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

• Published in: Journal of statistical mechanics Vol. 2021; no. 3; p. 33217
• Main Authors: Argolo, C, Tenório, V, Albuquerque, S S
• Format: Journal Article
• Language: English
• Published: 01.03.2021
• ISSN: 1742-5468; 1742-5468
• DOI: 10.1088/1742-5468/abe701

Abstract 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 → 2 B . 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.