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: *r *is a measure of growth rate, *A *is a constant, and the “deceleration of growth parameter” is given by , where *p *is between 0 and 1. Specifically, *p *has unique properties. If *p *is equal to 0, then the cumulative number of cases grows **linearly. **If *p *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:

*r *and *p *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 *p *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, *p *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):