Alessandro Vespignani Alessandro Vespignani

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Epidemic modeling:

dealing with complexity

The systematic study of population networks and their social/spatial structure has shown the ubiquitous presence of complexity features mathematically encoded in heavy-tailed statistical distributions, diverging fluctuations and emerging properties. Despite a variety of approaches have been developed in order to take into account the many complications and heterogeneities observed in the spread of epidemics, complexity is not the same as the sum of the merely complicated elements accounted for in sophisticate epidemic modeling. Indeed complex properties generally correspond to the breakdown of standard models. For instance this is the case of epidemic spreading in scale-free networks in which the lack of any intrinsic epidemic threshold generates a peculiar scenario with implications in immunization and containment policies. In this perspective we will provide a discussion of epidemic modeling that accounts for the presence of the network's complexity at various levels: connectivity pattern, traffic intensity, population heterogeneity. The introduction of complexity features leads to a rationalization of some of the puzzling characteristics of computer viruses and emerging diseases spreading, underlining the importance of considering the complex nature of systems as a key element in the understanding of the epidemic outbreaks evolution. Finally, we will discuss to which extent the protection of digital and biological populations, defined in the context of immunization policies designed to effectively reduce or prevent the large scale spreading of epidemics, is affected by the system's complexity.