Optimal timing of one-shot interventions for epidemic control

The interventions and outcomes in the ongoing COVID-19 pandemic are highly varied. The disease and the interventions both impose costs and harm on society. Some interventions with particularly high costs may only be implemented briefly. The design of optimal policy requires consideration of many intervention scenarios. In this paper we investigate the optimal timing of interventions that are not sustainable for a long period. Specifically, we look at at the impact of a single short-term non-repeated intervention (a "one-shot intervention") on an epidemic and consider the impact of the intervention's timing. To minimize the total number infected, the intervention should start close to the peak so that there is minimal rebound once the intervention is stopped. To minimise the peak prevalence, it should start earlier, leading to initial reduction and then having a rebound to the same prevalence as the pre-intervention peak rather than one very large peak. To delay infections as much as possible (as might be appropriate if we expect improved interventions or treatments to be developed), earlier interventions have clear benefit. In populations with distinct subgroups, synchronized interventions are less effective than targeting the interventions in each subcommunity separately. Author summary Some interventions which help control a spreading epidemic have significant adverse effects on the population, and cannot be maintained long-term. The optimal timing of such an intervention will depend on the ultimate goal. Interventions to delay the epidemic while new treatments or interventions are developed are best implemented as soon as possible. Interventions to minimize the peak prevalence are best implemented partway through the growth phase allowing immunity to build up so that the eventual rebound is not larger than the initial peak. Interventions to minimize the total number of infections are best implemented late in the growth phase to minimize the amount of rebound. For a population with subcommunities which would have asynchronous outbreaks, similar results hold. Additionally, we find that it is best to target the intervention asynchronously to each subcommunity rather than synchronously across the population.