The epidemic of COVID-19 reached different areas of China at different times. This means that different locations were at different phases of outbreak at the time of the Wuhan lockdown (23 January) and other provincial and national actions. This provides what is sometimes called a “natural experiment” because it is as if replicate epidemics had been induced and then intervened on at different times. By looking at the effect of timing on outbreak size, we can draw conclusions about the effect of delaying intervention, which may be informative to other countries that are considering taking action.
Here we look at the final size of the outbreak in each province as a function of the date that the first case was reported. The identity of each province and size of the outbreak can be viewed by hovering the pointer over a data point of interest.
Next we look at the final size of the outbreak in each province as a function of the size of the outbreak on 23 January.
These results illustrate the importance of taking early actions to mitigate transmission prior to confirmation of a large number of local cases. Importantly, at the time of the Wuhan lockdown, no province other than Hubei was reporting more than 40 cases. These results also support a calculation of the risks of delaying intervention. A linear regression quantifies the effect of delay on outbreak size. The correlation between outbreak size and days elapsed is about 0.9.
| Estimate | Std. Error | t value | Pr(>|t|) | |
|---|---|---|---|---|
| (Intercept) | 4824 | 448 | 10.77 | 1.204e-11 |
| cases$Date[outbreak.start] | -0.2637 | 0.02451 | -10.76 | 1.218e-11 |
| Test statistic | df | P value | Alternative hypothesis | cor |
|---|---|---|---|---|
| -10.76 | 29 | 1.218e-11 * * * | two.sided | -0.8943 |
The change in the logarithm of outbreak size is given by the slope parameter of this equation, i.e.
\[\begin{equation} \log10(Y) = - 0.26370x \end{equation}\]
Setting this change to one (i.e. a one log change in outbreak size), rearranging, and solving for days yields the number of days delay corresponding to a tenfold change in outbreak size.
\[\begin{equation} x = -3.79 \end{equation}\]
Now we investigate the same pattern, but look at outbreak size as a fraction of the total population. The idea is that since the least populated provinces were likely to be hit last, they might have smaller outbreaks just because they have smaller populations over all.
As shown by the figure and verified by numerical analysis, in fact the correlation between epidemic size as a proportion of population and the timing of the outbreak is just as strong (correlation: \(\rho = -0.9\)) as the correlation between absolute epidemic size and outbreak timing. Naturally, the regression equation is slightly different and estimated to be -0.19, As before, we can rearrange the regression and solve for the effect on oubtreak size of delaying intervention to find that every 5.3 days delay in intervention leads to a ten fold change in the proportion of the total population infected.
\[\begin{equation} \log10(Y) = - 0.19008x \rightarrow x \approx -5.3 \end{equation}\]
| Estimate | Std. Error | t value | Pr(>|t|) | |
|---|---|---|---|---|
| (Intercept) | 3470 | 316.9 | 10.95 | 8.103e-12 |
| cases$Date[outbreak.start] | -0.1901 | 0.01733 | -10.97 | 7.83e-12 |
| Test statistic | df | P value | Alternative hypothesis | cor |
|---|---|---|---|---|
| -10.97 | 29 | 7.83e-12 * * * | two.sided | -0.8976 |
A similar analysis can be performed at the smaller spatial scale of prefectures.
It is compelling that no new prefecture has been infected since 14 February.