Critical behavior of the stochastic SIR model on random bond-diluted lattices

Abstract: In this paper, we investigate the impact of bond-dilution disorder on the critical behavior of the stochastic SIR model. Monte Carlo simulations were conducted using square lattices with first- and second-nearest neighbor interactions. Quenched bond-diluted lattice disorder was introduced into the systems, allowing them to evolve over time. By employing percolation theory and finite-size scaling analysis, we estimate both the critical threshold and leading critical exponent ratios of the model for different bond-dilution rates ($p$). An examination of the average size of the percolating cluster and the size distribution of non-percolating clusters of recovered individuals was performed to ascertain the universality class of the model. The simulation results strongly indicate that the present model belongs to a new universality class distinct from that of 2D dynamical percolation, depending on the specific $p$ value under consideration.