Coronavirus appears to be accelerating in the U.S. as of 27th March, 2020. Here’s a chart…

One can see that after 18th March, the gradient steepens somewhat. The data is sourced from here; https://github.com/CSSEGISandData/COVID-19, specifically time_series_covid19_deaths_global.csv.

When a logarithmic plot of the raw data shows a straight line, it implies that such data can be described by an equation of the form…

d = n^{x}

…where d = number of deaths, x = number of days and n is a constant.

To determine the value of n, the least mean squares method will be used. However, before applying this method, need to define the equation that describes the logarithmic plot (converting the above by applying a base 10 log to both sides of the equation)…

log(d) = x.log(n)

The above equation makes the plot linear of the form y = mx + c. Now that it is in this form, the least mean squares method can be applied. However given the line in the above plot appears to show two distinct gradients, so going to calculate two y = mx + c results. Note that for the above equation, log(d) = x.log(n), log(d) is equivalent to y, log(n) is m and x is still x.

For the first y = mx + c, the data points between 4th March and 17th of March will be used. The number of deaths reported for each of those days is…

11,12,14,17,21,22,28,36,40,47,54,63,85,108

This gives the following value for m (according to Excel’s LINEST function)…

0.075338449.

To find n, need to perform the following calculation…

10^{0.075338449}

Which gives…

1.189429

Therefore the equation that describes the growth between March 4th and March 17th is…

d = 1.189429^{x}

Note that the ‘c’ in y = mx + c has been dropped as it does not help describe the rate of growth of deaths.

Now looking at the steeper part of the the above plot, namely number of deaths between 20th March and 27th March, the data for which is here…

244,307,417,557,706,942,1209,1581

Performing the same calculations as above yields a growth equation of…

d = 1.308964^{x}

Not the best of news and simply confirms mathematically what is visually obvious on the plot above.

Meanwhile, in Italy…

…one can see that the rate of acceleration is slowing down (although it’s still exponential). This basically means that in our original equation…

d = n^{x}

…after appearing to remain constant for a while, n is now decreasing.

It should be pointed out that all the data is cumulative, meaning the numbers will never decrease. The best that can be hoped for is that it stops at a fixed figure and grows no further.