of time", or occasionally "two weeks". Yet stay-at-home orders implemented today are likely to be in place and tightening for months ahead.
China managed to flatten their curve and are seeing declining numbers of new cases. Whatever we might think of their politics, they moved relatively early and according to accepted epidemiological practice. In two months, they were able to locally flatten and reverse spread. Nevertheless, they may miss a case or two, or be re-infected from the rest of the world which has not taken strident measures to date. Then it's start over with the same 'draconian' measures.
Of course, this presently high doubling rate we're discussing won't sustain.
Social distance and travel restrictions will slow the rate of growth (won't eliminate it without unAmerican resolve). But these flattening measures also prolong the period of pandemic by spreading cases over time. Even if no measures are taken, the spread slows as a higher percentage of the population acquires immunity or dies.
Social distance and travel restrictions will slow the rate of growth (won't eliminate it without unAmerican resolve). But these flattening measures also prolong the period of pandemic by spreading cases over time. Even if no measures are taken, the spread slows as a higher percentage of the population acquires immunity or dies.
Things won't turn on a dime. We are seeing measures ramp up late in the game, but early in the eventual spread. We hope to avoid the spike. At best, there will be tightening restrictions for months to come. Our best laid plans are all agley.
Meanwhile, the global economy is coming apart at the seams.
So provision up, batten down hatches and take a reef, me Hearties!
Were in the storm, sure enough!!
Were in the storm, sure enough!!
 | |
| The higher the dot, the slower the spread. From Scientific American article |
PS. Among the mitigation and travel restriction measures being implemented, travel by private vessel is being restricted in places around the globe. Even those of us who live aboard need to get where we want to be NOW, before rules and enforcement get around to our stretch of water!
Posted on behalf of JOHN:
ReplyDeleteDave,
As you implied later in your blog, the virus growth really isn't exponential. it's a Gaussian or Normal distribution, more commonly known as a bell curve. The rate of growth for COVID-19 will not/cannot keep increasing, as the term exponential growth implies.
The New York Times is updating a chart every day with deaths from COVID-19 in the US and select other countries. As you can see, the death rates in China, Iran and Italy are flattening -- especially China. The US is still on the steep-growth part of the curve.
https://www.nytimes.com/interactive/2020/03/21/upshot/coronavirus-deaths-by-country.html
And, as awful as it sounds, many of the people who will die from COVID (the aged and infirmed) are the least productive members of society, and therefore the most expendable. Italy is already issuing triage guidelines to its health care workers. We may have to as well.
https://www.reuters.com/article/us-health-coronavirus-italy-ethics-speci/all-is-well-in-italy-triage-and-lies-for-virus-patients-idUSKBN2133KG
If 2.2 million people in the US die because of COVID-19 (a worse case assessment by the Imperial College of London), that is less than 1% of the US population. Awful, but hardly catastrophic.
https://www.imperial.ac.uk/media/imperial-college/medicine/sph/ide/gida-fellowships/Imperial-College-COVID19-NPI-modelling-16-03-2020.pdf
(see page 7)
In my opinion, humanity itself will survive. However, like you, I'm very unsure how the economy will survive. I wonder if the Danish model could work for us?
https://www.theatlantic.com/ideas/archive/2020/03/denmark-freezing-its-economy-should-us/608533/
John
Hi John,
DeleteYes on the bell curve. Hosts and diseases eventually come to terms in most cases, with or without vaccines.
On the rest, I'm going to weigh in with different takes...
RE Productivity... It doesn't seem like we have to prioritize productive people (as, say, the Inuit needed to). In our societies, medical triage is a balance of prospects and benefit... who is likely to survive and how much benefit may they gain by survival.
As such, a hale and hearty 99 year old might have better chance of survival than a sickly child, but the expected benefit favors the child.
On the other hand, if the choice is between the same 99 year old and a 25 year-old who is in terminal sepsis, we'd do what we can for the oldster.
Productivity isn't part of the equation, per se.
RE Worst Case... I note that the worst case is not. They write:
"2.2 million in the US, not accounting for the potential negative effects of health systems being overwhelmed on mortality."
1 in 5 total infected (20%) need hospitalization, vs. 1-2.3% dying despite adequate healthcare. If healthcare collapses, death rates approach 20% for CV19, plus all other hospital preventable death rates increase. That's 2.2M x 10 to 20+.
RE Human and economic survival... IMHO, they are intertwined. If the global economy collapses (meaning industrial civilization is over), domestic nuclear plants and waste storage ponds will not be able to maintain coolant. Loss Of Coolant Accidents ensue, irradiating the northern hemisphere. Human survival may depend on how well the equatorial trough isolates hemispheres.
So it's not that CV19 would wipe us out directly, but it could set off the deadfall we've made for ourselves.
Here's a representative article that has its counterparts in finance, food supply, transport and the grid:
https://www.theatlantic.com/ideas/archive/2020/03/supply-chains-and-coronavirus/608329/
But here's hoping.
Dave Z
Posted on behalf of JOHN:
DeleteDave,
RE Productivity...
I used the term "least productive" as a catchall phrase to denote that in any triage situation (such as they are being forced to do in Italy) uncomfortable decisions have to be made as to who will get essential, but limited, medical services, and who won't. Deaths by COVID are happening to the weak/elderly/sick, just as a cheetah or a wolf will preferentially kill the weak/elderly/sick. Triage will force similar judgements.
RE Human and economic survival....
I'm wondering if your assessment of nuclear power plant shutdown procedures is too pessimistic? I'm certainly not a nuclear power plant expert, but I would feel comfortable assuming that after both the Chernobyl and Fukushima accidents nuclear power plant operators made careful reassessment of how to contain the "fallout" of both natural and man-made disasters. In the case of a civilizational collapse caused by COVID it seems reasonable to assume that plant operators would have days/weeks/months to prepare for an orderly plant shutdown, if necessary. It wouldn't be anything like what happened at either Chernobyl or Fukushima, which required a fast real-time response. Now whether they could literally lock the doors to a nuclear power plant, throw the key over their shoulders, and safely walk away -- I don't know. But even in spite of the massive radiation release of the Chernobyl accident there seems to be a remarkable recovery of plants and animals in the immediate region.
The article you referenced in THE ATLANTIC suggested that, at least in the US, we have plenty of food to manage until at least the next harvest. So, potentially, people can just sit tight at home for a few months and let the worst blow over. One of the article's biggest concerns was that the disruption of China's manufacturing abilities would cause a catastrophic ripple effect in the US (and, presumably, other developed countries). Yet we see that, with the flattening of the death rate from COVID, China's manufacturing ability is already starting to come back online. I'm wondering if, by the time the US completes its current manufacturing hibernation and is ready to restart production, whether the supply chains will already be on their way to being refilled? You didn't comment directly on the article I provided a link to exploring the Danish attempt to "freeze" business for a few months, and then restart everything? It seems that is sort of what the US is trying to do with the 2 trillion dollar stimulus package making its way through Congress. If only the Orange Man would just go play golf and let grownups make the important decisions!
Best Regards,
John
RE Triage... yep.
DeleteRE Human and Economic Survival... Plant shut-down isn't easy and it can take years to cool. Most need to be de-fueled before coolant is no longer necessary. Waste in storage pools can't be shut down at all, but must be safely stored.
Alas, no deep changes after Chernobyl and Fukushima. The common assumption to safety-in-depth is timely help from elsewhere.
Don't forget, Chernobyl was capped (the 'sarcophagus') and the area massively cleaned up. In total economic collapse, plant workers probably won't be on the job, and remediation is out of the question.
Even so, the bounce-back is encouraging.
RE Snapping Supply Chains and the Food Supply... This is the stuff of the Korowycz papers linked in my last post. They give the wider view most articles lack.
Snapping supply chains produce cascading failures from which the food supply is not immune (e.g., the supply of immigrant workers for fieldwork is a concern). Financew, fuel, parts, fertilizer and herb/pesticides, processing, marketing, distribution and retail all depend on interlocked supply chains.
Once it gets going, beyond some point it's hard to stop. Question is, will it, when and at what level?
Dave Z