Susceptible-infected-susceptible model on quenched directed scale-free networks

초록

The critical behavior of the susceptible-infected-susceptible model is investigated on quenched directed scale-free networks with the in-degree (k) distribution P-in(k) similar to k(-gamma in) in and the out-degree (l) distribution, P-out(l) similar to l(-gamma out). The correlation < kl > of each node is controlled. In the model, an infected individual becomes healthy with unit rate and infects all healthy neighbors with rate lambda. On quenched undirected networks with degree distribution P(q) similar to q(-gamma), the system is always in an endemic state for any gamma, so the critical threshold lambda(c) is always zero. Heterogeneous mean-field theory fails to predict the behavior of the quenched undirected networks. However, for quenched directed networks, we show via Monte Carlo simulations that the critical behavior of the directed quenched networks is well described by heterogeneous mean-field theory.

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