Predicting epidemic evolution on contact networks from partial observations.

The massive employment of computational models in network epidemiology calls for the development of improved inference methods for epidemic forecast. For simple compartment models, such as the Susceptible-Infected-Recovered model, Belief Propagation was proved to be a reliable and efficient method to identify the origin of an observed epidemics. Here we show that the same method can be applied to predict the future evolution of an epidemic outbreak from partial observations at the early stage of the dynamics. The results obtained using Belief Propagation are compared with Monte Carlo direct sampling in the case of SIR model on random (regular and power-law) graphs for different observation methods and on an example of real-world contact network. Belief Propagation gives in general a better prediction that direct sampling, although the quality of the prediction depends on the quantity under study (e.g. marginals of individual states, epidemic size, extinction-time distribution) and on the actual number of observed nodes that are infected before the observation time.

The Topology of a Discussion: The #Occupy Case.

INTRODUCTION: We analyse a large sample of the Twitter activity that developed around the social movement 'Occupy Wall Street', to study the complex interactions between the human communication activity and the semantic content of a debate. METHODS: We use a network approach based on the analysis of the bipartite graph @Users-#Hashtags and of its projections: the 'semantic network', whose nodes are hashtags, and the 'users interest network', whose nodes are users. In the first instance, we find out that discussion topics (#hashtags) present a high structural heterogeneity, with a relevant role played by the semantic hubs that are responsible to guarantee the continuity of the debate. In the users' case, the self-organisation process of users' activity, leads to the emergence of two classes of communicators: the 'professionals' and the 'amateurs'. RESULTS: Both the networks present a strong community structure, based on the differentiation of the semantic topics, and a high level of structural robustness when certain sets of topics are censored and/or accounts are removed. CONCLUSIONS: By analysing the characteristics of the dynamical networks we can distinguish three phases of the discussion about the movement. Each phase corresponds to a specific moment of the movement: from declaration of intent, organisation and development and the final phase of political reactions. Each phase is characterised by the presence of prototypical #hashtags in the discussion.