5 ms·
I think these models are extremely suspect, with nil predictive value. Where you have sustained exponential growth dynamics, as here, the results are fantastica
by throwaway_yy2Di 12y ago
I think these models are extremely suspect, with nil predictive value. Where you have sustained exponential growth dynamics, as here, the results are fantastically sensitive to the parameters which go in the exponent, which in this case you can't predict with enough accuracy.
The simplest ODE is something like:
du/dt = k(t) * u(t)
Whose solution locally looks like (for slow-varying k(t))
u(t) ∝ e^{ k(t) * t }
One possibility is k(t) > 0 sustained for 10 effective doubling times. One possibility is k(t) < 0. In this epidemic, either is plausible (?): the difference is only a small difference in some infection control parameters. A small uncertainty that translates into a factor of a thousand uncertainty in the outcome, because it gets blown up by a gigantic e^x.
And the estimates of k(t) seem to hover around the critical value of k(t) ~ 0. In the CDC model (their Excel spreadsheet is open source [0], and FYI won't import into LibreOffice), the shape of the epidemic is purely determined by the shape of their k(t) assumptions. Their defaults parameter exhibit, first, a fast growth phase, assuming k(t) > 0; then they assume a slight reduction to k(t) ~ 0, leading to slower growth; then slightly more reduction to k(t) < 0, causing the epidemic to halt. As far as I can tell k(t) is basically speculative, and completely determines the shape of u(t). So really you predict nothing.
[0] http://stacks.cdc.gov/view/cdc/24900 http://stacks.cdc.gov/view/cdc/24900
- robomartin 12y agoI have not had a chance to review these models yet. Since you have, I ask: How does the model account for isolation capacity constraints? In other words, hospitals have a finite capacity to deal with these kinds of patients. How does the model account for infection and mortality within the medical community? How does the model account for handling and or procedural errors? How does the model account for the threshold beyond which N percent of medical professionals will refuse to treat patients? Does that model estimate this threshold? This is pure conjecture on my part, I am guessing that if four or five nurses and doctors fall ill, or worst, die, it could trigger a really difficult scenario to deal with. Does the model account for some of the tens of thousands of afflicted in West Africa travelling outside of the hot zone while not showing symptoms and then infecting general populations during the initial phase of their sickness? Does the model assume a tolerance range for various parameters due to mutation or other factors, for example rate of reproduction, ease of communication, etc.?
- throwaway_yy2Di 12y agoThe CDC spreadsheet is supposed to model a single West African country, and doesn't explicitly model any of those things. It doesn't account for finite medical capacity. It assumes a specified fraction of patients are isolated in hospitals at a given time, a fraction that increases, regardless of the size of the epidemic. I think the burden is on users to check if the results make any sense (it does give you the # of beds in use at a time, so you get that feedback).
- diydsp 12y agohaha i can save you some time. there are two models. the first is hypersimplistic, reciprocal of an decaying exponential with four parameters and zero inflection points (although there's one visible in the data so far)... it does not even come close to addressing your questions. the second model at least accounts for decay - gee - but is still essentially two terms with three parameters- the result is two competing decay terms. This is, essentially, a trivial joke. it has no delay parameters for incubation, etc. I've only skimmed the article, but I can't find an actual attribution of these numbers to the model (the model itself is from a journal). It seriously appears like an editor said, "Let's get some scary-mathy-lookin stuff up there on Ebola). if it bleeds...
- robomartin 12y ago"Let's get some scary-mathy-lookin stuff up there on Ebola" That was funny. Yup, math is scary to a lot of people. Sad statement.
- quarterwave 12y agoWell put. A 'predictive model' should say 'if you do X then you will end up with Y' - and the X cannot be adjusting some number. The X has to be stuff like 'building ETU's in West Africa', or 'canceling all flights',... A predictive model should be able to say 'don't bother canceling flights, it's no use - instead do this...'. Note: I'm going to be teaching a course in Erlang programming next month where the homework assignment is epidemic modeling - 100K's of concurrent processes moving around, getting exposed to each other - that sort of stuff. Rather ambitious, but I feel it's a good use case for Erlang - a pandemic is a 'viral' chat application.
- tjmaglio 12y agoIs the course your teaching going be a MOOC or will the assignments be posted publicly? I'd love to try that assignment myself.
- quarterwave 12y agoCourse is classroom format. i will post the assignment on github.
- sieisteinmodel 12y ago> A 'predictive model' should say 'if you do X then you will end up with Y' - and the X cannot be adjusting some number. The X has to be stuff like 'building ETU's in West Africa', or 'canceling all flights',... A predictive model should be able to say 'don't bother canceling flights, it's no use - instead do this...'. This is just wrong. A predictive model does not necessarily have any "action" input. Example: weather forecast.
- danieltillett 12y agoI wish we put more effort into gathering data on what is really happening on the ground rather than modelling almost certainly wrong data. I guess on the upside the chance of catching Ebola is much lower doing studies like this.
- throwaway_yy2Di 12y agoMy comment was more about forward-prediction, but you're right.