The Numbers of Epidemics and Why Keeping Cafes Open is More Important than High Schools

This post has 1976 words. Reading it will take approximately 10 minutes.

There’s this old joke/riddle/maths puzzle: an algae is spreading in a lake so that every night, the covered area doubles. After 10 weeks, 70 days, the lake is fully covered. After how many days was the lake halfway covered? The correct answer is, of course (but very counter-intuitively), that it is half-covered after 69 days (nice!), on the penultimate day. Epidemics spread much the same way.

Our intuition is completely bunk because the case deals with exponential growth. The algae do not spread at the same amount every night, nor does it spread at a constantly increasing speed. We can mostly grasp those: if it grows with a constant amount, the lake will be halfway covered after half the time. If it grows with constantly increasing speed, the lake will be halfway covered after just over half the time (70% or half the square root of 2, so after 50 days). Exponential growth is treacherously slow to grow in the beginning but insanely fast near the end. We might ask how covered the lake is a week before it is fully covered? The answer is that less than 1% of the lake is covered (the exact number is 1/128 of the lake is covered). After 9 weeks the lake is covered to a point where it is barely noticable and just a week later it is fully covered.

For an infectious disease, the rate of infection depends on 2 things: how many are infected and how infectious the disease is. This leads to exponential growth like in the lake.

If a disease doubles, say, every week, one week before everybody is infected, 50% is, and 2 weeks before, “only” 25% is infected. A month before everybody is infected, a barely noticeable 6% is infected. Add to that that an epidemic like COVID has 1-2 weeks of incubation time before serious symptoms, and then one month before everybody is infected, only 1.5% of the population is showing symptoms.

That’s why the number of cases on Worldometer is irrelevant, except we can see that around 20 countries are one month from total infection in my thought-experiment as of today, including the US and Brazil. Even though the ticker mentions around 25M infections world-wide, if my case were true, we’re one month from 750M infections. I do not believe that to happen; this is just an example of how counter-intuitive the math is, so you don’t get to call gotcha in October.

That’s why arguments like “it’s no worse than a flu” mean nothing. Yes, in absolute numbers COVID is presently harmless. Yes, I’d consider the 0.85M deaths irrelevant considering it is eclipsed by “extinct” diseases like HIV/AIDS and self-caused ailments like tobacco and alcohol (each of them individually and often by significant margins). Our common sense is useless to decide whether an epidemic is a problem here and now and in the near future.

The only way to control this is to control the rate of infection. It turns out that the major decider for the rate of infection is the number of social interactions. There’s a slight nuance here, as distance in an interaction matters as does time, but let’s largely ignore that.

A very important point is that if the number of newly infected per case (R0) is greater than one, the growth is exponential and uncontrolled as illustrated above, while if it less than or equal to one, it is not (exactly one is a special case that doesn’t matter in practise). There is no nuance here. If it is 1.000001 we end in disaster, while if it is 0.999999 we do not. That means there is a hard limit of the number of social interactions we can allow: we can allow exactly so many that we are certain that the rate of infection is less than one. In that case, the disease dies out. If it is every so slightly above one, we end up with everybody infected and it can sneak up on us, so it does not matter whether there were more or less than new 100 infected today. We can even without too much danger use almost all of the social interactions up until we reach the magical number 1: the disease will still die out.

We therefore need to spend the social interactions in a smart way. A lot of people (in Denmark) are fighting great wars on Facebook (so brave!) about how it can be that high schoolers must stay home while cafes remain open. That’s because they cannot both be open or the infection rate goes above 1, and cafes are more important than high schoolers.

I’m not even being ironic here. It is more important to open cafes than to allow high schoolers back in school. High schoolers are old enough that parents don’t have to stay home to care for them, so keeping them home does not prevent others from going to work, and very little is lost by leaving them home. Teachers will cry about how their jobs are the most important and we are holding back the future, but the reality is that at worst, we delay high schoolers for one year. Too bad. We are all losing a year due to the epidemic, deal with it. Like, literally, if they fall behind due to remote teaching, have them retake the year.

It is very important to keep the economy going. If, say, 25% of the population cannot work, that is very, very expensive. How expensive? Well, if we assume the 25% is the low-pay jobs, and let’s say they make 2000/month and everybody else on average 3000/month. If we pay 50% in tax on average and a bunch of socialists will insist we cannot cut back on welfare, that means we have to pay the same in taxes as before. 4 persons would before the lockdown pay 3 * 3000 * 50% + 1 * 2000 * 50% = 5500, and people would take home 1500 or 1000. After the lockdown, only the 3 people would pay taxes, but would still have to pay 5500 in taxes. Realistically, they might even need to pay more as expenses are up for things like healthcare while earnings are down for things like childcare, but let’s ignore that. That means the three still in job in total only take home 3 * 3000 – 5500 = 3500, or 1166 per person.

If we decide that the take-home should also be shared with the fourth person who is forced home due to no wish or fault of their own, and we share the take-home according to the previous take-home, people now only get 954 and 636 or less than two thirds of their previous take-home pay. If the fourth person used to make the same as the three others, the numbers get even worse, and everybody only gets to take home 750 or half of what they did before. Let that sink in: if 25% of people are forced to be without work and we don’t humanely put them down and don’t reduce welfare, it means everybody only makes half of what they used to!

That is a huge problem: we cannot long-term continue spending as before if we are not willing to cut back on welfare, so it is very important to get people back to work as fast as possible. This is especially important with jobs like cafes, because reducing sales now does not mean sales will compensate afterwards. If I want to buy a new fridge or car now, but don’t because of an epidemic, I am very likely to buy one after the epidemic is over: my purchase is just postponed and not cancelled. People that wanted to buy a fridge after the epidemic will as well, so all of the fridges that would have been sold without the epidemic will also be sold with the epidemic, just postponed ½-1 year. Cafe visits don’t work the same way. If I go for a beer every Friday, but am unable to for a month or 6, that does not mean I’ll go twice as often or drink twice as much in the period afterwards. The lost sales during the epidemic are just gone. Heck, it may even be worse: maybe I’ll change my habit to just get drunk at home on twitch during the epidemic and keep doing that afterwards, leaving the cafe without any business even when things return to normal.

Shutting down cafes is hurting immediately and may even kill off an entire sector. The same may be true for other sectors. Some we may want to die, some may recover in the years afterwards (killing off current business owners paving the way for new ones 2-5 years down the line). Since this is a problem across all sectors that don’t produce tangible goods, these people cannot just get a job in a related or different sector, but we can expect huge unemployment for years as entire sectors are permanently wiped out simultaneously.

So, that’s an economic reason that keeping cafes open is more important. If you don’t believe in economics, there’s also a more immediate humanitarian reason why keeping cafes open is better than opening high schools: keeping cafes open reduces the number of social interactions. Without cafes, people would still meet up with a few friends. Maybe have a drink at home or in a park. Maybe people aren’t as good at keeping distance after a couple of drinks and washing hands becomes hard after pissing 3 beers into the bushes. But cafes on the other hand have strict guidelines for people: they need seats at appropriate distances and everything is disinfected. Sober staff make sure of this. People can better meet at a cafe without making significant social interaction than they can if left to their own.

I work in an office. Some of my colleagues have started going back to the office 1-2 days a week to keep social contact. I refuse to, because I think it is terribly egoist that people who can easily work from home don’t do so. Leave the social connections to the people that cannot work without them. Each person that goes to the office because they get bored working from home is taking a job from a person that has to be at the hospital, supermarket, or cafe to work. Heck, work from home for a week and meet up with colleagues or friends one evening at a cafe to get social interaction in a safer way that also supports people that unlucky enough to not be able to work via Zoom/Teams/Hangouts.

For the same reason, I believe that anybody that is traveling abroad, no matter the destination, this summer should be put in a 2 week self-financed mandatory 100% quarantine afterwards, and forfeit any rights to be treated by the health system for 2 months afterwards. That is the most egoist waste of social connections and I’d not be terribly sad to read about these people on the Darwin Awards.

So, in conclusion, we cannot use our common sense when dealing with exponential growth like an epidemic. Just because there are few infected and dead, exponentials sneak up on us! The only weapon is avoiding exponential growth, and the way this works does also not have a common sense interpretation; instead, there’s a very hard limit on the number of social interactions we can allow. That limit needs to be spent on people that cannot get by without it, which means that anybody that can should work from home even if the numbers don’t look bad. That includes office workers and students even if it may feel unfair to the individual, because other people need those social interactions for their job. We cannot continue ignoring that some jobs may just not be there to return to once the epidemic is over if we don’t let them return now even if it may seem counter-intuitive.

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