I find it very remarkable how, despite our cultural differences, all people of the world can be fit to this universal exponential curve. When it comes to this virus, we are all the same.
The next thing to note is that once the virus is contained, the exponential growth comes to a grinding halt and the number of new cases per day plummets. Each data point represents one day, so you can see that within a week or two, new cases can plummet relative to exponential growth.
What is clear is that China has done the best job in tackling the virus quickly, South Korea is a close second. The USA and Italy still have some work to do before they contain the virus. I hope they don't get to x=1 (everyone infected). Rather, I would like to see the daily new infections plummet well before we get to that point!
The point of no return?
China and South Korea performed large efforts to contain the virus, and were successful. For the US or Italy to contain the virus will taken a proportionately even larger effort at this point, since they have already outgrown the Asian case numbers. It may be past the point of no return, where the efforts required to contain the virus (millions of daily tests and even more strict lockdown) are not possible anymore. If that's true, I have a hard time seeing what will stop the virus from hitting x~=1 (we are all infected). I hope it will stop before it gets there, but without a full lockdown I don't see how that will happen. Maybe the virus will just lose steam once enough people properly implement social distancing. It is not the kind of experiment that I would voluntarily sign up to be a part of, that's for sure!
The math
On the x-axis is cumulative cases, normalized by population, and on the y-axis is daily new cases, normalized by population.Because exponential growth has the property that:
We get the funny property that when plotted on a log-log plot, the daily new number of cases (the derivative of cumulative cases vs time) as compared to the cumulative number of cases will be equal to a constant:
When we eyeball the world countries on the above graph, we see that 1/τ is equal to approximately 0.18. Thus, the virus is growing by a factor of e, every 1/0.18 = τ = 5.4 days. Or equivalently, the number of infections is doubling every τ*ln(2) = 3.8 days. That seems like a universal number for all humans.
data from here:
New York
I included New York in the same graph as the nations above, and it's clear that they are proportionately getting hit the hardest. New York is approaching a population-wide 1% infection rate, approximately 10x the national average, although it also fits the universal COVID-19 line, just like all the nations do. The only thing that makes nations different is at what point they break the exponential growth curve.
The big question still remains: will the virus get close to 100% in any nation or city's population? I am worried that it will, but I hope not!
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