April 1, 2020

Why population size is irrelevant for spread of epidemic, and why open borders truly did screw Sweden in coronavirus pandemic

The following tweet has gotten quite a bit of attention, pro and con, and shows the number of coronavirus deaths in Scandinavia: deaths in Sweden have exploded higher than in Denmark, with Norway showing the fewest. It got so much engagement because it pointed out the public policy difference, where Denmark sealed its border while Sweden has been defiantly laissez-faire about borders, lockdowns, etc. Conclusion: don't be like the libertarian Swedes if you want your country to survive.

Note that the number of deaths began rising at essentially the same time in all three countries (around March 14), so it's not as though one curve has exploded higher because it's had more time than the others to grow. If you want to begin counting time from "the date when the number of dead hit 10," that too is the same day in both Sweden and Denmark (March 18). Also note that the initial number of deaths is about the same in all three countries (around 5), so it's not as though one curve has exploded higher because it had a gigantic number of initial deaths that only got worse and worse.

(Norway is a separate case, since their date of reaching 10 dead lagged behind the other two, around March 23 or 24. That's 5 or 6 more days, and since the doubling time for this coronavirus is around 3-6 days, Norway's dead could wind up the same as Denmark's, for the same number of days after the epidemic claimed 10 dead. Hopefully their elites are not as callous as in Sweden, and they get spared the worse of the two cases.)

The latest figures say that Sweden has 180 deaths, Denmark 90, and Norway 39. Recently, Sweden has tended to have twice as many deaths as Denmark.

This damning indictment of open borders during a pandemic has forced the rationalizers to scramble for an excuse. They have never studied math or biology, let alone both at the same time, but they have spent a lifetime reading science-affiliating data dorks on the internet. So what's the first excuse they hit on? Adjusting for population size! The data above are sheer numbers of dead people, not their rate per capita. "After all," Sweden has twice as many people as Denmark. Ergo, it's only natural to discover that they have twice as many dead, revealing the death rate per capita to be the same for both countries.

This is cargo-cult data analysis -- whenever you see a sheer count for some group, automatically adjust it for the population size of that group. Don't think about whether or not it makes sense -- it always makes sense, because it's one of those magical rituals that purifies the data. Data, unadjusted by some analyst, can only begin in a polluted state, and need to be purified by his magic spells.

The view of "controlling for population size" is like saying there's a giant gun pointed at the entire population of Sweden, and the entire population of Denmark, all at the same time, and when the gun fires its one big shot, it kills say 5% of what it's aimed at. Pull the trigger, and 5% of Sweden dies, along with 5% of Denmark. But since Sweden has twice as many people, it will have twice as many total deaths.

But that is not how the growth process works for epidemics -- or any exponential growth process, for that matter. The contagious disease is not targeting the entire population at the same time, and it does not do its thing all at once. Contagious diseases are contagious -- they have to start somewhere, and then work their way out from the starting point, at some growth rate. The initial number of infecteds has to pass it on to the next round of infecteds, and so on and so forth.

To take a numerical example, suppose it starts with 1 person, and then doubles with each step of time (it doesn't have to be a day -- it's however long it takes to double in size). So it goes: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, etc. In these 10 time steps, it's multiplied by about 1000 (from 1 to 1024).

That's how it will proceed in any country -- it starts with 1 initial infected and multiplies by 2 after each time step. It has nothing to do with total population size, because at first the disease only "sees" the first infected, and then it "sees" double that number, and double that number, and so on. It does not, and cannot, "see" the entire population beyond these initial rounds of infecteds. It's spreading from person to person, and has no point of view from which to survey the entire population.

It is not supplying a demand, as though a cell phone company saw the entire population size of the two countries, and ordered twice as many cell phones to supply the Swedish market as the Danish market. There is no national-level disease source that is supplying twice as many viruses to Sweden as to Denmark, in order to accommodate their higher population size. It's just blindly moving from one infected individual to the next, without a clue as to how far its reach, in sheer numbers, will eventually extend by the end of the epidemic.

To put it more bluntly, remember those 10 time steps during which it rose from 1 to 1000? What would it matter if the population within which it's spreading were 1 million or 10 million? It's only growing to 1000 -- not even close to exhausting the "smaller" population of 1 million, so what good would it do the virus to have an additional 9 million people in the overall population? They would be useless for fueling greater growth in the larger population.

It does matter if the population size is 100, or 1000, or something small. Then there's no way it can complete all 10 time steps and reach 1024 infecteds. But if you're talking 100K, let alone millions, 10s of millions, billions, etc. -- then no, differences in population size do not help or hinder it from reaching a certain number of infecteds, during the early stage.

When it eventually reaches its peak -- let's say at 50% of the population (hopefully nowhere near that close in our case) -- then of course population size matters. If it eventually peaks at 50% in both Sweden and Denmark, then it will have produced twice as many infecteds in Sweden. If the death rate among infecteds is the same for both countries, then Sweden will also have twice as many deaths at that later stage. But not in the early stage, which we're still in for awhile.

Worse for the rationalizers, we don't even know that the peak percentage of the population that gets infected (and separately, who die) will be the same for Sweden and Denmark. It's not necessarily a matter of Sweden ultimately reaching the same maximum per capita rate as Denmark will, only getting there faster. It could be that Sweden will reach a higher maximum in the per capita rate of infecteds (and so, of deaths). If so, then its exploding numbers in this early stage are a harbinger of a much more dire situation at its peak, compared to Denmark at its eventual peak.

For now, all we know is that it's spreading faster in Sweden than in Denmark, because the initial number of infecteds was essentially the same in both countries, and the process started about the same time in each country. In the equation for exponential growth, the number at any given time is only a function of the initial number, the amount of time that's passed, and the growth rate. That leaves only the growth rate as differing between Sweden and Denmark, if Sweden has become so much worse off by now.

Denmark closed its borders on March 15, and the effects take about two weeks to observe, given the time to catch the disease, show symptoms, and then die. Within two weeks of this divergence in public policy, the divergence in number of dead was clearly evident. Swedish elites chose to sacrifice their people on the alter of libertarianism and open borders, while the realigning Social Democrats in Denmark have begun fusing populism with nationalism (meaning, anti-globalism), and have saved a good fraction of their citizens who would have surely perished if the elites had followed the open borders model.

My guess is that, after conceding the point on this matter, the rationalizers will next grasp for the excuse that open borders only caused deaths to double, rather than amp up by a full order of magnitude or more. As long as your policy decision only kills 9.99 times as many people as the alternative, what can the peons possibly complain about? They're practically the same outcomes!


  1. Charts of death totals for many countries, including Sweden and Denmark, with a note that Sweden's open borders and anti-lockdown policies have given it a steep slope:


    See the rest of that thread, including a little video where he explains why per capita rates do not describe epidemic growth. There's another chart in the thread showing the lack of correlation between population size and total deaths.

    Burn-Murdoch is from the Financial Times -- as usual, the finance people are more straight about what's going on than the ideological / emotional retards on the left and right.

  2. Viruses are the population that matters, not us. We are just their food.

    Give a single individual some food, and they'll convert that into making more copies of themselves, by reproducing and then ensuring their offspring are well-fed in their turn.

    Each of those offspring will be well-fed, reproduce like mad, and so on and so forth. Exponential growth, as each individual begets multiple offspring.

    But when they're just starting out their population growth, how much food can they possibly need? If there's hardly any food around, sure, increasing the amount of food will strongly increase their reproductive rate. They go from avoiding starvation to being well-fed.

    But as there is more and more food in the environment, it becomes less and less useful to fueling further growth. Pretty soon, there could be 10, 100, 1000 times as much food as before, and it won't make any difference -- because the population eating that food could not possibly chew through even a small fraction of all that abundance.

    The vast majority of such superabundant resources will remain idle in the early growth stage.

    Only after a long period of exponential growth will those resources start to be targeted by the population. And by that point, there will be stiff competition over them.

    When the population has exploded to such a size that it's setting its sights on the full extent of the resources, then a damping mechanism kicks in. During this saturation stage, resources have gone from abundant to dwindling. With only so much food to go around, competition gets fierce, and not everyone gets well-fed -- or even fed at all. Population growth slows.

    For contagious pathogens, this saturation stage happens when they've burned through so much of the susceptible population that there are no longer superabundant targets left to infect. That is the only limit on the disease's spread -- the dwindling number of targets for each infected to transmit the disease to.

    But we're nowhere near that saturation stage -- this sucker has just gotten started and is accelerating like a drag racer on a straight open road, with no obstacles in sight for a long while.

    That's why that chart from the FT writer shows no correlation between population size and growth of the epidemic. Give the initial virus 1 million, 10 million, 100 million, or 1 billion units of food to chew through -- it can't even put a dent in the smallest buffet, let alone anything larger.

    So, it will grow to roughly the same size, after the same number of days, no matter which population size country it lands in. The only difference is the growth rate, which determines how fast it reaches those milestone markers. In an open borders country, faster. In a closed-border, lockdown, mask-wearing country, slower. With enough protective measures for long enough, maybe it even decreases in size.

    But none of that has to do with the population size of the food source (us).

  3. The chart showing no correlation b/w pop size and epidemic growth is not even necessary, and I hesitate to mention it.

    Putting it out there makes it seem like it's an empirical question to be resolved by gathering data and analyzing them. As though there's no theory that tells us ahead of time what that result will be. This is the approach of the data fetishist / cargo-cult analyst.

    The simple theory of population dynamics tells us a priori that the amount of resources is not going to fuel further growth of the population using them, beyond a certain amount, in the early stage. Applying that theory to our case of the coronavirus spreading in nations that are at least 1 million in size, and up to 1 billion, in the early stage of growing -- we know without examining a single data point, that there will be no correlation b/w pop size and growth of infecteds (or # of dead).

    It's OK to provide charts like that for illustrative purposes -- to exemplify a larger pattern from the theory. "Theory says such and such will happen, see figure 1 for an example."

    But on the internet, no one has studied anything, they've just taken in a shitload of factoids, charts, etc., from other non-theoretical people. So every question is a mystery that can only be resolved by "getting a bunch of data" and analyzing them. "What do the data say?" That what goes up, comes down? Wow, I fucking love big data science!

    Some of these things are so basic, yet are treated as unresolved mysteries that a massive project must be funded in order to answer.

    Some things *are* empirical, of course. Which particular gene influences your eye color? Which particular sound patterns have been trending in baby names over some time period? And perhaps more detailed theoretical problems need to be put to an empirical test.

    But not everything -- not necessarily most things that are the most talked about in "the discourse". For most of those topics, empirical data are only going to illustrate an already understood pattern.

  4. Re: commentators who "haven't studied theory," I don't mean credentialing (taking out debt to finance a grade-inflated degree). They could be self-taught, whether in some narrow hobby interest, or in wide-ranging curiosity.

    People who never studied population dynamics / ecology / evolution / etc., who don't know theory, who can't do basic math (let alone phase plane analysis), and so on -- that includes a good share of experts, unfortunately, not just random retards on the internet.

  5. Sweden-Denmark gap widening further: 239 vs. 104 dead by 4/2. Sweden started with a little under 2 times as many dead, then 2, now 2.3. Heading in the wrong direction -- but that's predictable, given their policy decision.

    Sweden's decision wasn't even to merely "stay the same," as opposed to closing the border, locking down, etc. It was to intensify the status quo. If we normally hung out in public places for 1 hour a day, make it 2! If we normally kept 3 feet of personal space, make it 1! If we normally covered our mouths when coughing, let's cough and sneeze directly into someone else's mouth! Let's invite twice as many foreigners and tourists into the country!

    Again, it's tempting to say "Karma is a bitch" or "Live by virtue signaling, die by virtue signaling". But it's the elites who made those decisions, whereas the commoners will be bearing a disproportionate burden. It's just another case of the elites forcing higher costs onto the commoners.

  6. Even worse! Sweden 308 (up 30% in a day), Denmark 123 (up 20% in a day). Sweden now has 2.5 times as many dead as Denmark, and that gap is only widening.


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