Optimal, near-optimal, and robust epidemic control

Abstract

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.

The COVID-19 pandemic has demonstrated the need for non-pharmaceutical epidemic mitigation strategies that can be effective even if they are limited in duration. Here, the authors derive analytically optimal and near-optimal time-limited strategies for limiting the epidemic peak in the Susceptible-Infectious-Recovered model and show that, due to the sensitivity of such strategies to implementation errors, timely action is fundamental to non-pharmaceutical disease control.