Category: Covid-19

Ten million companys’ immunization and contact tracing processes

Pushing responsibility down as far as possible (local government, companies, individuals) is nice in theory, but we keep running up against the reality that people *aren’t* responsible. And we end up with a menagerie of policies that are, best case, uncoordinated and worst case at odds with each other. Go from town to town, you’ll encounter different restrictions. Go from store to store, you’ll encounter different restrictions. I get wanting freedom — I don’t want someone telling me what colour car I am going to drive or what we’ll be doing to relax Friday night. But I don’t see a difference between “the government taking my freedom” and “the company that I work for taking my freedom”. People like to pretend that it’s my choice to work there, thus not really something being forced upon me. Sure, in theory, you can go find a different workplace (University, elementary school, etc) that doesn’t have the restriction to which you object. The practical reality, though, is different. You need money to support yourself – buy food, pay rent, make sure the heat is on – so you cannot just not work. You may not be able to move halfway across the country to work at your perfect employer. Your perfect employer may not have any openings. Or they may elect to hire someone else. Being financially coerced into ceding my freedom isn’t better than the government enacting a restriction.

And there are just some things that are ineffective without a centrally coordinated policy. And that means that, occasionally, you lose the right to chose for yourself.
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Math Time – Delta Edition

An update to my previous mathematical analysis of covid transmission now that I’ve seen R0 estimates for this delta variant …

The R0 value for the delta variant seems to be between 5 and 8. Looks like just over 46% of the US population is vaccinated. The vaccines are published as being 90-something percent effective. That makes an effective transmission rate between (5 * (1- (0.46 * 0.95))) and (8 * (1- (0.46 * 0.9))). Between 2.9 and 4.7 — somewhat surprising given the R0 of slightly under 3 that was published at the start of the SARS-CoV-2 outbreak. That means that, as health orders and mandates are lifted, we’re basically exactly where we were a year ago even though about half the population is vaccinated.

A mathematically interesting thing — if you could get the vaccine efficacy up to 100% (a third shot, a tenth shot, a different vaccine, whatever)? We’d still have an effective transmission rate between 2.7 and 4.3 — the value goes down, but not significantly. On the other hand, increasing the percentage of fully vaccinated individuals by 10% gives us an effective rate of transmission between 2.5 and 4.0. Having 70% of the population vaccinated would yield an effective rate of transmission between 1.8 and 3.0. We’d need to get somewhere between 90 and 98% of the population vaccinated to bring the delta variant’s effective rate down below 1 (the point where it would die out naturally)!

That tells me this virus is going to be around for a long time — especially since the R0 for some upcoming variants might be higher. Also, I’m curious to see if the government authorizes a third dose given the minimal impact increasing efficacy has on the effective rate of spread.

Freedom!!?

About a year ago, my boss observed that this entire pandemic sitch is just a nightmare for those with analytical thought processes.. Engineering, science, analytic types. Mathematically? The country was basically in a worse place when the health orders were lifted than it was when the orders were put in place last year. That was astonishing to me. And kind of like the anti-environmentalists who don’t seem to realize they need to drink the water and breath the air … even if you’re vaccinated and have a very good probability of avoiding hospitalization? Getting sick for a week sucks. It sucked ten years ago, it’ll suck ten years from now. But, if you can mitigate your risk of feeling like an elephant is roosting on your chest for a week … what’s the reasonable thought process that leads to someone saying “I’m going to show how very free I am by getting painfully ill”?!
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I mean, there are plenty of ways to partake in your American Freedoms that aren’t painful illness. Head out to the range, rent a gun for a few hours, and fire off a couple dozen 50 caliber rounds. Publish a rant against whatever part of government irked you this week. Spend the weekend attending church services for ten different religions. Hell, marvel at the fact there’s not an uninvited soldier camped out in your spare bedroom and that the cops aren’t rifling through your belongings. And that just covers the first five articles in the bill of rights.

In fact …

Article Way to enjoy it
I Spend a weekend attending services for a dozen different churches (synagogs, mosques, etc)
II Hire a gun at a range and spend the afternoon popping off 50-cal rounds
III Marvel at how your spare bedroom is not occupied by an uninvited soldier
IV Notice how the police are not rifling through your personal belongings just because they can
V, VI, VII, VIII Don’t know that I’d commit a crime just to enjoy my right not to provide evidence against myself, be subjected to cruel or unusual pubishment, or experience a speedy, public trial … but you do you.
IX Go to work?
X Oooh, experience all of the things your state does control — maybe hang at the DMV and renew your license
XI Umm … well Michigan hasn’t sued Ohio today. Does that count?
XII Well, you cannot be part of the electoral college … but you CAN vote
XII No more slaves
XIV The state isn’t depriving me of life, liberty and such.
XV My rights aren’t being abridged because of my race
XVI Taxes were withheld from my paycheque this week. Yeah!???
XVII My state has tw senators
XVIII Grab a pint!
XIX I’m a woman, and I can vote!
XX Watch the certification of the election
XXI Grab another pint!

Math Time — COVID Edition

Scott’s dad gets on our cases about being paranoid hypochondriacs (or whatever) because we’re still wearing masks and have Anya in online school for another year. The governor dropped the health orders, after all. Anya is too young to be vaccinated, but he’s safe … and kids don’t get sick anyway. Now, I don’t believe the latter two “facts” — kids do get sick, even if it’s less virulent. And I’ve never seen anything published that indicates vaccinated individuals don’t spread the virus. Just that they don’t feel unwell (which, in my mind, makes them more likely to spread it ’cause they don’t know they are sick … the Yankees having so many vaccinated people test positive sticks in my mind. They wouldn’t have known they were sick if it weren’t for what I assume is routine team-wide testing). And it’s difficult to explain to someone who has already made a decision … but the math just doesn’t support the “it’s all good” attitude people are adopting. I’m not an epidemiologist — I went to school for theoretical physics and work in computer science. I have done a lot of data mining and analysis, so I’ve got a decent understanding of the math side of epidemiology without any of the “so what do we do about it” medical knowledge. That being said … the math side of it can be helpful.

There’s a rate of spread for infections — computer viruses or human, in fact. There’s an initial rate of spread when no one has any immunity / has patched their computer (R0 to epidemiologist). If one person gets the virus, they give it to x people over the course of their infection. This is where you either see the total number of infected people trend toward zero of infinity — that is, if one infected person infects 0.5 (i.e. for every two infected people, you get one more person infected) … eventually the virus dies out. If one infected person infects ten others? This is a ever increasing progression — those ten each infect ten more for 100 infected people. Who each infect 10 for 1000 infected people. Which doesn’t seem bad — but those each infect 10 for 10,000 infected. Then 100,000. For each iteration, the number of infected people is 10^n — 10,000,000,000 is ten iterations down.

But preventative measures get taken — in one case, a computer virus caused my employer to shut down the LAN facing ports on every router in the company. Techs had to walk around with a fix-it CD, clean up every computer on a subnet, and then request the subnet be returned to the network. And, if we saw the virus propagating from that subnet? It got locked down again. Highly disruptive, but effective. And that’s where we were last spring with stay-at-home orders.

There are less severe precautions — computers have anti-virus software that look for virus-like activity for day zero identification. In human terms, that means we’re washing our hands after coming home from an outing. Or, as of last spring, wearing masks. Any of these precautions reduce the R0 value — but it can be difficult to predict exactly how much these actions will reduce the rate of spread.

Vaccines, on the other hand, have a quantified (and published) impact on spread. That efficacy and the percentage of the population that has been vaccinated scale the R0 value. The effective rate of spread is R0 * (1 – ( (vaccine efficacy) * (% of population that is vaccinated) ) ). If a vaccine prevents infection for half of the people who are exposed, then the effective rate of spread after vaccination is R0 * (1 – 0.5 * % of population that is vaccinated)). If a vaccine can prevent 90% of infections from occurring, the effective rate of spread after vaccination is R0 * (1 – 0.9 * % of population that is vaccinated)).

For convenience, I am going to ignore partially vaccinated individuals because I don’t know how effective a partial dose is at preventing transmission. The R0 published last year was around 3 — with about 40% of the population vaccinated with a 95% effective vaccine, that’s an effective rate of spread around 1.86 without other precautions being taken.

Now my numbers aren’t perfect — but this is almost a best-case effective rate of transmission. Another ten percent or so of the population is half-way vaccinated even if I don’t want to get that granular with my maths. But plenty of people got a 80-something percent effective vaccine, too. And the efficacy of each vaccine is reduced against variants. Having an effective transmission rate hovering around 2 seems, to me, like a premature time to cease taking other precautions.

Unmasking

The CDC’s revised health guidance has a lot of people celebrating — taking off their masks and rejoicing. From a psychological standpoint, I get it. But, from a functional perspective? I don’t get the mask hatred. There’s some work we do outside (cleaning chicken coops, mowing grass, using a chainsaw) where it’s great not to inhale dust and pollen. Since we’ve got masks, we wear them. Even if SARS CoV-2 were completely eliminated from the solar system, I don’t want your cold. Or your flu. Or whatever other respiratory illness.

Before we had Anya, I thought I had an amazing immune system. I was rarely sick — like once every five or ten years. Since Anya started school — preschool, grade school — I’ve learned that I just didn’t have much exposure to pathogens. With a kid in school, everyone in the household was sick basically from November through April. I cannot believe vast swaths of the population spend half of the year sick! This past year, though? Not a sniffle (well, at least not a sniffle until pollen started blowing around in visibly yellow clouds). Why wouldn’t we continue to wear a mask and avoid the gamut of respiratory illnesses?!

Military Intel, Russia, and COVID

As I’m reading that Russia tripled their reported COVID death toll, I cannot help but recall an old rule of military intel analysis. If the report is a good thing (e.g. amount of grain produced this year), halve it. If the report is a bad thing (here, the number of people dead from a virus), double it. I never took the maxim literally, but rather thought of it as a reminder that ‘the bearer of bad news’ was not something you wanted to be within the Russian government. Thus numbers picked up from internal reports were apt to be CYA inaccurate.

Not sure if that rule was meant to apply to revised numbers (basically our fake numbers are off by a power of ten, so we’re going to adjust within the half/double rule to produce stats that are within the realm of possibility) or if not (reality was so readily apparent that the official numbers had to be revised close to reality).

School’s out for winter

My local school district is moving to remote learning for what’s left of December and a few weeks in January. Not unexpected, and a part of the reason we chose a different learning option for Anya this year. The Superintendent’s message highlights the two big problems I expected with in-person learning. Firstly, 28 positive cases resulted in 467 quarantined individuals. That’s about 16 people in quarantine for every infected individual. The district had about 3,000 students before some percentage opted to use virtual learning this year. Add some 300 staff — they’ve had about 15% of the school out in quarantine in the past three weeks. And that’s before any increase in infections from Thanksgiving. Secondly, people who send their kids to school with COVID-like symptoms (I believe they have a special nurse’s office in each school for those kids to hang out in all day so people who have to swing by the nurse’s office to get medication or a scrape patched up aren’t exposed to a room full of sick kids) and even while awaiting test results.

Liberatarianism is great in theory … but, in practice, the entire point of the belief system is that you’re free to make whatever choice you decide to make. Even if you want to ignore the bears.

Understanding Exponential Growth

Using the data from https://covidtracking.com/data/national/cases: in the most recent seven day span (10-16 November), 1,056,346 people in the US have been infected with this coronavirus. The total number of cases yesterday was 11,047,064. That means 9.562% of the *total cases* in the US were new cases in the past week.

 

This is how exponential growth works — and why you heard a lot about ‘flattening the curve’ earlier in the year. If you put a penny on the first square of a chess board, double it and put two pennies on the second square, double it and put four pennies on the third square, and continue in that fashion … mathematically, you have 2^n pennies on each square, where n is the numeric sequence of the square, 0-63. On the last square in the first row, square #7, there are 2^7 pennies — 128 pennies, or a buck and twenty eight cents. Not a lot. And the end of the second row, you have 2^15 pennies — 32,768 pennies. That’s $327.68 — over three hundred bucks. A lot more than a buck, but not a huge amount of money. But you’re up to 2^23 at the end of the third row — 8,388,608 pennies or $83,886.08. Eighty three grand is a lot of money. By the time you get to the mid-point on the board, the end of the fourth row, you have 2^31 pennies on a square. 2,147,483,648 pennies for $21,474,836.48 — over twenty million dollars. A lot of money, but it’s possible. The second half of the chessboard is where exponential growth becomes unsustainable. The end of the fifth row is 2^39 — 549,755,813,888 pennies. The end of the sixth row is 2^47 — 140,737,488,355,328 pennies. The end of the seventh row is 2^55 —  On the final square, you have 2^63 … 9,223,372,036,854,775,808 pennies for $92,233,720,368,547,758.08 … 92 quadrillion dollars. If the going price of Earth is only five quadrillion dollars, you’re putting a marker for the entire solar system (and then some) on that last square.

And that ignores the accumulating total — while you have 92 quadrillion dollars on the final square, you have another 92 quadrillion dollars on the entire rest of the board. Now, obviously, we are not doubling our rate of infections every day. But we’re entering “second half of the board” territory just the same.

Large Numbers

It’s often difficult to conceptualize large numbers — something that allows statistics dealing with large numbers to convey something other than reality. I think I heard Trump say the government is ready to vaccinate 200k people a day. That sounds like a lot of people (it is a lot of people), but there are a lot of people in the US: an estimated 328.2 million according to a quick Google search.

 

That’s four and a half years to vaccinate the current population of the US at 200k a day, every day. Which doesn’t take into account new people being born (or aging into the range where a vaccine is administered). The CDC shows 3.79 million births in 2018 — of course that number changes every year, and it’s been decreasing. But at 3.5 million births per year, new people still add a few months to the vaccination timeline. About four and three quarter years to vaccinate the US population. And that assumes a one-dose vaccine. Administering two doses to everyone, at 200k people per year, would take just under ten years. Saying ‘it could take us five years to vaccinate everyone’ isn’t nearly as impressive sounding as ‘we can administer 200,000 vaccines each day’ — but it’s the same thing.