Stochastic Modeling of Epidemic Dynamics: Scaling Behavior and Universality in SIR and SIS Systems

Epidemic spreading processes provide a natural framework to study non-equilibrium phase transitions and universality in stochastic systems. We investigate spatially extended susceptible--infected--recovered (SIR) and susceptible--infected--susceptible (SIS) models through individual-based simulations to examine how stochastic fluctuations and spatial correlations influence epidemic dynamics near the critical threshold. From these simulations, we extract the critical exponents that characterize the scaling behavior of both systems. Our results confirm that SIS dynamics belong to the directed percolation (DP) universality class, while SIR dynamics correspond to dynamical percolation (DyP). We have further examined the impact of the infectious agents' diffusion to determine whether spatial transport modifies the critical exponents or alters the universality class.