Optimal Timing of Non-Pharmaceutical Interventions During an Epidemic

In response to the recent outbreak of the SARS-CoV-2 virus governments have aimed to reduce the virus's spread through, \emph{inter alia}, non-pharmaceutical intervention. We address the question when such measures should be implemented and, once implemented, when to remove them. These issues are viewed through a real-options lens and we develop an SIRD-like continuous-time Markov chain model to analyze a sequence of options: the option to intervene and introduce measures and, after intervention has started, the option to remove these. Measures can be imposed multiple times. We implement our model using estimates from empirical studies and, under fairly general assumptions, our main conclusions are that: (1) measures should be put in place not long after the first infections occur; (2) if the epidemic is discovered when there are many infected individuals already, then it is optimal never to introduce measures; (3) once the decision to introduce measures has been taken, these should stay in place until the number of susceptible or infected members of the population is close to zero; (4) it is never optimal to introduce a tier system to phase-in measures but it is optimal to use a tier system to phase-out measures; (5) a more infectious variant may reduce the duration of measures being in place; (6) the risk of infections being brought in by travelers should be curbed even when no other measures are in place. These results are robust to several variations of our base-case model.