Note: this post has been updated to bring the data up to March 19, 2020, and further updated to March 26, 2020, to demonstrate the accuracy of the projection.
A little family secret: my maternal grandparents were very fecund.
This word is not used much in normal conversation these days, and indeed it sounds a bit nasty. However, it simply means that they “went forth and multiplied,” which indeed they did fifteen times, with thirteen of those children living well into late adulthood. My enduring memories of my grandfather, who died about 60 years ago, were that he was a jovial guy, while my grandmother always seemed tired.
Two and three generations later, the fecundity rate of that genetic lineage has dropped precipitously, which is mostly a good thing.
The “novel Coronavirus” causing the disease officially called COVID-19 (usage and capitalization rules seem to still be in flux here), is very fecund, as illustrated by the above graph. For the first two weeks of March, identified cases of COVID-19 in the U.S. grew at a compounded rate of 38% per day! At the end of three weeks, that rate had barely dropped, to 37% daily, and the last two days have actually see an uptick in that rate. That growth rate cannot continue indefinitely, but it is worth reviewing the very non-intuitive math of compounding growth rates because they are at the heart of nature’s replication process, whether it be humans or viruses.
We appear to be tracking on an identified case curve similar to Italy but about ten days behind. Over the last few days, the daily new case rate in Italy has dropped below 20%, which is still a very scary number. We will look at the math implications later.
In that graph above, the blue line indicates the number of confirmed cases in the U.S, and as you can see, the curve as started bending, which had been predicted nearer the beginning of the month, the orange line. The gray line indicates where this virus goes if we just consider the last ten days, and that still looks ugly.
This fecund virus
In his paradigm-changing 1976 book The Selfish Gene, biologist Richard Dawkins identified three traits of DNA in its gene form that were critical to life on Earth as it has evolved over the last 3.5 billion or so years.  In addition to fecundity (the ability of an organism to replicate itself frequently), Dawkins cites longevity (the ability to survive a sufficient time) and fidelity. 
Fidelity is a two-sided coin. On one hand the copy that the gene makes of itself must be close enough to its original to carry its key survival-focused traits. On the other hand, without some tiny aberrations in that copying process, we would not be here. Most “copy errors” are benign, having no effect. Some errors may be fatal to that “child gene.” And finally, a tiny proportion of copying mutations improve the child gene’s adaptation to its environment, and an “improved creature” has evolved. And here we are, each of us a unique end-product of billions of years of fecundity, longevity and fidelity.
Viruses are bits of DNA, or the simpler RNA in the case of this virus, that are in a form that replicates itself inside the cells of a host organism, such as a human. Our cells are actually filled with the remnants of non-fatal viruses from generations past. The novel Coronavirus (many conspiracy theories notwithstanding) appears to have mutated from an existing virus, perhaps long present in other animals, that “found a way” to replicate with great fecundity in humans.
How fecund is this thing?
Perhaps the scariest part of any new highly fecund virus is that we can only measure the cases that we detect. The “bullets that you don’t hear” can be many times more prevalent than the ones that strike. And nature almost always replicates itself on an exponential curve, one that curves upward rather than progressing in a straight line.
The easiest way to get your brain around exponential growth rates is the Rule of 72. Simply take the percentage growth rate and divide it into 72 to determine about how long it takes for the number of cases to double. For instance, as of March 19, the cumulative growth rate works out to the total case count doubling every two days. 
If you get that daily rate down to 20% cases will still double in just under four days. A 14% growth rate would take the doubling to five days.
When does the doubling end?
Near-40% exponential rates are mathematically unsustainable, but they can wreak havoc until they slow. At current rates, the U.S. will have well over one-half million infections by April 1. How long will we be on this curve that quickly gets asymptotic (headed nearly straight up)?”
Even if we can reduce this growth by, say, 1% per day (from 36% to 35% to 34%, etc.) we will still have twenty times as many cases as currently reported by April 1 as we know about today. As has been widely noted, however, this slowing is necessary to make sure that medical facilities do not get overwhelmed by sheer numbers of critical cases. In addition, the longer that this infection can be delayed in the population, the more likely that we will have an effective vaccine, or perhaps receive the grace of a seasonality dip in virulence.
Stay safe and play the odds by dodging the biggest hails of bullets.
Update: How prophetic was this curve?
One week later — exponential math wins this round!
- For those still struggling with the science, timeline and theology of evolution I recommend this past post on these “fightin’ words.”
- Dawkins also coined the term meme (for “memory gene”) to describe any form of social communication that takes on these three characteristics and spreads rapidly through a population. Ironically, the word meme has itself become a meme in recent years as ideas and images “blow up” through social media such as Facebook, Reddit, and Imgur.
- Note that this rule is a “ball-park” estimate and it is much more accurate at “normal” growth rates, say under 10%. At 40% growth rates it understates the doubling period by a little bit.