Martin has been kind enough to put together a Guest Post on Data Modeling in the Epidemic. Part 2 will be posted on Thursday afternoon.
Martin is standing by in case we have questions.
Take it away, Martin!
Questions on Data Modeling in the Epidemic: Part 1
So, like Cheryl (such good company I find myself in!) I thought I’d provide some information on data modeling this grand experiment we find ourselves all in. I do have a statistics background and do a fair bit of data modeling of population behavior. I’m not an epidemiologist, but good data modeling always requires some degree of understanding the context the model operates in so that means spending some time becoming a ratchet epidemiologist – knowing just enough to understand how to make the model work.
Epidemiologists arm us with a bit of information regarding the behavior of this particular virus. We have the R0 (r naught) or the reproduction number that says that each person who is infected will infect R0 other people. That is determined by the infectious period (how long you can give it to someone else), the mode of transmission (air, water, touch, etc.), and the contact rate (how many people you are likely to interact with). We also know how long before symptoms appear, how long before fatality is likely, how long to recovery. These are statistical values and vary from person to person. Early in an epidemic you have fairly small sample sizes so it often just looks like chaos, but later when sample sizes are much larger those statistical values start to really show up.
Why is this such a big thing?
Well, there’s a few things going for it. An incomplete list:
1) Nobody has natural immunity, so for the contact rate above, every person an infected person comes in contact with is a potential new infection. One reason why the flu doesn’t do this is that depending on the strain of flu, there’s people walking around immune, so it doesn’t spread through them. That’s what herd immunity does – if enough people are immune, an infected person can’t find enough others to pass it along to for it to explode through the population. (This is a good place to ask Cheryl about how nuclear reactions and nuclear moderators work – basically the same process)
2) Nobody has artificial immunity. No vaccine. Again for the flu, that flu shot not just protects you personally, but helps add to the herd immunity.
3) Good modes of transmission – inhalation, contact, and fecal transmission. Hong Kong had some apartment blocks spread it through the sewer system, even when people were locked down. This is a combo that is notoriously hard to protect against.
4) Durability – it can hang in the air for hours and on surfaces for days, boosting that contact rate. It can live long enough that if the stocker at the grocery store spread it to the jug of milk overnight, it can still be there when you put it in your refrigerator.
5) It looks like other diseases – early symptoms are flu-like, so rather than rush off to the doctor, we tend to keep acting like it’s the flu, treating it like the flu, and protecting ourselves like it’s the flu. But it’s not the flu, so those things don’t work sufficiently. Ebola struggles to spread because it’s in the ‘holy fuck this guy is dying’ category, not the ‘take some Advil and go to work’ category.
6) It doesn’t affect everyone the same way. This is more important than it might seem. The 1918 flu killed young people more than old people. That allowed old people to unknowingly spread it much further than if they had fallen ill at the same rates. Covid is the opposite. Where that really matters is with testing. If you only test people who are really sick, you leave a whole bunch of people only slightly sick to run around and spread it. And it’s hard to get people to stay home sick if they don’t feel sick.
R0 is important because it tells us roughtly just how fucked we are. An R0 value of 1 means that everyone who gets it will give it to one other person. That leaves you with a fairly constant population of sick people which is very easy to deal with. An R0 value that is less than one will eventually die out on its own, or at least shrink to the size that it’s no more than a nuisance. An R0 greater than 1 means that the population of people who get infected will grow expoentially until you see things like herd immunity show up and start to knock that rate down by shrinking R0 by slowing the contact rate. An R0 value well above 1 means we’re going to go through some shit. The estimates out of China was that Covid had an R0 of around 2.7.
But R0 is not a property just of the virus but also of the population and their behavior. We calculate it for the population at large but every context will be different. A highly dense city like NYC will almost certainly have a higher R0 than a less dense city like Des Moines. When I lived in NYC we lived in a 5 story walk-up. There was no elevator, so you had to climb the stairs to our 4th story apt. There were about 100 people living in that building, all using the same front door handle, all touching the same mailboxes, all running their hands along the same handrails. That’s a lot of contact. I now live in a detached single family house. Only 4 people ever touch the front door or the railings. Much lower contract rate. When my wife comes home with a week to two weeks worth of groceries everyone heads out to unload the car and bring them in. But when you live in a 5 story walk up, you don’t do multiple trips to haul in 2 weeks of groceries, instead you maximize each trip. You know you’re going to climb those stairs at the end of every work day so you bring a single load of groceries with you every time – about a days worth. That means you’re going to the store roughly every day, interacting with others, etc. Again, that’s a lot of contact. In a university, a 500 seat lecture hall has roughly 10x more contact than a 30 seat K-12 classroom. That’s why universities moved to online instruction so early. Our R0 value was going to be massively higher than your kids 2nd grade classroom. Nurses have more contact than accountants, etc.
Why are some places blowing up worse than others?
Well, for NYC, the population density and community behavior of more regular store trips, more frequent eating out, and so on means that their R0 value could be much higher than 2.7, while a lot of California which saw the virus earlier than NYC has a value that might be somewhat lower than 2.7. Italy is denser than the US on average, so they’re having a bit harder time with it. Canada is lower than the US, so they’re having a bit easier time.
A containment strategy basically means to identify and isolate the infected so that their R0 reaches 0. For ebola that might mean a perimeter around the village so nobody goes in or out until nobody is infectious. You’re going to knock down the contact rate to 0 until the infection period is over, and it can’t be spread. For measles, it means isolating the person’s home the same way. But it relies on being able to identify who is infected, and then tracing where they’ve been, who they’ve been in contact with and prophylactically isolating those people before they become infectious and only releasing them after testing.
This strategy failed in the US because we couldn’t test and isolate as fast as the infection spread. It succeeded in South Korea because they could. It failed in Wuhan for a few reasons – a little bit of denial at first, but that was only a few days, but then a lack of a test.
The goal of containment is R0 = 0.
When containment fails, you mitigate. You’re giving up on R0 = 0. You can’t do it. But you can do R0 < 1, so you’re trying to get the number of cases to shrink to a small enough value that you can either maintain that state until something like a vaccine shows up, or you get the problem to be small enough that you can try to make containment work again.
That’s what China did. They mitigated, shrank the problem, and outside of Wuhan appears to have achieved containment. Jury is still out on whether they can get there for Wuhan as well.
That’s what the US is doing – reduce the contact rate. What is needed? Well, probably more for NYC than for Des Moines. Social distancing and hand washing might work in Montana but not Des Moines. A lockdown sufficient for Des Moines might not be sufficient for NYC. And if people don’t follow the rules, you might need to do more.
The goal of mitigation is R0 < 1
So, how do we know if containment is working and for how long do we need to do this?
That’s where the modeling helps us in Part 2.