Norway in Lockdown - The Math Behind

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13 March 2020

Today I didn't head down to Flesland to run a half marathon this weekend in Cyprus. Cyprus got 2 cases of Coronavirus Tuesday and it got cancelled. Even though Cyprus would likely be fun I decided not to go. Was it a dumb decision based on fear? Well, I'm not really afraid of getting Covid-19, but I am worried about get stuck somewhere. It's pretty likely when I tried to come back next Wednesday all the airports in Norway would be closed. Even if I did get back in, I'd still have to undergo a mandatory 14 day quarantine - as if the country with the 2nd highest infection rate (171 cases per million to Italy's 292) should really be worried about it coming in rather than us spreading it elsewhere. The Helsedirektoratet here yesterday issued sweeping regulations the effectively shut down Norway. Schools, gyms, restaurants, hairdressors, you name it - all shut down until at least March 26th. Bergen kommune went even further.

But there are only a few hundred cases of which only a handful are serious and only one person has died. Is this not shutting down all the roads in the country for one serious accident? How is this not a gross over-reach of government power? Long time readers of this blog will know that I come with a libertarian leaning perspective on the world, but I'm also a math guy by training. I am deeply distrustful of how the Norwegian government is handling their medical resources (the state runs healthcare after all), especially if government employees get to go to the front of the line for care if the outbreak requires rationing. It's a short step further to start euthanizing patients that have been declared terminally ill to free up hospital beds for those deemed more likely to recover. Sure, that's probably way too dystopic, but how many years ago was Quisling? Odds are it won't come to that though because of the government's broader heavy-handed apporoach, which, if you believe force is okay to achieve policy aims, is not bad math. Here's why:

Infectious epidemics increase exponentially.

Infectious epidemics increase exponentially, so graphing it logarithmically (below) one can see that it looks linear. This is a good way to see if a model fit (in this case linear regression) is a good fit. The model for the first couple weeks of infection is

cases = 10 ^ (0.162 * days + 0.462)

based on this early data. This means by when I would have been flying home next Wednesday Norway is likely to have around 7000 tested cases (the asymptomatic and unreported infections aren't being counted), which means there'll be around 250 serious cases. Norway only has a couple hundred respirators so that's beyond capacity already. By month's end if the exponential trend continues there will be nearly a million case in Norway and people will be lucky to get pallative care as this is only a country of 5 million people.

So is this government overreach to shut things down now in Norway as best they can to try and flatten the infection curve to keep it from completely overwhelming capacity? Let's say best case scenario this disease tops out at a few hundred deaths because of these measures that cause people to lose two weeks of their productive lives.

2 weeks * 5 million people / 52 weeks in a year = 192,307 years lost

But if the mortality rate is 3.4% then a million cases means 34,000 deaths. Most people dying are over 60, which means that they have less life to live. Let's say minus coronavirus they would average 10 more years:

1 million people * 3.4% mortality rate * average 10 years lost = 340,000 years lost

So these government measures might just be saving humanity 150,000 years of life collectively. And that's just in the little country of Norway. Of course we can't run a control experiment to be sure, but let's just take the Spanish Flu as our historical control because it had a similar ~3% mortality rate. Norway's population was half what it is now and they lost between 13,000 and 15,000 people. So it's a good bet without doing something there would be a similar result. So it still begs the question why am I staying home when there's such a small danger to me beyond the inconvenience of getting back? Because I love my 93 year old grandmother and I bet you love yours too.

And if you want to see the data I used (courtesy of in days from the first case on 2/26):

Days Cases log(Cases) Model
0 1 0 3
1 4 .602 4
2 - - 6
3 15 1.176 9
4 - - 13
5 25 1.398 19
6 33 1.519 27
7 56 1.748 39
8 86 1.934 57
9 113 2.053 83
10 - - 121
11 169 2.228 175
12 192 2.283 255
13 277 2.442 370
14 489 2.689 537
15 621 27.93 780
16 1,132
17 1,644
18 2,388
19 3,467
20 5,035
21 7,311
22 10,617
23 15,417
24 22,387
25 32,509
26 47,206
27 68,549
28 99,541
29 144,544
30 209,894
31 304,789
32 442,588
33 642,688
34 933,254
35 1,355,189

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This file last modified 14 March 2020 by Bradley James Wogsland.

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