## Impact of intervention

How quickly was the impact of the 23 January “lockdown” felt? How long did it take to achieve containment? Since there is an $$\approx 5$$ day serial interval, on day $$i$$ we crudely estimate the reproduction number five days before (day $$i-5$$) from the number of case notifications $$X_i$$ as $$Z_i = R_{i-5} = \frac{X_i}{X_{i-5}}$$. A plot of $$Z_i$$ for every province on every day shows that the reproduction number did indeed decline, especially following 23 January (vertical red line). The grey lines represent simple linear regressions of $$Z_i$$ against time, one for each province. We shift these lines by 5 to obtain models for the change in $$R_i$$ over time (blue lines). On average, the critical value $$R_i=1$$ was reached on Day 30.4 (February 9). Rearranging these equations solves for the average lag of 17.3 days from 23 January (which, of course, isn’t actually perceived in the data for another 5 days).