Extended Data Fig. 8: Simulating reduced-form estimates for the no-policy growth rate of infections for different population regimes and disease dynamics.

We examine the performance of reduced-form econometric estimators through simulations in which different underlying disease dynamics are assumed (see Supplementary Methods section 2). Each histogram shows the distribution of econometrically estimated values across 1,000 simulated outbreaks. Estimates are for the no-policy infection growth rate (analogous to Fig. 2a) when three different policies are deployed at random moments in time. The black line shows the correct value imposed on the simulation and the red histogram shows the distribution of estimates using the regression in equation (7), applied to data output from the simulation. The grey dashed line shows the mean of this distribution. The 12 subpanels describe the results when various values are assigned to the mean infectious period (γ⁻¹) and mean latency period (σ⁻¹) of the disease. σ = ∞ is equivalent to SIR disease dynamics. In each panel, S_min is the minimum susceptible fraction observed across all 1,000 45-day simulations shown in each panel. In the real datasets used in the main text, after correcting for country-specific underreporting, S_min across all units analysed is 0.72 and 95% of the analysed units finish with S_min > 0.91. Bias refers to the distance between the dashed grey and black line as a percentage of the true value. a, Simulations in near-ideal data conditions in which we observe active infections within a large population (such that the susceptible fraction of the population remains high during the sample period, similar to those in our data for Chongqing, China). b, Simulations in a non-ideal data scenario in which we are only able to observe cumulative infections in a small population (similar to those in our sample for Cremona, Italy).