# Exponential growth

I think most people have heard (in one form or another) the old story in which the inventor of chess asks his king to reward him with a quantity of rice, according to the following rule: a single grain of rice is to be placed on the first chess square, doubled on each successive square. The bemused king readily agrees, only to find that he needs to place more than a million grains of rice on the 20th square and more than 18 quintillion (18,000,000,000,000,000,000) grains of rice on the 64th square. D’oh!

And yet, despite the popularity of this fable, it appears that most people really do not understand the awesome power of exponential growth. For example, does the average American grasp the implications of this chart?

The caseload represented by the blue line looks tiny, right? Comment by LZ (Investing in Chinese Stocks):

I’ve been posting the covid-19 case count with two x-axis to show the growth rate more clearly, but for today I put them both on one axis. It shows the rest of the world has a similar number of cases and a similar slope pre-quarantine China.

Even after China initiated a full lockdown on Wuhan, followed by strict nationwide travel restrictions and work closures, it still experienced exponential growth because of cases already in the system. Given the U.S. response to this point, I think it is almost inevitable U.S. cases will soar past China’s.

Note that the full lockdown on Wuhan was implemented January 23.

Here is the same chart with a secondary vertical axis:

In the absence of the kind of brutal containment measures that China has imposed, how widely will coronavirus spread in the US? I’m not sure; I’ve been trying to get a clearer picture of that, but my understanding is that it will likely spread very widely indeed. Harvard epidemiologist Marc Lipsitch predicts, with certain caveats, that the number of infections could reach 40 to 70% of adults worldwide:

Why do I think 40-70% infected? Simple math models with oversimple assumptions would predict far more than that given the R0 estimates in the 2-3 range (80-90%). Making more realistic assumptions about mixing, perhaps a little help from seasonality, brings the numbers down. Pandemic flu in 1968 was estimated to _symptomatically_ infect 40% of the population, and in 1918 30%. Those likely had R0 less than COVID-19.

The next important question is, what is the fatality rate? As far as I can tell, scientists have only a very rough grasp of what that might be, mostly because we have no idea how many people are walking around with undiagnosed infections. One Chinese study published in the Journal of the American Medical Association finds a case fatality rate (CFR) of 2.3%.

Let’s take the lower end of Professor Lipsitch’s estimate and assume that 40% of American adults (209 million x 0.40 = 83.6 million) get infected. With a 2.3% fatality rate, that equates to 1.9 million deaths.

But the fatality rate could be far lower in the US than in China for any number of reasons: perhaps our health care system is better equipped to handle an outbreak, or the far lower incidence of smoking and better air quality in the US mean that patients are less likely to have the kind of underlying respiratory conditions that increase morbidity.

Assuming a lower CFR of 1%, we are talking about 836,000 deaths, or roughly the population of San Francisco.