Diffusive epidemic process in 3D: a two-species reaction–diffusion phase transition

By the use of Monte Carlo simulation we study the critical behavior of a three-dimensional stochastic lattice model describing a diffusive epidemic propagation process. In this model, healthy (A) and sick (B) individuals diffuse on the lattice with diffusion constants d _A and d _B, respectively, and undergo reactions B → A and A + B → 2B. We determine the absorbing phase transition between a steady reactive state and a vacuum state. We obtained the order parameter, order parameter fluctuations, correlation length and their critical exponents by the use of steady state and short-time dynamics simulations. We studied three different diffusion regimes: the case of species A diffusing much slower than species B (d _A ≪ d _B), the case of species with equal diffusion constants (d _A = d _B) and the case of species A diffusing much faster than species B (d _A ≫ d _B). We found only second order transition for all three cases. We did not identify any signal of first order transition for the case d _A > d _B as predicted by field theory in first order approximation. (paper)