  In the absence of drugs and vaccines, policymakers use non-pharmaceutical
interventions such as social distancing to decrease rates of disease-causing
contact, with the aim of reducing or delaying the epidemic peak. These measures
carry social and economic costs, so societies may be unable to maintain them
for more than a short period of time. Intervention policy design often relies
on numerical simulations of epidemic models, but comparing policies and
assessing their robustness demands clear principles that apply across
strategies. Here we derive the theoretically optimal strategy for using a
time-limited intervention to reduce the peak prevalence of a novel disease in
the classic Susceptible-Infectious-Recovered epidemic model. We show that broad
classes of easier-to-implement strategies can perform nearly as well as the
theoretically optimal strategy. But neither the optimal strategy nor any of
these near-optimal strategies is robust to implementation error: small errors
in timing the intervention produce large increases in peak prevalence. Our
results reveal fundamental principles of non-pharmaceutical disease control and
expose their potential fragility. For robust control, an intervention must be
strong, early, and ideally sustained.
