Abstract
The susceptible–infected–removed spreading model in a directed graph is studied. The mean-field level rate equations are built with the degree–degree connectivity correlation element and the (in, out)-degree distribution. And the outbreak threshold is obtained analytically—it is determined by the combination of connectivity probability and the degree distribution. Furthermore, the methods of calculating the degree–degree correlations in directed networks are presented. The numerical results of the discrete epidemic processes in networks verify our analyses.
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