Italy and the U.S. – How Strong is the Case for Lifting the Lockdown?

Italy and the U.S. – How Strong is the Case for Lifting the Lock-down?

April 14, 2020 Update

There is beginning to be a fair amount of talk about “lifting the lock-down” or at least easing up on restrictions, in various countries.  There is a legitimate concern that it not last excessively long, but also that it not be lifted prematurely, resulting in a re-occurrence (and perhaps a much worse one) of the corona virus, or COVID-19.

It is instructive to look at the progress of the pandemic in the different countries and compare it to what we might call the index case, i.e. China, which seems to have successfully negotiated at lease one cycle of the viral outbreak.  That might give a fair indication of when it is safe to lift restrictions.

The blog presents a graphical and mathematical heuristic for making these comparisons, in a simplified form that should be understandable to a wide audience.  I will focus on Italy and the U.S. as examples of the reasoning.

Italy

Italy appears to be following in China’s footsteps, in terms of New Cases Per Day, though with a longer period of time on the plateau of the epidemic, so to speak.  The fact that Italy took longer to initiate a general lock-down probably explains the longer length of the projected outbreak, as shown on the graph below.

Using the graph, a very simple method of estimating when Italy could reasonably consider lifting the lock-down is simply to eye it up, and estimate when the function will approach 0 New Cases per Day again.  Doing this indicates a date within two to three weeks.  That’s about 75 days since the earliest quarantines (Feb 22), or about 55 days since the nation-wide lockdown on March 9 (18 days after the earliest quarantines). 

So, that’s about 3 weeks from today, or about May 5.  That’s not necessarily to say that they should let up then – there is a good argument for caution.  It is just to say that they should wait until at least then.

The second graph reproduces much of the first graph, but focuses on the period of the pandemic in both countries where Cases per Day exceeded 200 per day, which we might think of as the main part of the pandemic.  I did that to eliminate the early phases, which have fairly small counts and therefore a certain amount of random variance, which can influence a best-fit line and obscure the more important pattern.  This shows a very similar result, such that the pandemic should drop to a relatively low New Cases per Day within about 2 to 3 weeks.

The graphs also give best-fit lines and a projections of those lines, using quadratic functions for China and Italy.  That’s a bit more sophisticated than a simple visual inspection, though it is far from a really complex model, such as an agent-based epidemiological model or a matrix-based demographic projection, using age/sex/comorbidity/etc. risk functions.

And, when you think about it, this is a sort of demographic model, but we are tracking the demographic path of the virus i.e. the interaction of its “birth rates” rates and “death rates” as the Cases per Day rise, then plateau, then drop.  A simple quadratic best-fit line might be compared to a ballistic path – the virus is launched with a high velocity (lots of unaware and susceptible hosts to help in quickly spreading the virus), then slows down (it becomes harder to find new hosts as some have immunity or have died and others are now social distancing) and eventually falls back to near 0 (it has become too difficult for the virus to effectively reproduce, so is dying out). 

I should note that complex models aren’t  necessarily more accurate than simple models, as anyone (such as myself) who has done practical demographic modelling can attest.   Keyfitz, in his book Applied Mathematical Demography has an interesting example of this (page 277) where he gives a table of historical examples, comparing simple and complex population projections, with the result that the simple models often turned out to be more accurate than complex models.

  

United States

The U.S. appears to be in an earlier stage of this progression.  Visually, it does appear to be in the “plateau” stage, but the quadratic function has not yet turned negative (i.e. a ballistic path), so it is probably still too early to make any firm plans about lifting restrictions.  There is still a significant risk of fast growth on the part of the virus, should a premature end to the lock-down be implemented, though it is likely that that will turn around soon.

It is interesting to compare the Chinese outbreak to the U.S. outbreak, in terms of the relative magnitudes of the two functions.  Clearly, the U.S. has had a worse time of it, even though it has a much smaller overall population.  Presumably this is because of the difficulty of implementing an effective lock-down in a large (geographically and demographically) democracy like the U.S., relative to a large collectivized polity like China. 

Looking at the more focused graph (days with New Cases greater than 200), the situation is much the same.  The U.S. data still doesn’t show a really clear sign of reliably hitting the turn-around point.  Visually, it looks like it could still go either way, though the evidence does seem to point to a ballistic path taking shape, which could be confirmed in the near future.

It is interesting to use this method (one could say heuristic) to explore the situation in other countries, as the pandemic makes its way around the world.  I will look at some other countries in later blogs.

It is also clear that people (regular people and economists) are getting antsy to go back to normal.  The time for that does seem to be drawing near, but there is still room for caution. 

And, here’s a more pleasant travel story than anticipating the worldwide journey of a virus.

A Drive Across Newfoundland

U.S.: https://www.amazon.com/dp/B07NMR9WM8

U.K.:  https://www.amazon.co.uk/dp/B07NMR9WM8

Germany: https://www.amazon.de/dp/B07NMR9WM8

Japan: https://www.amazon.co.jp/dp/B07NMR9WM8

Canada: https://www.amazon.ca/dp/B07NMR9WM8

Australia: https://www.amazon.com.au/dp/B07NMR9WM8

India: https://www.amazon.in/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.