Critical behavior of a one-dimensional diffusive epidemic process

We investigate the critical behavior of a one-dimensional diffusive epidemic propagation process by means of a Monte Carlo procedure. In the model, healthy (A) and sick (B) individuals diffuse on a lattice with diffusion constants $D_A$ and $D_B,$ respectively. According to a Wilson renormalization calculation, the system presents a second-order phase transition between a steady reactive state and a vacuum state, with distinct universality classes for the cases $D_A{=D}_B$ and $D_A<D_B.$ A first-order transition has been conjectured for $D_A>D_B.$ In this work we perform a finite size scaling analysis of order parameter data at the vicinity of the critical point in dimension $d=1.\mathrm{}$ Our results show no signature of a first-order transition in the case of $D_A>D_B.$ A finite size scaling typical of second-order phase transitions fits well the data from all three regimes. We found that the correlation exponent $\nu =2\mathrm{}$ as predicted by field-theoretical arguments. Estimates for $\beta /\nu$ are given for all relevant regimes.