Not a Common Core exercise, though.

A lot of folks, including many of the public faces of government response, don’t seem to really understand what’s going on here.


Scary word; very scary problem.

So let’s look at what that problem is.

I’ll use my local county’s numbers to do some simple estimations. I’m going to be estimating very generously, erring very much on the side of minimizing the problem; this is because the numbers will still be terrible, even in this best-case scenario.

We have around 750 hospital beds in the county, most of which are in use at any given time. They’re trying to arrange other facilities for the non-epidemic patients, so let’s say they’re amazingly good at clearing those out for epidemic patients and that we have 500 hospital beds available for this.

Let’s also be really generous and say we have the staff, supplies and equipment to effectively use all 500 of those beds; we don’t, not by a long shot, but we’re doing a best-case scenario.

Around 20% of the patients who test positive for this virus require hospitalization, so we can effectively manage around (5 * hospital beds) cases in the county.

So that means we can, at most, manage 2,500 concurrent cases of COVID-19.

As of last night, the number of test-confirmed cases here was 29; this was 4x the number a week ago, so that doubled in 3.5 days.

(This is also really generous; the county is doing only minimal testing so we don’t actually have good numbers for this. That’s OK for this post, though, since the hospitalization rate is based on only testing suspected cases and the doubling period is based on that level of testing so the math still works.)

We can’t handle 2,500 new cases every day; each hospitalization for COVID-19 takes about a week, so we can actually only manage about 357 new cases each day, or 1,250 new cases each 3.5 days.

So, how long do we have before we get to that?

Starting at 29 cases, and doubling every 3.5 days, we will have more new cases per day than we can manage in less than 6 doubling periods.

That’s 21 days.

3 weeks.

Let’s say that again: in a best-case scenario we have 3 weeks before we have more new COVID-19 cases every day in this county than we can possibly manage.

There’s some really bad news in that, too.

Around 3.4% of COVID-19 patients die.

So, that 357 new cases per day that the scenario supposes we can manage? That also means about 12 deaths per day.

That’s the best-case scenario for what things will look like here in 3 weeks if the numbers don’t change.

And it gets much, much worse when you pass the point where all serious cases can be treated properly in a hospital.

There is also some good news, though.

It takes a week or two for changes in behavior to show up in the infection stats, since the virus takes a week or two after you get it before you get sick.

And most of the “social distancing” measures started around a week ago.

So maybe, just maybe, we can slow this down long enough that we never have more new cases per day than we can manage.


But that chance depends on all of us being as effective as we can be at minimizing our possibility of being infected.

So, seriously: shut it all down.

And start reorganizing your lives and work to keep it shut down.

(Other posts on this topic are here.)

3 thoughts on “What’s The Problem: Math From The Back Of An Envelope

  1. Fortunately, it has not continued to double every 3.5 days.

    Today will be the 7th day since I wrote the post, and at the moment we’re at 73; if the doubling rate had stayed the same we’d be at 120.

    So that’s good: going from 30 to 60 took around 5 days, so we’re definitely “flattening the curve” noticeably.

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