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We study a general epidemic model with arbitrary recovery rate distributions. This simple deviation from the standard setup is sufficient to prove that heterogeneity in the dynamical parameters can be as important as the more studied structural heterogeneity. Our analytical solution is able to predict the shift in the critical properties induced by heterogeneous recovery rates. Additionally, we show that the critical value of infectivity tends to be smaller than the one predicted by quenched mean-field approaches in the homogeneous case and that it can be linked to the variance of the recovery rates. We then illustrate the role of dynamical--structural correlations, which allow for a complete change in the critical behavior. We show that it is possible for a power-law network topology to behave similarly to a homogeneous structure by an appropriate tuning of its recovery rates, and vice versa. Finally, we show how heterogeneity in recovery rates affects the network localization properties of the spreading process.
We introduce a general stochastic model for the spread of rumours, and derive mean-field equations that describe the dynamics of the model on complex social networks (in particular those mediated by the Internet). We use analytical and numerical solu
Spreading processes have been largely studied in the literature, both analytically and by means of large-scale numerical simulations. These processes mainly include the propagation of diseases, rumors and information on top of a given population. In
Models of disease spreading are critical for predicting infection growth in a population and evaluating public health policies. However, standard models typically represent the dynamics of disease transmission between individuals using macroscopic pa
Spreading processes are ubiquitous in natural and artificial systems. They can be studied via a plethora of models, depending on the specific details of the phenomena under study. Disease contagion and rumor spreading are among the most important of
A model for epidemic spreading on rewiring networks is introduced and analyzed for the case of scale free steady state networks. It is found that contrary to what one would have naively expected, the rewiring process typically tends to suppress epide