Sunday, April 5, 2020

COVID-19: Is Italy — and Mass Quarantine — "Flattening the Curve" or Riding the Trend?

March 16:
To take the COVID-19 pandemic "seriously", must we institute a mandatory shut down, AKA a mass quarantine?

This question prompted me, as always, to ask: has this been tested?

March 16:
Without going through the entire history of epidemics and measures designed to stop them, it can be said that clearly quarantine is one tool to stop the spread of disease.

Nevertheless, as observed in the Journal of School Health in 1951 [1]:
"Anderson and Arnstein in "Communicable Disease Control," 1948, in discussing poliomyelitis, say: "School closure, as well as closure of moving picture theaters, Sunday schools, and other similar groups, is frequently attempted in response to popular demand that 'something be done.' Although tried repeatedly, it is of no proved value, never altering the usual curve of the epidemic: nor has the disease been more prevalent or persistent in those communities with the courage to resist those demands.""
Mass Quarantine and Polio [1]
Now no one would suggest that polio is not a serious disease. While many forget the annual polio epidemics that once terrified Americans, there are few diseases in history that were more serious.

Additionally, since polio was an annual disease, much like influenza, they had a pretty good data set of interventions that worked.

Quarantining the sick to prevent them from spreading the disease was the practice. Quarantining everyone to prevent disease spread through the population was not.

In the case of COVID-19, this is the difference between the intervention pursued in South Korea [2], where the infected and their contacts were tracked:
"“South Korea is a democratic republic, we feel a lockdown is not a reasonable choice,” says Kim Woo-Joo, an infectious disease specialist at Korea University."
And Italy, where the whole country was locked down on March 9. (The Italian lockdown started in the region of Lombardy where the worst infection emerged, on February 21 [3] and spread to all of Lombardy on March 7 [4] then the entire country on the 9th.)

So as Italy developed into the one of the worst COVID-19 outbreaks in the world, I was curious to see if there was any evidence that the severe measures they took had a discernible effect.

For starters, I was curious about the claims of exponential growth. The influential Imperial College (IC) report (whence the phrase "flatten the curve") stated:
"Infection was assumed to be seeded in each country at an exponentially growing rate (with a doubling time of 5 days)..." [5]
This allowed IC to predict that 81% of Americans (220 million) would be infected 90 days out. There are some other problems with these assumptions, but first let's look at that one.

Exponential Growth

Is the spread of this virus exponential?

Exponential means a given initial value, and a constant rate of increase. In order to get to their projected infection prevalence of 220 million Americans, the IC people must have used a "seed", an assumed value of infected people, and then a rate of increase each day of around 15%.

In looking at the Italian data [6], it quickly becomes apparent that the initial spread of COVID-19 in Italy was remarkably fast, far faster than that predicted by the IC in their worst-case analysis. I created two exponential curves, one to match the actual cases on March 9, when the lockdown occurred, and one to match cases on March 27, when I started looking into this.

In this chart, March 9 is indicated in the X axis labels, and you can see there's an inflection in the cases recorded on the date the lockdown was implemented (red arrow). The exponential growth rate for the March 9 curve was 39.72%, and 28.24% for the March 27 curve. (I didn't bother graphing the IC grown projection, as it was almost a flat line at the bottom of the graph.  But what's also immediately apparent is that the curve of the actual cases is not exponential, as the rate of increase appears to be steadily declining (the line crosses both of the exponential curves). Growth is higher early on, but steadily declines.

To drill down on what was actually happening, I next graphed the percentage increase in actual cases.

The orange line again represents the actual number of cases, showing the actual percentage change for each date. The green line again marks the 39.72% exponential growth curve, and the blue line the 28.24% curve. (Since exponential growth is a constant percentage rate of growth, those lines are flat.)

This chart makes it very apparent that the initial increase was explosive, with a 425% increase on one day—from 4 cases to 21. But that sort of increase isn't sustainable. The next day was 276%, then 99%, then 46%.  These early increases are likely artifacts of discovering new cases, so don't represent an actual growth rate, however the spread of the virus was certainly real.

The fascinating thing about looking at the actual data is the things you learn. We already see how fast the initial rate of growth is, but we also see that it's clearly not exponential, it's a steadily declining growth rate.

We also see that the initial rate of increase was worse than the worst-case scenario in the IC paper, in the short term.

Yet, despite implementing draconian lockdown measures, there's no evidence of an inflection point in the curve of the epidemic in Italy. In the initial chart there was what looked like an inflection point on March 9, the day of the full lockdown, but in this view of the data it's clear that was just a tick down in the declining growth rate, which increased back to trend line the following day.

So the next thing to look at is the trends in the data.

"Flattening the Curve"

This chart shows the same as the above, with the increase to 425% truncated out. I think it's an outlier, and not worth considering in looking at the data. When I first did this analysis, I truncated all the data prior to 2/24, but got similar results (with much higher R2), so here I leave it in.

The green line is a logarithmic trend line, the red a 10-day moving average. I picked the 10-day moving average because the median incubation period for COVID-19 is 5 days, with 5 days expected for serious symptoms to occur.

So we see that after an initial explosive growth in cases, the growth rate rapidly declines, and the trends for growth also rapidly decline. The increase on 3/29 is 6%, the increase on 3/31 (not shown) is 4%. The IC expectation for the worst-case was 15% at this point. There's no apparent change in the trend after the nation-wide lockdown of March 9.

So what's clear is that the predictions of exponential growth of 15% per day absent draconian measures was grossly wrong. Actual growth in cases was far higher. There is no clear effect of the implementation of draconian lockdown measures in the curve of growth, as predicted in 1948 [1]:

Riding the Trend
"Although tried repeatedly, it is of no proved value, never altering the usual curve of the epidemic..." [1]
When I started this analysis, I expected to see that the lockdown would have had some effect, what I was surprised to see was the high growth rate initially and the lack of any apparent effect at all.

Unfortunately, given the nature of this epidemic and the lack of testing for it (which is typical of epidemics), cases might be the wrong measure to look at. Cases are dependent on testing, and it's possible that cases are being missed, due to mild effects, in fact it's pretty much guaranteed that mild cases are under-counted.

So I also looked at deaths.

But the curves are almost the same same. Which implies that we may be missing the mild cases, but the cases being tracked do have a close relationship to the death rate. What we do see now though, is that it appears that the deaths track pretty closely to the exponential line (40.6% p/d) up until the lockdown was implemented. This is of course likely why the lockdown was implemented.

If we zoom in to see the details of the growth rate:

Again, an explosive early increase, delayed behind the increase in cases. The date rate increase tracked with the two exponential lines until around the time of the lockdown.

So I also ran the trendlines:

Here the inflection point is closer to the lockdown date, but it still seems to precede it by a few days.

If the nationwide lockdown had caused the downturn in the increases in the deaths, we would expect that we would see an inflection point after the lockdown, not before it.

The concordance between these death and cases lines suggest that the rate of infection shown by the actual cases data is a pretty good indication of some level of serious infection, although we are probably missing a lot of mild and asymptomatic cases. There's also an indication that deaths in Italy may be over-counted, but if so it at least seems to be a consistent over-counting. [7] Unfortunately, due to lack of data from widespread testing and inconsistencies between how statistics are counted in different countries, it's hard to estimate a non-serious infection rate.

I have read that the failure of the lockdown in Italy to prevent Italy from becoming a worst-case scenario is due to the nature of the Italians, who have a reputation for enjoying life without the highest regard for regulation. Whatever the truth of that view may be, I don't think it explains this phenomenon.

A few quotes:
"Residents of Lombardy describe deserted streets and panic after seven virus deaths.... “It’s a surreal situation,” Enrico Bianchi, who owns a veterinary pharmacist, told the Guardian. “People are locked in their houses for fear of going out. It is really strange to go around the town, the few people around are wearing masks.” [1]
From February 24. From March 20 [8]:
"Italian authorities have pressed charges against more than 40,000 people for violating the lockdown, according to figures from the interior ministry."
And the gem:
"Giuseppe Conte, the prime minister, had said the beneficial effects of the lockdown would be felt two weeks from its start as the coronavirus is thought to carry an incubation period of two to 14 days."
That would be March 23rd:

There doesn't seem to be much of a change in the data at that point. His prediction doesn't seem to have born fruit.

But perhaps the most interesting evidence for the compliance of the Italians with the lockdown is this new service from Google [9] which tracks compliance of their users with the lockdown orders, using data they collect from their Android cell-phone operating system.

Italian compliance is far higher than what is happening in the U.S. right now, where workplace reduction numbers are in the order of 38% (in the area where I live).

Italians are clearly obeying the lockdown, and in large numbers, and non-compliance is being dealt with. I'm not aware of a single person that has been arrested in the U.S. for non-compliance.

Life has ground to a halt in Italy, apparently.

"However, the work at hand does provide some cause for limited optimism, suggesting that, even at today’s rapid pace, if a city acts quickly it can buy time even when the pandemic appears at its gates."
That is from a review [10] of two papers analyzing the Influenza Pandemic of 1918. [11, 12] What those papers make clear is that while lockdowns can be effective in containing a quarantine, they are most effective when implemented before a community is infected. This should surprise no one, as even people living in medieval times knew that the best barrier to plague was to live within a walled city. [13] But as a Japanese study looking at influenza in schools noted, looking at the results of their model:
"[Reactive] School closure has a remarkable impact on decreasing the number of infected students at the peak, but it does not substantially decrease the total number of infected students."
Even the peak closure decrease of 24% was in the model, the actual observed data was higher. Reactive closure means closure after the school has been exposed to the pathogen, it's in the community, and while communication from one student to another in school may be blocked, there are other routes of transmission. So whatever benefit reactive closures offered, it was small, and short-lived, as once closures were ended, influenza came right back, infecting most of those students in missed in the first (or second) pass.

So mass quarantine seems to be effective if you are living in a walled city in Spain or in a simulation. As we can see from the Italian case, it seems to be quite ineffective in real life, even in a situation where serious police enforcement is in place to ensure compliance.

It appears to be clear from the Italian data that the claimed success of the lockdowns is simply a matter of the natural course of the epidemic. Comparing Italy to the rest of the world, as the Financial Times does [14] reveals that the gradually-decreasing curve of growth of infections in Italy is typical of the epidemic in other countries:

From Financial Times' COVID-19 Tracking Site
With the notable exception of South Korea, where lockdowns have not been used.

It seems apparent that if you are actually looking to "flatten the curve", then lockdowns are not the most effective means of doing it.

It also seems apparently that the apocalyptic growth estimates used by the Imperial College and others were both too hysterical as to later growth trajectories and also not severe enough to recapitulate the actual course of the epidemic and the ability of authorities to proactively implement mitigation strategies, based on the Italian experience.

Should polio close schools? Journal of School Health. 1951;21(7):249-252. doi:10.1111/j.1746-1561.1951.tb01445.x

How Italy, South Korea differ in tackling coronavirus outbreak | News | Al Jazeera. Accessed March 16, 2020.

Palermo AGLT in. Italians struggle with “surreal” lockdown as coronavirus cases rise. The Guardian. Published February 24, 2020. Accessed March 30, 2020.

Northern Italy quarantines 16 million people. BBC News. Published March 8, 2020. Accessed March 30, 2020.

Ferguson NM, Laydon D, Nedjati-Gilani G, et al. Impact of Non-Pharmaceutical Interventions (NPIs) to Reduce COVID- 19 Mortality and Healthcare Demand. London: Imperial College; 2020:20.

Italy Coronavirus: 105,792 Cases and 12,428 Deaths - Worldometer. Accessed April 1, 2020.

Global Covid-19 Case Fatality Rates. CEBM. Accessed April 3, 2020.

Why Italy’s coronavirus death toll continues to spike despite lockdown – and what the UK can learn. The Independent. Published March 20, 2020. Accessed March 30, 2020.

COVID-19 Community Mobility Report. Accessed April 3, 2020.

Morse SS. Pandemic influenza: Studying the lessons of history. PNAS. 2007;104(18):7313-7314. doi:10.1073/pnas.0702659104

Markel H, Lipman HB, Navarro JA, et al. Nonpharmaceutical Interventions Implemented by US Cities During the 1918-1919 Influenza Pandemic. JAMA. 2007;298(6):644-654. doi:10.1001/jama.298.6.644

Public health interventions and epidemic intensity during the 1918 influenza pandemic | PNAS. Accessed April 3, 2020.

CNN. The hilltop fortress town that cut itself off from the world — and coronavirus. CNN. Accessed April 4, 2020.

Smith A, Blood D, Tilford C, et al. Coronavirus tracked: the latest figures as the pandemic spreads. Published February 8, 2020. Accessed April 3, 2020.


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  2. Boom! Good stuff, as typical, Tuck. One point is particularly troubling, among many. South Korea did not employ lockdowns? That one fact alone, if true, would seem to invalidate all talk of #FlattenTheCurve and #SocialDistancing. Does it? If not, why not? Thanks for doing this.

  3. Thank you! I am wondering what Sweden’s line looks like on the last graph you presented.

    1. I just went to the Financial Times site, and it looks like Sweden is tracking closely with China. In other words, no lockdown appears to have the same effect as having one.