Chasing the ghost of infection past: identifying thresholds of change during the COVID-19 infection in Spain

Luis Santamaria; Joaquin Hortal

The analyses performed on the number of cases from Madrid are consistent with the results for the whole country. The model with two breaking points (Model 3) provided the best fit (Table 2) . Fitted breaking points were placed on day 12.7 (14/3/20, estimated infection on 4/3/20) and 26.6 (28-29/3/20, estimated infection on 18-19/3/20) (Figure 2 ). The growth rate of the number of cases decreased by 65% (from 0.18 to 0.06) after the first breakpoint (14/3/20) and decreased again by 59% (from 0.08 to 0.03) after the second breakpoint (18-19/3/20). An inspection of the values and fits ( Figure 2) shows that the apparent jump in the number of cases detected on 9/3/20 (estimated infection on 28/02/20) was caused by the combination of a decrease during the weekend (7-8/3/20) and an increase the following Monday -which kept the point in line with the previous and posterior values. Indeed, the only fitted model that identified a change of slope (Model 4, breaking point at day 9.0, i.e. on 10/3/20, estimated infection 29/2/20) showed a 19% decrease in the growth rate (from 0.18 to 0.15) at such point -although it provided a non-significant improvement in goodness-of-fit relative to a more-parsimonious model without such breaking point (Model 3) . Similarly, the model with two breaking points involving a change of intercept and a change of slope (Model 5), which resulted in a 11% increase in the intercept (from 1.3 to 1.45) on day 7.1 (8/3/20, estimated infection 27/2/20), did not result in a significantly better fit compared to Model 2 ( Table 2 ). Here it is worth noting that a similar 'decrease-and-jump' in the number of cases was observed one week before, from Saturday 29/2/20 to Monday 2/3/20, although dates before 1/3/20 were not included in the analysis owing to the low number of registered cases (below the ten-cases threshold).