# Coronavirus and Exponential Growth

I’m continuing to marvel at just how well an exponential model fits the number of confirmed cases of coronavirus.  The plot below shows the real number of confirmed cases (on a log10 scale) for Italy, US, Spain, and France to the left of the black vertical line.  It’s nearly perfectly linear!  To the right of the vertical black line we have the projections should this exponential growth continue.  I’ve also provided some basic output from the models for each country, including estimated regression coefficients, R^2 (i.e. how close to exponential is it), and when each country is expect to hit certain number of cases if the current trend were to continue.

Here is what is looks like on the raw scale:

All models are simple linear regression with log(confirmed cases) as the response and time since March 1 as a predictor (i.e. March 1 is 1, March 2 is 2, etc.).  Projections are based on the assumption that exponential growth continues as current rates (hopefully this turns out to be a bad assumption!)

# United States

Current number of confirmed cases (as of March 17): 6,421

beta = .283 (.275, .290)

growth rate = exp(.283) = 1.327 (1.317, 1.336)

R^2 = .9978 (!!! That’s so exponential!!!!)

Expected to be at X cases:

X = 10,000: March 19

X = 100,000: March 27

X = 1,000,000: April 4

X = 10,000,000: April 13

# France

Current number of confirmed cases (as of March 17): 7,699

beta = .257 (.239, .275)

growth rate = exp(.257) = 1.293 (1.270, 1.316)

R^2 = .9846

Expected to be at X cases:

X = 10,000: March 18

X = 100,000: March 27

X = 1,000,000: April 5

X = 10,000,000: April 14

# Spain

Current number of confirmed cases (as of March 17): 11,748

beta = .322 (.308, .337)

growth rate = exp(.322) = 1.380 (1.360, 1.401)

R^2 = .9931

Expected (or actual date) to be at X cases:

X = 10,000: March 17 (Actual Date)

X = 100,000: March 24

X = 1,000,000: March 31

X = 10,000,000: April 7

# Italy

Current number of confirmed cases (as of March 17): 31,506

beta = .186 (.178, .194)

growth rate = exp(.186) = 1.204 (1.195, 1.214)

R^2 = .9939

Expected to be at X cases:

X = 10,000: March 10 (Actual Date)

X = 100,000: March 23

X = 1,000,000: April 4

X = 10,000,000: April 17

________________________________________________________________

Code can be found here.

Follow me coding on Twitch here.

________________________________________________________________

Cheers!