learning wrote: ↑Tue May 19, 2020 7:46 pm
Thank you for your very clear explanations about herd immunity in reply to JL13 a few pages back. For an astrophysicist you are very knowledgeable about epidemiology. Looking at the first few pages of this thread, you already knew this before this current pandemic started. Did you take a course in epidemiology? Would you recommend a textbook on something like Infectious Disease Epidemiology but not specifically the mathematics? Something for understanding thoroughly the basics, but especially herd immunity.
Have you looked at "overshoot" at all in relation to herd immunity? Is it true that once the herd immunity threshold is reached an estimated 33% of the remaining uninfected population is still infected? Clearly, this 33% would depend on many local variables. Do you know any sources that discuss overshoot in more detail?
No courses, but I did have a prior interest in infectious diseases (I seem to always pick the morbid hobbies) and I have read some books (I read a lot). Many of the epidemiological modelling techniques have overlap to previous works in physics and finance, so I have some (10+ years) experience in the strengths and weaknesses of such models. Where/when to apply them and where/when not to. How to modify, etc. Also means I can read professional papers and somewhat understand what they're doing. However, given no formal background, I lack domain knowledge. I suppose an analogy would be if you were fluent in the Java# programming language and saw a python program for the first time, you'd have a pretty good idea of what was going on and be able to learn it pretty fast, but you'd still have significant holes in your knowledge about specific and possibly important details. For example, I'm learning as we go along on the medical/diagnostics side which is pretty far away from my expertise.
I've mostly read popularized nonfiction (books with no equations) for the background + wiki pages and scientific papers for the details. Textbooks are murderously expensive (especially when buying them randomly trying to find a good one), so I don't have any good recommendations. The ones 7wb5 mentioned looked good, but I haven't pulled the trigger yet. For a cheap and good intro, I did like
https://www.amazon.com/Epidemiology-Sho ... 19954333X/
So to answer your question if I understand it correctly. The recent exchange with 7wb5 discusses this in some detail + the last reply to JL13. The (R0-1)/R0 solution presumes random uniform infection transmission, that is, everybody in the entire population can randomly infect everybody else. That is, of course, extremely simplifying (The very simplest model anyone can imagine). In reality, we don't meet randomly with people---although it's a good assumption in a restaurant(*). We meet some people (spouse, children) more than others (colleagues). Some we meet every now and then (friends, neighbors, gym buddies) and some we meet daily (colleagues). Some we practically never meet (most people living far away). But then again, there's a reason that 5 degrees of Kevin Bacon is a surprisingly fun game.
(*) Or is it? Not everybody goes to restaurants and frequent guests might know each other. Same thing with train commuters.
It still holds that in order to survive, the disease still has to tag >=1 new person before the infected person recovers or dies. However, one can imagine all kinds of ways that this would be possible in ways that actually exceed (R0-1)/R0. This is where domain knowledge becomes crucial. For example, an airborne disease is much closer to obeying a random assumption, especially if it travels far (measles) with a high R0. An oral-fecal disease like polio would be more likely to travel along the sewerage/water system and thus would be better described by network theory. Sexually transmitted diseases are even more selective---they'd resemble social networks. Think HIV in the early days. Or just think about how the dominant transmission mode of CV19 has changed from droplet (pre-lockdown) to fomite (surfaces) (where properly locked down) thus requiring a different model.
The proper model (is it random? is it a network?) therefore very much depends on the transmission mode. This requires domain knowledge to figure out.
But yes, even the random transmission model's herd immunity is only a threshold and in practice there will be some overshoot as soon as people at the threshold cluster just a little bit. A good example of this measles. In the US we're right around herd immunity for this, but clusters of anti-vaxxers are NOT random and so if the virus gets into those clusters, it will wash through the entire cluster. Another way of saying this is that assuming random => assuming social distancing (to everybody else in the population) is random as well---but it's clearly not. A model is only as good as its assumptions.
Advanced: A complex model can still be (and often is) "reduced" to a simpler model in order to communicate it better. This is done by fitting the simple model (for example the (R0-1)/R0 herd immunity) onto the results of the complex model. The reason this is done is that experts have a solid fundamental (they're mentally wired in) understanding of the simple models (like the randomized infection), so if a complex agent based model (that has no innate awareness of herd immunity) has the disease die out at 56% infected,
experts will still talk about "herd immunity" as a short-hand for the more detailed result. It is similar to how we talk about "temperature" of something instead of talking about the velocity distribution of its microscopic constituents. This is useful as long as everybody is on the same page. But they're not if we (laymen) start thinking that that simplification is an accurate description of what experts are actually doing or the depth of their concerns.
WIRED has these great videos in which an expert explains something at five different levels (5th grader, teen, college student, grad student, and expert). It's cool to see the difference between how scientists talk to the general public (5th graders and teens), decision makers (teens and college students), and each other (grad students and experts). The parent-child and adult-adult interactions I was talking about earlier. Here's an example with CRISPR.
https://www.youtube.com/watch?v=sweN8d4_MUg I think this video (and the other ones in the series) illustrates how easy it is to Dunning Kruger oneself as a non-expert or even someone who has never taking a single course in the subject or took one a long time ago. It's for this reason that I prefer to focus on learning a [solid] framework for thinking about some problem and then build on that when learning about a new subject. Listening to various people (experts, journalists, twitter, medium posts, ...) and trying to make sense of what they're saying without having a framework to translate such information into knowledge makes one prone to misinformation or emphasizing the wrong things. Coherency and self-consistency is king for knowledge. In my case, I focused on learning the SIR model so I try to view information in the framework of that... and if something doesn't fit, I try to figure out why.
