Epidemic spreading in annealed directed networks: Susceptible-infected-susceptible model and contact process

摘要

We investigate epidemic spreading in annealed directed scale-free networks with the in-degree (k) distributionnPin(k) ∼ k−γin and the out-degree (u0003) distribution, Pout(u0003) ∼ u0003−γout . The correlation u0003klu0004 of each node on thennetworks is controlled by the probability r(0 u0002 r u0002 1) in two different algorithms, the so-called k and u0003nalgorithms. For r = 1, the k algorithm gives u0003klu0004 = u0003k2u0004, whereas the u0003 algorithm gives u0003klu0004 = u0003u00032u0004. For r = 0,nu0003klu0004 = u0003ku0004u0003u0003u0004 for both algorithms. As the prototype of epidemic spreading, the susceptible-infected-susceptiblenmodel and contact process on the networks are analyzed using the heterogeneous mean-field theory and MontenCarlo simulations. The directedness of links and the correlation of the network are found to play important roles innthe spreading, so that critical behaviors of both models are distinct from those on undirected scale-free networks.