Optimal timing for social distancing during an epidemic

Oscar Patterson-Lomba

An important assumption in this exercise of finding an optimal time for initiating social distancing, is that individuals that are infected or immune are all perfectly ascertained and tracked (i.e., no underreporting of cases) such that decision makers have perfect knowledge of the R 0 and the effective reproduction number (via estimation from epidemic data), as well as the number of new cases at any given point. Early in an epidemic, particularly when in the presence of a novel pathogen like SARS-CoV-2, there is typically a large amount of uncertainty around most epidemiological parameters, especially R 0 [9, 23] . This uncertainty is the result of several factors, including lack of reliable data on the true number of cases, differences in the formulations and assumptions underlying the statistical models used to estimate R 0 , and the geographic heterogeneity of the disease spreading patterns. This uncertainty around the value of R 0 should also be carried over to the estimate of the optimal time for initiating social distancing. Hence, assuming the true R 0 lies within a range (e.g., 95% confidence intervals), the estimation of the optimal t 0 should account for this uncertainty. Moreover, if a (Bayesian posterior) distribution is available for R 0 , then one could also get a distribution for the optimal t 0 , which would in turn allow to compute the probability that the optimal t 0 is within a given range, or lower/higher than a given time of interest (e.g., two weeks from now). Then, it would be up to the decision makers to determine what level of uncertainty is considered acceptable in order to proceed with a given social distancing strategy. Of note, if the level of uncertainty on R 0 is very large and a decision needs to be made promptly, it is arguably better to initiate social distancing sooner, as opposed to later, than the optimal t 0 inferred from the available data; therefore, a conservative approach could be to assume R 0 is equal to the upper bound of its %95 confidence interval, and compute the corresponding (shorter)