Droplet finite-size scaling theory of asynchronous SIR model on quenched scale-free networks

We present a finite-size scaling theory of the asynchronous susceptible–infected–removed model on scale-free networks, which models epidemic outbreaks and gives a non-vanishing critical threshold. The susceptible–infected–removed model can be mapped in a bond percolation process, as stressed by P. Grassberger, allowing us to compare the critical behavior of site and bond universality classes on networks. We employ a droplet heterogeneous mean-field theory, adding the effect of an external field defined as the initial number of infected individuals. One can choose the external field scaling as N−1, where N is the number of network nodes, and compare theoretical results with simulations on the uncorrelated model and Barabasi–Albert networks. The system presents a percolating phase transition where the critical behavior obeys the mean-field universality class, as we show theoretically and by extensive simulations.