Optimal non-pharmaceutical pandemic response strategies depend critically on time horizons and costs.

The COVID-19 pandemic has called for swift action from local governments, which have instated non-pharmaceutical interventions (NPIs) to curb the spread of the disease. The swift implementation of social distancing policies has raised questions about the costs and benefits of strategies that either aim to keep cases as low as possible (suppression) or aim to reach herd immunity quickly (mitigation) to tackle the COVID-19 pandemic. While curbing COVID-19 required blunt instruments, it is unclear whether a less-transmissible and less-deadly emerging pathogen would justify the same response. This paper illuminates this question using a parsimonious transmission model by formulating the social distancing lives vs. livelihoods dilemma as a boundary value problem using calculus of variations. In this setup, society balances the costs and benefits of social distancing contingent on the costs of reducing transmission relative to the burden imposed by the disease. We consider both single-objective and multi-objective formulations of the problem. To the best of our knowledge, our approach is distinct in the sense that strategies emerge from the problem structure rather than being imposed a priori. We find that the relative time-horizon of the pandemic (i.e., the time it takes to develop effective vaccines and treatments) and the relative cost of social distancing influence the choice of the optimal policy. Unsurprisingly, we find that the appropriate policy response depends on these two factors. We discuss the conditions under which each policy archetype (suppression vs. mitigation) appears to be the most appropriate.