An international comparison of the second derivative of COVID-19 deaths after implementation of social distancing measures

William Thomas Pike; Vikas Saini

Data was obtained from European Centre for Disease Control website [2] on 24/03/2020. All reported deaths from confirmed cases of COVID19 were extracted into a time series of daily deaths for eight countries: China, Italy, Spain, France, USA, UK, Netherlands, Germany, and South Korea. In order to ensure that all included countries had sufficient counts to derive the necessary statistics, countries with fewer than 120 cumulative deaths were excluded. Daily fatality rates from the included countries were then used to calculate estimates of the relative second derivative of total deaths, N, 1/N d 2 N/dt 2 , for a period of at least ten days. All these countries have initiated social distancing measures at different points in time. Iran has been excluded as the very low variance in the data is not compatible with the statistics seen in the other seven countries analysed. The cumulative deaths for each country, N(t), were estimated by deriving a multiplier N final /N(t conv ) at the time of convergence, t conv , to the Chinese trajectory, N final being the total number of deaths in China and applying this multiplier to Chinese data for times beyond convergence. The daily deaths were derived by taking the differences in cumulative deaths. Fig. 1 shows the relative second derivative plotted as a times series for each country compared to China, calculated after total deaths reached at least 20. An exponential rate corresponds to a constant value over time, but for China the daily rate has been falling from an initial 50% to very close to zero, with the fall occurring over a 30-day period after lockdown was announced for Wuhan on 23/01/2020. In fig. 1 , the time series of the other countries have been aligned to best match the trajectory seen in China, with the announcement of lockdowns and implementation of social distancing measures in each country marked. Comparing to China, the daily growth rate in total deaths in Italy has been closely following the trajectory for the last 15 days subsequent to the announcement of lockdown in Lombardy on 8/3/2020. Spain has also seen some convergence on China's trajectory for the last seven days following a national lockdown implemented on 12/3/2020, but with a higher variance. In the case of France, lock-down measures came into force on 16/3/2020, and the trajectory has converged, again with a higher variance, for the last six days. The USA also shows some convergence for the last four days, with lockdowns implemented only to the state level at the time of writing. The UK has converged on China's trajectory for the last seven days, with a higher initial variance which in part is due to the sampling statistics from a relatively low fatality count to date; although no lockdown has been announced, general social distancing was advised by the government on 16/3/2020. Germany implemented social distancing in phases from Mar 8 until Mar 16 when stringent measures were announced nationally while the Netherlands did the same later and more slowly from 12/03 through 23/03/2020, ending in "targeted" lockdowns.