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', 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. (c) 2023 Elsevier B.V. All rights reserved.