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Understanding how emerging infectious diseases spread within and between countries is essential to contain future pandemics. Spread to new areas requires connectivity between one or more sources and a suitable local environment, but how these two factors interact at different stages of disease emergence remains largely unknown. Further, no analytical framework exists to examine their roles. Here we develop a dynamic modelling approach for infectious diseases that explicitly models both connectivity via human movement and environmental suitability interactions. We apply it to better understand recently observed (1995-2019) patterns as well as predict past unobserved (1983-2000) and future (2020-2039) spread of dengue in Mexico and Brazil. We find that these models can accurately reconstruct long-term spread pathways, determine historical origins, and identify specific routes of invasion. We find early dengue invasion is more heavily influenced by environmental factors, resulting in patchy non-contiguous spread, while short and long-distance connectivity becomes more important in later stages. Our results have immediate practical applications for forecasting and containing the spread of dengue and emergence of new serotypes. Given current and future trends in human mobility, climate, and zoonotic spillover, understanding the interplay between connectivity and environmental suitability will be increasingly necessary to contain emerging and re-emerging pathogens. Here, using a dynamic modelling approach, the authors find that the spread of dengue through Mexico and Brazil is shaped by specific interactions between human mobility, climate, and the environment. Their models can also be applied to predict future spread in these geographic areas. [ABSTRACT FROM AUTHOR]