Lessons from being challenged by COVID-19

•We present results of different approaches to model the evolution of the COVID-19 epidemic in Argentina•We first highlight the relevance of interpreting the early stage of the epidemic in light of incoming infectious travelers from abroad.•we critically evaluate certain proposed solutions to contain the epidemic based on instantaneous modifications of the reproductive number.•we build increasingly complex and realistic models, incorporating mobility estimates from cell phone location data.•We discuss the strengths and limitations of the proposed models, and caution in the adoption of non-pharmaceutical interventions backed by numerical simulations.