Note that this simulator appears to be someone’s class project. However, its behavior seems to track more or less with what I’d expect. But I’d love for someone with more experience to reproduce this relatively simple model and check it.
I have limited confidence that I’ve understood it correctly, so take this for what it’s worth. It looks to me the time step used in this simulator is one day. So the gamma parameter (rate of recovery per unit time) should be (Wikpedia says) 1/D where D is the duration of the disease. (For transmission modeling purposes, this should be the infectious duration, not the duration of symptoms.) I chose gamma=0.7, meaning D ~= 14 days, semi-arbitrarily, based on https://www.medrxiv.org/content/10.1101/2020.03.05.20030502v1 (which says 10 days after start of symptoms) and the general figure of 14-day quarantines.
The beta parameter is the transition rate from “susceptible” to “infected” per person infected per unit time. (That is, betaI is the transition rate overall.) I think therefore R = Dbeta (the total number of new infections per person should equal the duration times the number of infections per unit time), so beta = R/D = R*gamma.
All that being said, given those assumptions, here are what I think the plots look like for various R values. (Note that the names of the parameters given in the URL do not appear to match the names in the UI. I think the URL parameter names are just wrong; the model behaves as I would expect it to. It’s a very simple model and I’d love for someone to independently check this.)
So it looks to me like very substantial curve-flattening ought to be possible, based on this simplified model, at quite realistic R values. Whether it’s possible to flatten it enough to prevent health system overload is anybody’s guess—likely not everywhere—but it looks like there are substantial benefits possible.
Thanks for pointing me in this direction. I think the key worry highlighted in the post is that the health care system gets overwhelmed with even just a few percent of the population being infected. So even if we can bring peak infections down by a factor of 2-4 by slowing transmission, the health care system is still going to be creamed at the peak.
I’ve now built a discrete-time, Bay Area version of the SIR model (+ hospitalization) in this Google sheet. I assume 20% of infections need hospitalization, of which 20% need intensive care, and use raw bed-to-population ratios (non-COVID utilization vs stretching capacity should roughly cancel out). Hospital bed availability at peak infections is 4% (25x over capacity) in the uncontrolled beta=0.25 scenario and only improves to 10% (10x over capacity) in the “controlled” beta=0.14 scenario. Even if my hospitalization/ICU numbers are too high by a factor of 5 the “controlled” scenario still looks pretty terrible. Any feedback on the model assumptions would be super useful.
I haven’t checked your models quantitatively, but qualitatively I absolutely believe you that the options here are “bad” and “really really bad”, and that neither one of them gets us down to where we need to be.
The difference between 4% and 10% could still save a lot of lives; at that level it may be close to 1:1 (every bed freed up is a life saved), since only the most critical cases will be getting beds at that point.
But you’re right that this is clearly not adequate, and the graphic showing the flatter curve as peaking under the capacity line is pretty misleading. (There are versions of the graphic which don’t, but they appear to have been memetically outcompeted by those that do.)
I think it’s still true that “flattening the curve” will save lives, potentially a lot of lives, so even if the graphic might be a bit misleading as to the possibility of flattening it below the critical threshold, I think it’s still a reasonable meme to promote.
But really the ultimate goal has to be reducing R below 1, which will arguably flatten the curve, just not quite in the way the meme seems to be trying to get at. I don’t want to steer too close to dark side epistemology here, but if the meme gets people to stay inside, cancel their parties, and wash their fucking hands… it’s hard for me to be too against it, and I think it’s probably true enough?
I don’t know how other people react. I took the epidemic fairly seriously but my initial reaction to the meme was one of reassurance/complacency—OK so I can’t avoid eventual exposure anymore, but at least things will proceed in a somewhat orderly fashion if we cancel big events, wash hands, stop touching our face, etc. I feel like this is the sort of attitude that contributes to, and allows the public to accept, decisions like the capitulation in Sacramento. The mental image of mitigation is “basically trying to mitigate the risk to those who are most at risk: the elderly and those with chronic underlying conditions”. The reality is that we’ll be forced to let all the old and sick die in hospital parking lots.
It seems to me fairly likely that the public will ultimately accept the Hubei-style lockdowns that will result in containment, but this meme probably is responsible for delaying that moment by at least a few days :(
I saw the meme as mostly targeting people who were currently even more complacent “eh, there’s nothing we can do, so fuck it”, and getting them to instead go “okay, there’s stuff that’s actually worth doing.”
Hospital bed availability at peak infections is 4% (25x over capacity) in the uncontrolled beta=0.25 scenario and only improves to 10% (10x over capacity) in the “controlled” beta=0.14 scenario.
Alex, I’m looking at your spreadsheet and I don’t understand where you got these bold numbers from. It looks like you tweaked your sheet a bit since writing this comment, but still I can’t figure out what you are looking at when you say 25x and 10x over capacity. Could you explain?
Yeah I got better hospitalization/ICU rates from Bucky and upped beta to 0.3 in uncontrolled scenario to make a point on Twitter. Hospital/ICU bed availability % is graphed in each scenario tab, by overcapacity I mean the inverse of availability. Alternatively take ratio of peak to line in the Charts tab. Looks like ~15x and 5x now for hospital beds.
That’s an interesting question that seems like it ought to be able to be checked numerically.
I made an attempt using this simulator of the fairly-naive “SIR” model of disease transmission:
http://www.public.asu.edu/~hnesse/classes/sir.html?Alpha=0.3&Beta=0.07&initialS=1000&initialI=100&initialR=0&iters=50
Note that this simulator appears to be someone’s class project. However, its behavior seems to track more or less with what I’d expect. But I’d love for someone with more experience to reproduce this relatively simple model and check it.
You can read about the model at https://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology#The_SIR_model .
I have limited confidence that I’ve understood it correctly, so take this for what it’s worth. It looks to me the time step used in this simulator is one day. So the gamma parameter (rate of recovery per unit time) should be (Wikpedia says) 1/D where D is the duration of the disease. (For transmission modeling purposes, this should be the infectious duration, not the duration of symptoms.) I chose gamma=0.7, meaning D ~= 14 days, semi-arbitrarily, based on https://www.medrxiv.org/content/10.1101/2020.03.05.20030502v1 (which says 10 days after start of symptoms) and the general figure of 14-day quarantines.
The beta parameter is the transition rate from “susceptible” to “infected” per person infected per unit time. (That is, betaI is the transition rate overall.) I think therefore R = Dbeta (the total number of new infections per person should equal the duration times the number of infections per unit time), so beta = R/D = R*gamma.
All that being said, given those assumptions, here are what I think the plots look like for various R values. (Note that the names of the parameters given in the URL do not appear to match the names in the UI. I think the URL parameter names are just wrong; the model behaves as I would expect it to. It’s a very simple model and I’d love for someone to independently check this.)
R=4.82 (beta=0.34) (upper cited estimate from Wikipedia): http://www.public.asu.edu/~hnesse/classes/sir.html?Alpha=0.344&Beta=0.07&initialS=1000&initialI=100&initialR=0&iters=50
R=3.5 (beta=.25): http://www.public.asu.edu/~hnesse/classes/sir.html?Alpha=0.25&Beta=0.07&initialS=1000&initialI=100&initialR=0&iters=50
R=2.28 (beta=.16) (estimate based on the Diamond Princess data, https://www.ncbi.nlm.nih.gov/pubmed/32097725): http://www.public.asu.edu/~hnesse/classes/sir.html?Alpha=0.16&Beta=0.07&initialS=1000&initialI=100&initialR=0&iters=50
R=2 (beta=.14): http://www.public.asu.edu/~hnesse/classes/sir.html?Alpha=0.14&Beta=0.07&initialS=1000&initialI=100&initialR=0&iters=50
So it looks to me like very substantial curve-flattening ought to be possible, based on this simplified model, at quite realistic R values. Whether it’s possible to flatten it enough to prevent health system overload is anybody’s guess—likely not everywhere—but it looks like there are substantial benefits possible.
Thanks for pointing me in this direction. I think the key worry highlighted in the post is that the health care system gets overwhelmed with even just a few percent of the population being infected. So even if we can bring peak infections down by a factor of 2-4 by slowing transmission, the health care system is still going to be creamed at the peak.
I’ve now built a discrete-time, Bay Area version of the SIR model (+ hospitalization) in this Google sheet. I assume 20% of infections need hospitalization, of which 20% need intensive care, and use raw bed-to-population ratios (non-COVID utilization vs stretching capacity should roughly cancel out). Hospital bed availability at peak infections is 4% (25x over capacity) in the uncontrolled beta=0.25 scenario and only improves to 10% (10x over capacity) in the “controlled” beta=0.14 scenario. Even if my hospitalization/ICU numbers are too high by a factor of 5 the “controlled” scenario still looks pretty terrible. Any feedback on the model assumptions would be super useful.
I haven’t checked your models quantitatively, but qualitatively I absolutely believe you that the options here are “bad” and “really really bad”, and that neither one of them gets us down to where we need to be.
The difference between 4% and 10% could still save a lot of lives; at that level it may be close to 1:1 (every bed freed up is a life saved), since only the most critical cases will be getting beds at that point.
But you’re right that this is clearly not adequate, and the graphic showing the flatter curve as peaking under the capacity line is pretty misleading. (There are versions of the graphic which don’t, but they appear to have been memetically outcompeted by those that do.)
I think it’s still true that “flattening the curve” will save lives, potentially a lot of lives, so even if the graphic might be a bit misleading as to the possibility of flattening it below the critical threshold, I think it’s still a reasonable meme to promote.
But really the ultimate goal has to be reducing R below 1, which will arguably flatten the curve, just not quite in the way the meme seems to be trying to get at. I don’t want to steer too close to dark side epistemology here, but if the meme gets people to stay inside, cancel their parties, and wash their fucking hands… it’s hard for me to be too against it, and I think it’s probably true enough?
I don’t know how other people react. I took the epidemic fairly seriously but my initial reaction to the meme was one of reassurance/complacency—OK so I can’t avoid eventual exposure anymore, but at least things will proceed in a somewhat orderly fashion if we cancel big events, wash hands, stop touching our face, etc. I feel like this is the sort of attitude that contributes to, and allows the public to accept, decisions like the capitulation in Sacramento. The mental image of mitigation is “basically trying to mitigate the risk to those who are most at risk: the elderly and those with chronic underlying conditions”. The reality is that we’ll be forced to let all the old and sick die in hospital parking lots.
It seems to me fairly likely that the public will ultimately accept the Hubei-style lockdowns that will result in containment, but this meme probably is responsible for delaying that moment by at least a few days :(
I saw the meme as mostly targeting people who were currently even more complacent “eh, there’s nothing we can do, so fuck it”, and getting them to instead go “okay, there’s stuff that’s actually worth doing.”
You’re probably right.
Alex, I’m looking at your spreadsheet and I don’t understand where you got these bold numbers from. It looks like you tweaked your sheet a bit since writing this comment, but still I can’t figure out what you are looking at when you say 25x and 10x over capacity. Could you explain?
Yeah I got better hospitalization/ICU rates from Bucky and upped beta to 0.3 in uncontrolled scenario to make a point on Twitter. Hospital/ICU bed availability % is graphed in each scenario tab, by overcapacity I mean the inverse of availability. Alternatively take ratio of peak to line in the Charts tab. Looks like ~15x and 5x now for hospital beds.