How to calculate the doubling rate for infections? I'm playing with the JHU nCOV data and looking to calculate the doubling rate in my region (Western Australia) - I can get it down to an integer value via a kind of brute force (halve the current case value, use excel maxifs to look at the most recent date where the case value is =< take the difference)
Is there a better way?
 A: In the early periods of an infection, we can model the number of people sick as
$$ y = \beta_0 \exp(\beta_1 t) $$
We are looking for a time, $\Delta t$, so that
$$ 2 y = \beta_0 \exp(\beta_1 t + \beta_1\Delta t)$$
This means that 
$$ 2 = \exp(\beta_1\Delta t)$$
or
$$ \dfrac{\log(2)}{\beta_1}  = \Delta t$$
So, the time required for the exponential to double is $\log(2) / \beta_1$.  We need an estimate of $\beta_1$, $\hat{\beta}_1$.  If you have infection data, the easiest way to do this is to do a linear regression on the log scale where $\hat{\beta}_1$ will be the coefficient of time. Generally speaking, this is not integer valued.  My own estimates from the United States are approximately 2.6 days (though we shouldn't take this estimate very seriously).  Since this isn't integer valued, you have to round up to 3 days.  Why round up?  After 2 days, the number of infections hasn't quite doubled. After 3 days, the number of infections is a little more than double.  So, in order for the infection to double, we have to wait $3 = \lceil 2.6\rceil$ days.
