Growth rate estimators

[adrian-lison]

The growth rate is currently estimated via the log derivative of infections, see

EpiNow2/inst/stan/functions/generated_quantities.stan

Lines 33 to 39 in 35483d0

	vector calculate_growth(vector infections, int seeding_time) {
	int t = num_elements(infections);
	int ot = t - seeding_time;
	vector[t] log_inf = log(infections);
	vector[ot] growth = log_inf[(seeding_time + 1):t] - log_inf[seeding_time:(t - 1)];
	return(growth);
	}

I know that this is the classical interpretation of the growth rate, but wanted to point out the alternative version suggested in Parag et al. which instead computes the log derivative on the infectiousness (and shifts it by the mean generation time). When testing this in EpiSewer, it seemed to be slightly more stable and r=0 had a better temporal matching with Rt=1.