Among the realistic ingredients to be considered in the computational modeling of infectious diseases, human mobility represents a crucial challenge both on the theoretical side and in view of the limited availability of empirical data. To study the interplay between shortscale commuting flows and long-range airline traffic in shaping the spatiotemporal pattern of a global epidemic we (i) analyze mobility data from 29 countries around the world and find a gravity model able to provide a global description of commuting patterns up to 300 kms and (ii) integrate in a worldwide-structured metapopulation epidemic model a timescale-separation technique for evaluating the force of infection due to multiscale mobility processes in the disease dynamics. Commuting flows are found, on average, to be one order of magnitude larger than airline flows. However, their introduction into the worldwide model shows that the large-scale pattern of the simulated epidemic exhibits only small variations with respect to the baseline case where only airline traffic is considered. The presence of short-range mobility increases, however, the synchronization of subpopulations in close proximity and affects the epidemic behavior at the periphery of the airline transportation infrastructure. The present approach outlines the possibility for the definition of layered computational approaches where different modeling assumptions and granularities can be used consistently in a unifying multiscale framework.complex networks ͉ computational epidemiology ͉ human mobility ͉ multiscale phenomena C omputational approaches to the realistic modeling of spatial epidemic spread make use of a wide array of simulation schemes (1) ranging from very detailed agent-based approaches (2-6) to structured metapopulation models based on data-driven mobility schemes at the interpopulation level (7-10). All these approaches integrate a wealth of real-world data. However, it is not yet clear how to discriminate the effects of the inclusion/lack of real-world features in specific models. This limitation is mainly related to our incomplete knowledge of human interactions and mobility processes, which are fundamental aspects to describe a disease spread. Although recent efforts started to make available massive data on human mobility from different sources and at different levels of description (11)(12)(13)(14)(15)(16)(17)(18)(19)(20), the multiscale nature of human mobility is yet to be comprehensively explored. Human mobility can be generally described by defining a network of interacting communities where the connections and the corresponding intensity represent the flow of people among them (13,14). Global mobility flows therefore form very complex multiscale networks (21) spanning several orders of magnitude in intensity and spatiotemporal scales ranging from the long-range intercontinental air traffic (13,15) to the short range commuting flows (17)(18)(19). A multitude of heuristic models for population structure and mobility patterns have been proposed, but they a...

Network modeling plays a critical role in identifying statistical regularities and structural principles common to many systems. The large majority of recent modeling approaches are connectivity driven. The structural patterns of the network are at the basis of the mechanisms ruling the network formation. Connectivity driven models necessarily provide a time-aggregated representation that may fail to describe the instantaneous and fluctuating dynamics of many networks. We address this challenge by defining the activity potential, a time invariant function characterizing the agents' interactions and constructing an activity driven model capable of encoding the instantaneous time description of the network dynamics. The model provides an explanation of structural features such as the presence of hubs, which simply originate from the heterogeneous activity of agents. Within this framework, highly dynamical networks can be described analytically, allowing a quantitative discussion of the biases induced by the time-aggregated representations in the analysis of dynamical processes.

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Background: On 11 June the World Health Organization officially raised the phase of pandemic alert (with regard to the new H1N1 influenza strain) to level 6. As of 19 July, 137,232 cases of the H1N1 influenza strain have been officially confirmed in 142 different countries, and the pandemic unfolding in the Southern hemisphere is now under scrutiny to gain insights about the next winter wave in the Northern hemisphere. A major challenge is pre-empted by the need to estimate the transmission potential of the virus and to assess its dependence on seasonality aspects in order to be able to use numerical models capable of projecting the spatiotemporal pattern of the pandemic.