Application of Optimal Stopping Theory to Pandemic Lockdown Policies

During the COVID-19 pandemic, governments are facing challenges in determining the optimal time to exit the lockdown in their countries. A trade-off between health-related aspects and economic aspects should be achieved.This paper uses a discrete-time Markov Chain (DTMC) SIS model to find the optimal time to stop the lockdown. Two models are proposed: Model 1 assumes that the reproduction number R is constant over time, while Model 2 considers that R is time-dependent. The analysis of Model 1 leads to simple optimal policies.