The spatial and temporal spread of infectious pathogens is a complicated process involving many different components. Of these components, the ones leading to the introduction of the pathogen in a location, its amplification there and subsequent exportation are critical. Here, I will focus on introductions of a pathogen into locations from which it is currently absent. Motivated by examples from SARS-CoV-2 and influenza, I will discuss several models that consider the early stages of the presence of a pathogen in a location.