Critical behavior of the diffusive susceptible-infected-recovered model

The critical behavior of the classical non-diffusive susceptible-infected-recovered model on lattices, where at least the recovered individuals stay immobile, had been immensely studied and well understood. By performing numerical simulations on a square lattice, we show that diffusion for all agents in the susceptible-infected-recovered model constitutes a singular perturbation, which induces asymptotically novel dynamical and stationary critical behavior distinct from the non-diffusive model. Dynamical simulations starting from a single infected seed yield diffusion-rate independent exponents that still render the hyperscaling relation held. Moreover, data collapse results for the number of active agents reveal that there exists an asymptotic universal scaling function independent of the implemented diffusion rate. Stationary critical properties obtained from finite-size scaling analysis further corroborate the dynamical critical properties through conventional scaling relations. In particular, the diffusive model exhibits a crossover from the classical model before the asymptotic long-time, large-scale regime is approached.