Human mobility and spatial structure represent key ingredients in the geographical spread of an infectious disease. The flows of traveling people form a network characterized by complex features, such as strong topological and traffic heterogeneities, that unfolds at different temporal and spatial scales. Theoretical frameworks that consider reaction-diffusion processes on a network of populations are able to provide understanding on the interplay between individual mobility and epidemic dynamics. However many biological and behavioral factors relevant for disease dynamics are not included in such models. We focus in particular on two of them. The first one is the pathogen genetic diversity that often determines the co-circulation of different strains: the role of human spatial structure and mobility on multi-strain interaction and competition is subject of intense debate. Beside this biological complication another factor related to human behavior, namely the time scale of human traveling represented by the trip duration, further increases the level of heterogeneity of the systems and thus may alter the spreading dynamics of an epidemic. We address these two problems separately. In both cases reaction-diffusion models are able to provide clear understandings. Within this framework we show by means of analytical calculations and numerical simulations, that the degree of such heterogeneities, characterizing pathogen on one side and humans on the other, crucially affects the global epidemic dynamics altering the ability of a disease to invade the system and to reach pandemic proportions.
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