Analysis

Growth factor is a common way to measure the spread of a virus. It is defined as the ratio between new cases on a particular day and new cases on the previous day. $$G_f = \frac{\Delta N_d}{\Delta N_{d-1}}$$ In real data however, this factor is hard to estimate, as cases are not reported at exactly the same time every day, and also depends on testing rates. The plots below can show quite large variation in this value.

Another way to examine the growth of the virus is through the doubling time, this is the amount of time it takes for the cases to double, given the current exponential fit. The confirmed cases should eventually show a logistic function (as china's is now), but during the initial spread, an exponential curve can indicate the doubling factor, until we start to see a reduction in growth. $$ \frac{N_i}{N_0} = a \exp(\lambda t)$$ $\lambda$ indicates the growth rate of the virus. We want this to be as small as possible for our healthcare service to be able to deal with the influx of patients! Therefore the doubling time for Ireland given the best exponential fit over the last 2 weeks is $$\delta_2 = ln(2) / \lambda$$Also shown is the standard deviation ($\sigma$) for an exponential and linear fit, we want to minimise $\sigma$, giving the best fit.