Similarity of epidemic spreading and information network connectivity mechanisms demonstrated by analysis of two probabilistic models

Abstract

The modelling of epidemic spreading is essential in understanding the mechanisms of outbreaks and pandemics. Many models for different kinds of spreading have been proposed throughout the history of modelling, each suited for a specific scenario and parameters. On the other hand, models of information networks provide important tools for the analysis of the performance and reliability of such networks. We have previously presented a model for simulating the spreading of infectious disease throughout a social network and another one for simulating the connectivity of data traffic in an information network. We argue that these models are similar in that they produce equivalent results with appropriate parameters when run on the same network. We explain this by reasoning that the manners in which the models carry out their calculations, although devised from different assumptions, turn out to be equivalent. We also show empirical results of applying the models to calculate the spread of contagion and information connectivity on two complex networks suitable for the models. Based on the results, we calculate centrality metrics reflecting the outcome of the application, highlighting its important properties. We note that the centrality values obtained by running the epidemic model and the connectivity model turn out to be mutually equivalent, as predicted by their similar fashions of calculation. As the models were independently developed for their own applications, the equivalence in their calculation can not be explained by the models purposefully built similarly. Thus, not only are the two apparently completely separate areas of interest analysable with a single model but there appear to be inherent similarities in the mechanisms of epidemic spreading and determining network connectivity.