Lessons Regarding the Effectiveness of Lock-downs, from Chinese Corona Virus Statistics
March 22, 2020
Over the past few weeks, Corona Virus (Covid-19) case rates
and death rates have increased dramatically, in many countries around the
world. Since the virus first appeared in
China, and thus that country was the first to (apparently) successfully deal
with it, it is instructive to have a look at some statistics, based on their
tracking of cases and deaths.
(This data is from the website below). https://www.worldometers.info/coronavirus/
The graphs below show some key features of the outbreak in
China and their efforts to contain it.
1. New Cases per Day (the orange dashed line, and left axis)
- Indications of trouble began to be seen in December 2019. The Wuhan market was closed on Dec 31, as it is widely believed that the virus jumped to people there (wild game was slaughtered and sold there).
- The first death from the virus was reported on Jan 11.
- The graph begins on January 23, when the number of New Cases per Day in China hit about 250. At that point, the city of Wuhan was locked down, in an attempt to stop the spread, via quarantines and social distancing. There had been some related measures earlier, but this could be considered the start of really extraordinary measures at containment.
- The number of new cases per day continued to explode, hitting about 5000 by the end of the first week in February. The graph peaks at about Feb 5, but given uncertainties in case reporting, the actual turning point could be considered to be in the period from about Feb 5 to 10.
- So, it was about 14 to 20 days from lock-down to the peak of the epidemic, or at least that wave of epidemic, in terms of new cases.
- New Cases per Day now declined, eventually hitting roughly 250 by the last week of February. It stayed at about that level for about the next week.
- So, it was about 28 to 35 days from lock-down to the new case rate falling back to the level it was at lock-down.
- The number of new cases per day continued to fall, with the number of new cases at Wuhan hitting 0 by Marc19 (though there were 34 new cases in other parts of China that day).
One possible inference that can be made from this data, is
that there were a lot of asymptomatic cases in the population at the time of lock-down. Obviously, there must have
been new cases caused by spreading from previously known cases as well, as no lock-down could be 100%
effective immediately. Still, the fact
that the case rate continued to climb exponentially for 2 to 3 weeks would seem
to indicate that there were a lot of asymptomatic infected people at the time
of the lock-down, who would become sick in the next few weeks.
Once the majority of those people who had gotten sick had either recovered or died, and new infections were being largely stopped by social distancing and quarantine, the
rate of new cases could begin to fall.
That said, the graph is somewhat asymmetric, indicating that the growth
of the epidemic can be expected to be faster than its fall, once measures have
become effective.
2. Deaths per Day (the blue solid line, and right axis)
I have shown the graph again, for clarity when reading the
text.
- At the start of the graph, January 23, the death rate was over 10 per day.
- It took longer for the death rate to peak and the peak is somewhat more difficult to ascertain, as the Number of New Deaths per Day is more “spiky” than the number of new cases. However, it seems reasonable to say that the peak occurred sometime around Feb. 20.
- So, it was about 20 to 30 days from lock-down to the peak of the epidemic, or at least that wave of epidemic, in terms of new deaths. That would support the finding of a lag of about 10 days from case reports to a death reports, at least at the aggregate level.
- The number of new deaths then falls steadily, finally getting back to the base level (the level when lock-down was implemented) by about March 10.
- So, it was about 40 to 45 days from lock-down to the death rate per day falling back to the level it was at lock-down.
- Deaths continued to dwindle, eventually hitting less than 10 per day, by March 22.
3. Deaths per Day vs Cases per Day (time lag from case to death)
Here is the same graph, but with deaths lagged by 9 days. As you can see, there is a fairly decent
visual fit between the two graphs, and the correlation coefficient is high, at
0.89 (a correlation coefficient of 1.00 would indicate a perfect mathematical
relationship between the two lines).
It turns out that the statistically most likely lag time
from this dataset is somewhere between 5 and 11 days, with the correlation between Cases and
Deaths being highest for the 8 and 9 day lags, with correlations coefficients
of about 0.89. To be sure, the
values for 5, 6, 7, 10 and 11 days are high as well, all over 0.80 (the blue line shows the calculated correlation coefficient at each lag, while the lines above and below that one give 95% confidence intervals).
As a result we can quite confidently say that the time
between being recorded as a case and a death (for those who succumb) is most likely to be about 8
or 9 days, on average. This corresponds well with
recent case level analyses published in Lancet.
Note that this is just an average figure - individual cases will differ and most likely be spread around this average value (likely a normal distribution with a standard deviation of 2 or 3 days, just based on a visual inspection of the graph).
This yields a death rate of about 4.1% (deaths per
day/cases per day) at the 9 day lag.
Actually, since the epidemic has basically run its course (at least this
wave) in the Chinese data, all of the lagged death rate calculations in that
range are pretty close to 4%, regardless of the lag used. Eventually, the rates for all lags should equalize, as deaths catch up to cases.
4. Implications for Other Countries
It is difficult to say whether or not these results will
hold for other countries, since:
- Reporting standards are likely to differ from place to place, so that just what it means to become a case (or when) will not necessarily be comparable.
- Deaths are deaths, but they may not always be recorded the same way. Some areas may tend to err or the side of recording them as virus-related while others might tend in the opposite direction.
- The level of medical facilities will differ between countries, so that a person who recovered in one place might have died in another, due to things such as the availability of ventilators.
- Weather may play a role, as there is speculation that the virus is less active in warmer and more humid areas.
- Population density and various cultural/legal/political factors may make social distancing more effective in some areas than in others (e.g. public vs private medicine).
- There may be statistically significant genetic differences between populations in how they respond to the virus, for instance at the cellular level of lung tissue.
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And, here’s a more pleasant travel story than anticipating
the worldwide journey of a virus. It is something to think about and perhaps plan for, once things return to normal and travel has become a reasonable possibility again.
A Drive Across Newfoundland
Germany: https://www.amazon.de/dp/B07NMR9WM8
Australia: https://www.amazon.com.au/dp/B07NMR9WM8
Newfoundland, Canada’s most easterly province, is a region
that is both fascinating in its unique culture and amazing in its vistas of
stark beauty. The weather is often wild, with coastal regions known for steep
cliffs and crashing waves (though tranquil beaches exist too). The inland areas
are primarily Precambrian shield, dominated by forests, rivers, rock
formations, and abundant wildlife. The province also features some of the
Earth’s most remarkable geology, notably The Tablelands, where the mantle rocks
of the Earth’s interior have been exposed at the surface, permitting one to
explore an almost alien landscape, an opportunity available on only a few
scattered regions of the planet.
The city of St. John’s is one of Canada’s most unique urban
areas, with a population that maintains many old traditions and cultural
aspects of the British Isles. That’s true of the rest of the province, as well,
where the people are friendly and inclined to chat amiably with visitors. Plus,
they talk with amusing accents and party hard, so what’s not to like?
This account focusses on a two-week road trip in October 2007, from St. John’s in the southeast, to L’Anse aux Meadows in the far northwest, the only known Viking settlement in North America. It also features a day hike visit to The Tablelands, a remarkable and majestic geological feature. Even those who don’t normally consider themselves very interested in geology will find themselves awe-struck by these other-worldly landscapes.
This account focusses on a two-week road trip in October 2007, from St. John’s in the southeast, to L’Anse aux Meadows in the far northwest, the only known Viking settlement in North America. It also features a day hike visit to The Tablelands, a remarkable and majestic geological feature. Even those who don’t normally consider themselves very interested in geology will find themselves awe-struck by these other-worldly landscapes.
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