If you think 100–200k is a lot, consider this "gut-check math", or what @sinafala correctly described as a heuristic for one scenario. It's growing and now stands at over 500,000.
Let's consider how realistic this approach is. First, it uses daily cumulative-total deaths. This is pretty well measured, in one sense. Thread, linked below, gets down in the weeds of some of the ways it's not right, however. (Spoiler: undercounts.)
Next, it uses (deaths/cases) as a naïve estimate of the case fatality rate, but uses an adjustment factor to convert it to an infection fatality rate — viz., including asymptomatic and/or unidentified cases. This adjustment factor is discussed below.
The naïve CFR estimator...
The naïve CFR estimator...
Cont'd
... is well understood to be problematic. Nick Jewell and others did some fine work on this in SARS (2003).
It can underestimate early, since deaths lag. And it can overestimate, since deaths are more easily identified than cases.
On case identification rates...
... is well understood to be problematic. Nick Jewell and others did some fine work on this in SARS (2003).
It can underestimate early, since deaths lag. And it can overestimate, since deaths are more easily identified than cases.
On case identification rates...
Cont'd
... we're kinda "passing the buck" to the adjustment factor (on which, more below).
On the lagging deaths, this would tend to make these calculations overly OPTIMISTIC, all else equal. (The pandemic is still expanding in the US of A.)
... we're kinda "passing the buck" to the adjustment factor (on which, more below).
On the lagging deaths, this would tend to make these calculations overly OPTIMISTIC, all else equal. (The pandemic is still expanding in the US of A.)
Another aspect by which this may be in error: e.g. New York City is over-represented in the current data, relative to what it will be in the final data. So if we believe that the NYC experience to date is better/worse than the nation will fare as a whole... that biases.
All these problems discussed so far can be considered somewhat countervailing to first order (hand-wave argument...), so might be a wash. Who knows?
The real issue is the adjustment for inflating case numbers to total infections. I have used a factor of 10.0.
The real issue is the adjustment for inflating case numbers to total infections. I have used a factor of 10.0.
That is to say, for every 1,000 reported cases, the mini-model assumes 10,000 total infections.
Until we get better testing and/or serology, this is really anyone's guess. To the extend that the mini-model gets it right or gets it badly wrong, a lot depends on this assumption.
Until we get better testing and/or serology, this is really anyone's guess. To the extend that the mini-model gets it right or gets it badly wrong, a lot depends on this assumption.
I think a factor of 10 is a reasonable guess, of course, but it's a guess.
The mini-model is highly sensitive to this assumption.
If factor is 5 then there are half as many true infections producing same number of deaths. The virus is worse, and final death toll is doubled.
The mini-model is highly sensitive to this assumption.
If factor is 5 then there are half as many true infections producing same number of deaths. The virus is worse, and final death toll is doubled.
Conversely, if the factor is 20, the virus is whimpier than the baseline assumption, requiring twice as many infections to produce the same number of deaths, and the final death toll is halved.
*MUCH* depends on the adjustment factor. We need serology studies *NOW*.
*MUCH* depends on the adjustment factor. We need serology studies *NOW*.
Lastly, the final size of the epidemic is taken to be 70% of the population. This is anyone's guess.
This number *very* roughly corresponds to an R0 of 3.33, but that is an approximation with its own sets of assumptions. ...
This number *very* roughly corresponds to an R0 of 3.33, but that is an approximation with its own sets of assumptions. ...
Cont'd
... If you prefer a smaller R0 (<3.33), then, all else equal, the final herd immunity threshold is less than 70% and ostensibly the final size is smaller too.
This lowers the death toll of the mini-model.
... If you prefer a smaller R0 (<3.33), then, all else equal, the final herd immunity threshold is less than 70% and ostensibly the final size is smaller too.
This lowers the death toll of the mini-model.
In any case, 200,000 COVID-19 deaths in the United states does not at all seem pessimistic to me. From where things stand now, I think we will be fortunate to escape so lightly scathed.
Addendum: There is no time-frame, express or implied.
The "mini-model" produces a crude estimate but it does not mean "the next 4 weeks". Nor, even, "the next 52 weeks".
The "mini-model" produces a crude estimate but it does not mean "the next 4 weeks". Nor, even, "the next 52 weeks".
But... there will be >135,000 deaths by 1 August 2020. 😉
