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).

For comparison, we might have thought we could estimate the time at which transmission became subcritical from the day on which the maximum number of cases was reported. On average, the peak reporting day minus the 5-day serial interval occurred 9.8 days after the 23 January lockdown. The two approaches to estimating the lag from intervention to subcritical transmission are indeed correlated (\(\rho=0.41\)), but the relationship is not especially strong and all points lie above the one-to-one line. This result implies that achieving subcritical transmission actually occurred considerably after the peak in case notifications was observed. In fact, we estimate that, on average, subcritical transmission occurred 17.3 days after intervention and that this occurred \(17.3-9.8=7.5\) days after the transmission associated with peak cases.

##
##  Pearson's product-moment correlation
##
## data:  u and time.to.peak5
## t = 2.1813, df = 23, p-value = 0.03964
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.02259184 0.69539476
## sample estimates:
##       cor
## 0.4140268