I was so excited by learning how to embed R code in my blogpost on Monday that I didn’t explain the motivation behind my post very well 
Recently a lot of "flatten the curve" graphics have been doing the rounds recently on Twitter. This is a typical example which is presented and explained in more detail in this post.
and here is a slightly more sophisticated version showing much the same thing. Though oddly it’s not based on a logistic curve which suggests to me it is just a graphic artist drawing pretty curves. Not that this really matters.
They have been widely lauded as great communication. However I wonder whether they are actually rather misleading. As a scientist I want to see those axes labelled and scaled properly, and the "capacity" line put in the right place.
So that’s why I did the simple calculations in the previous post. My numbers are not authoritative but on the other hand at least there are numbers involved, which can be queried and tested, rather than just pretty lines on a page. Back of the envelope calculations suggest that "capacity" in the UK and elsewhere is actually right down near the zero line compared to plausible epidemic peaks, rather than being about half way up even in the uncontrolled case as these graphics suggest. I’d love to have people tell me why I’m wrong here. From what I’ve read, the healthcare system in Italy is totally overwhelmed and they are only right at the start of the upslope with 10,000 cases nationally (under 0.02% of their population).
I also saw a real UK-based doctor on a forum saying that their healthcare centre had done some calculations and thought they could cope if the peak was stretched out over 10 weeks, but not if it came over 3. I asked about the basis of the numbers but didn’t get a reply. If a total of a million people are infected over a period of 10 weeks, that means 14,000 per day, maybe 1000 needing admission to hospital for treatment. Per day. Every day, over a long period. Of course they don’t all stay in hospital indefinitely, but this still seems to be a huge additional load. And that’s if we assume only a million cases in total, which is well under 2% of the population. Epidemics can easily reach a third (eg 1918 "Spanish flu", 1957 "Asian flu").
So, I don’t really get it. Are they assuming (hoping) that there is a huge proportion of undetected, uninfectious, asymptomatic cases such that each recorded diagnosis actually represents 5 or 10 cases? That would give a far lower fatality rate per case and allow for a widespread infection without overwhelming healthcare. It seems lot to pin your hopes on though.
If my calculations are reasonable, then the message would be that we need to actually control the epidemic fully by getting R0 down below 1, not just stretching out the doubling time a bit. R0 here is the reproductive rate, ie number of new cases that each case generates, currently thought to be about 2-3 in the case of no social distancing. China achieved this by locking down a whole city (and South Korea may be achieving similar results with less draconian action). We’ll see how Italy performs shortly. It currently looks like the UK is aiming to emulate them rather than learn from them.
2 comments:
"Are they assuming (hoping) that there is a huge proportion of undetected, uninfectious, asymptomatic cases such that each recorded diagnosis actually represents 5 or 10 cases?"
Here in the USA there are certainly indications that each recorded diagnosis might represent 10 to 20 cases. But that's because we are minimizing the number of people tested (on a per capita basis, we're testing 6.7% as many people as you are in the UK).
But I doubt that those hidden cases are all "uninfectious, asymptomatic".
I've posted elsewhere a now obsolete calculation that no society today could cope with a 1% infection rate. The correct result is probably under 0.2%. And that's only for rich and well organized societies. Poor societies can't do the sort of isolation to prevent spread, and can't provide more than water and rest to the sick. The age distribution will reduce the death rate somewhat.
The only tools we have to avoid a breakdown of health care are social distancing and testing/isolation/"case tracking" for the exposed and infected. These tools work, China is now less than half of the reported cases. Singapore has perhaps done the best. South Korea seems to be past the peak.
https://www.worldometers.info/coronavirus/country/south-korea/
Regardless of whatever nonsense your government is saying, stay out of crowds, wash hands, avoid getting close to people other than people in your household. Takeout don't go out.
The life you save might be your own. Or your father. Or your grandmother.
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