by Charley Presigny, Piero Poletti, Stefano Merler, Manlio De DomenicoThe global warming effects of climate change favor the stable residence of invasive vectors, such as the mosquito Aedes albopictus, in temperate areas, like the Mediterranean basin or north America. Thus, favorable weather conditions, together with human mobility, increase the likelihood of large-scale vector-borne disease epidemics in areas where they were historically not endemic. While mathematical modeling acknowledges the relevance of human mobility in the persistence or prevalence of vector-borne diseases in endemic areas, the combined role of host-mediated vector transport and long-range airline travel in the emergence of epidemics in non-endemic areas is poorly understood. In this context, the impact of specific modeling formulations of human mobility on the epidemic predictions remains elusive. To bridge this gap, we compare two alternative models - one based on the force of infection from different source locations and one based on the explicit physical diffusion of individuals - that incorporate intra- and inter-country human mobility (considering air traffic flows), vector dispersal, and human-mediated vector mobility (e.g., vectors in cars/trains), with applications to diseases such as chikungunya, dengue and Zika. Through extensive computational and analytical analysis, we assess how implicit assumptions and the inclusion of different mobility components influence model estimates of epidemic emergence risk, the timing of potential epidemics and the risk of epidemic spread. The comparison between the two frameworks is illustrated using synthetic networks and Italy as a realistic case study. Our findings show that different model formulations of human mobility yield divergent risk assessment, affecting predictions of large scale outbreaks and importation times driven by explained mechanistic difference. Despite these differences, both models show consistent qualitative patterns in the spatial risk and the likelihood of concurrent local outbreaks. Integrating multiple mobility components and carefully identifying assumptions that reflect observed mechanisms are essential for understanding epidemics in currently non-endemic areas.