In this paper we use spatial econometric specifications to model daily infection rates of COVID-19 across countries. Using recent advances in Bayesian spatial econometric techniques, we particularly focus on the time-dependent importance of alternative spatial linkage structures such as the number of flight connections, relationships in international trade, and common borders. The flexible model setup allows to study the intensity and type of spatial spillover structures over time. Our results show notable spatial spillover mechanisms in the early stages of the virus with international flight linkages as the main transmission channel. In later stages, our model shows a sharp drop in the intensity spatial spillovers due to national travel bans, indicating that travel restrictions led to a reduction of cross-country spillovers.