ABSTRACT
Roughly six months into the COVID-19 pandemic, many countries have managed to contain the spread of the virus by means of strict containment measures including quarantine, tracing and isolation of patients as well strong restrictions on population mobility. Here we propose an extended SEIR model to explore the dynamics of containment and then explore scenarios for the local extinction of the disease. We present both the deterministic and stochastic version fo the model and derive the R0 and the probability of local extinction after relaxation (elimination of transmission) of containment, P0. We show that local extinctions are possible without further interventions, with reasonable probability, as long as the number of active cases is driven to single digits and strict control of case importation is maintained. The maintenance of defensive behaviors, such as using masks and avoiding agglomerations are also important factors. We also explore the importance of population immunity even when above the herd immunity threshold.