Optimal Timing of Interventions during an Epidemic

The recent outbreak of the SARS-CoV-2 virus, causing infectious disease COVID-19, has shown that government (non-pharmaceutical) intervention can have a significant impact on the rate at which a virus spreads. It has been deemed imperative to reduce and delay the peak ("flattening the curve"). Flattening the curve is especially important when considering the impact of an outbreak on the health care system. Delaying the peak gives hospitals and (local) governments more time to prepare for later outbreaks and the (anticipated) influx of patients, but, more importantly, when the peak number of people requiring care simultaneously is reduced, there is a lower risk of the healthcare system being overwhelmed. It remains unclear, though, under what circumstances non-pharmaceutical intervention is optimal and perhaps even more importantly, once measures are in place, when to stop non-pharmaceutical interventions. When measures are lifted too early a second outbreak could appear. Intervention lasting too long could lead to unnecessary long term economic consequences. This paper uses a continuous-time Markov chain model to study the value and optimal exercise decision of two (sequential) options: the option to intervene and, after intervention has started, the option to end it.