The SIR Model of Epidemics
jaydaigle.net
jaydaigle.net
I currently live in a country with absolutely no infrastructure to handle this. Our first confirmed case was reported almost three weeks ago. Within a week we ran out of testing kits.
Last night I started researching on the topic to see if there is a formula to calculate the current number of infected people in the country. I don't care about accuracy, it just needs to give an approximate.
The current official figure is less than ten and I feel that by having an estimate (from what I've been able to read, time is a bad indicator, it is what it is) it would help change what I believe to be a false sense of security if one is looking at the official figures.
Is there any such formula or should I use the SIR model? (which currently is a bit over my head)
He wrote a model that roughly estimates infection rates in a population based on either deaths or confirmed cases: https://docs.google.com/spreadsheets/u/1/d/17YyCmjb2Z2QwMiRR...
The model is oriented around companies, but could be applied to any gathering of people. There may be more sophisticated or accurate models out there, but I found his relatively quick to understand and apply.
I want to encourage you not to try to use this formula or anything like it to make concrete predictions. You are, unfortunately, right that the numbers we have access to are crap. But that doesn't mean that our modeling will be any better; we'd need to use the public numbers as input. And those public numbers are crap.
There are people whose entire job is to figure out ways to make useful predictions from the information we have. Their estimates aren't great, in part because the numbers they're using as input are crap.
But the numbers they have for input are as good as what we have, so we're unlikely to manage better. And in the worst case we can easily Epstein ourselves and generate predictions that are wildly, embarrassingly off the mark.
I'm not saying you should trust the official or expert numbers. But they're almost certainly better than what you'll manage on your own.
http://covid19.healthdata.org/projections
paper here: http://www.healthdata.org/research-article/forecasting-covid...
"The Institute for Health Metrics and Evaluation (IHME)" launched in 2007 "with the goal of providing an impartial, evidence-based picture of global health trends to inform the work of policymakers, researchers, and funders. Main supporters are the Bill & Melinda Gates Foundation and the state of Washington."
Edit: once I read the claim "That methodology looks extremely dodgy" or "doesn't make it right" (in the answer below) I'd expect some specific information which would support that claim. Especially when the same person writes "you" to the poster posting the link to the study of an independent institute residing at the University of Washington.
But it's just curve-fitting. And it depends on certain things, like people being smart. You get your parameters from what you observe.
If you have a better way to do it please share.
We only have the same curves if we put in the same restrictions as Wuhan, or get R down as much. Yet we still have megachurches holding services.
And politicians are using these as worst-case scenarios already, which will make them complacent about the urgent need for more ventilators, masks and PPE supplies.
But if we behave and practice social distancing and don't do stupid things, this is the estimate we have today (or a couple of days ago) of the timeline.
If I were a leader of the United States, I would challenge the population to beat these numbers.
All that said, the math is brutal and you're right about things not being immediately apparent in the statistics. There's a delay for symptoms, and then another for deaths.
Unless another country epicly fubars their response, the USA should maintain its #1 spot. All the more so if states don't encourage social distancing for another week.
More interesting to me is that we have a measure by which we can evaluate our leader's response. Deaths well north of 200K means he severely screwed up.
Of course we'll never convince his base of that should it come to pass.
And to be fair, if he keeps the number of deaths in the 100K range then he will have done a good job from the point at which he started taking action.
Everything in excess of that is a shocking mix of incompetence, hubris and malice - including refusing help to states whose governors aren't sufficiently deferential.
The models I've seen with the peak in April have been the truly apocalyptic scenarios. Most models that incorporate social distancing push the peak out into May and beyond.
The doubling time is in many places only 3 days. From my point of view the model which is off by only a week could still be quite correct.
The model projected 437 deaths for March 28th (tolerance bands of 380 - 508).
According to [0], the deaths were actually 264.
But the model predicted around that only two days prior ( 273 deaths on March 26th).
I’d say it’s pretty accurate - off only by a couple days.
Understatement of the century lol, especially for fully Bayesian versions.
In this model, change in the number of people is function of the number of people infect, that's it. The number of potentially infectable people is so large that changes in it's value won't enter into consideration until the US is at WWII-invasion level of fatalities.
dS/dt = Sr, for some value of r.
A simple differential equation indeed, solved by S = e^(t*R); exponential growth as we see (note, I'm not claiming my r here is R0 or whatever).
> Also, mine is a SIRD model (guess what the D stands for). People didn't use to include mortality in these because it depletes the population you are trying to simulate, but I've been able to run large enough numbers that you can include it as long as your disease is not too lethal ... and if it is that's also a result of sorts.
[1] Substantial undocumented infection facilitates the rapid dissemination of novel coronavirus (SARS-CoV2) Li et al. DOI: 10.1126/science.abb3221 https://science.sciencemag.org/content/early/2020/03/24/scie...
The lines of hundreds/thousands of people waiting to recover the ashes of relatives from several cremation facilities, along with the documented arrival of roughly 45,000 urns to Wuhan alone belies the rotten data that even now claims only 3,300 total deaths in .cn
Western propaganda has trained its people to think the Chinese communist party is as stupid as it is authoritarian. Quick quiz, if you don't know who Li Keqiang is then you more likely than not treat the CCP as a black box controlled by Winnie the Pooh.
I submit https://www.reddit.com/r/dataisbeautiful/comments/ez13dv/oc_... as illustrating my earlier point.
I also submit https://www.taiwannews.com.tw/en/news/3871594