Two-dimensional diffusive epidemic process in the presence of quasiperiodic and quenched disorder

Abstract

This work considers the diffusive epidemic process model coupled to the square lattice, the Penrose quasiperiodic lattice, and the Voronoi–Delaunay random lattice. The main objective is to verify if spatial disorder influences critical behavior. According to the Harris–Barghathi–Vojta criterion, quenched or quasiperiodic disorder can change the critical behavior of the system, depending on the disorder decay exponent of the lattice. We employed extensive Monte Carlo simulations of the relevant quantities. Furthermore, we estimate the critical exponent ratios. Our results suggest that the disorder does not change the critical behavior when comparing the critical exponent ratios for the three studied lattice structures. In addition, the critical exponents depend on the three possible diffusion regimes: (1) where diffusion is dominated by susceptible individuals, (2) where infected and susceptible individuals have the same diffusion constant, and (3) where diffusion is dominated by the infected individuals.