Coronavirus: How are we doing? (methodology)

To create my metric, I make use of a 2-parameter model pioneered by Viboud et. al. Specifically, it measures number of cases on day t, C(t), using the following parameters: is a measure of growth rate, is a constant, and the “deceleration of growth parameter” is given by p = 1-\frac{1}{m}, where is between 0 and 1. Specifically, has unique properties. If is equal to 0, then the cumulative number of cases grows linearly. If is equal to 1, then the cumulative number of cases grows exponentially. Everything in-between displays sub-exponential growth. Cases with sub-exponential growth can be modeled using the following formula:


and can be estimated by applying current data and nonlinear least squares (NLS) to the above formula. In practice, as p approaches 0, a plot of cumulative cases is better represented by a linear model than an exponential one. Conversely, as approaches 1, a plot of cumulative cases is better represented by an exponential model. This can be seen by plotting for each country the difference in the r-squared of a linear model and the r-squared of an exponential model against p. We see a strong correlation (correlation = -0.89). Somewhere around p = 0.5, a linear model better explains the data:


As such, can be used as a “metric” of whether the cumulative case profile of a country can be represented by a linear model or an exponential one. As we know, there is a large difference between exponential and linear growth — this difference is so stark that r, or the growth rate, is almost irrelevant. A higher p indicates a better fit to an exponential model than a linear one, and vice versa. Some examples may help further illustrate this point.

Spain (p = 1.00, ~8,000 cases):

Bahrain (p = 0.52, 214 cases):


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