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) MUCH LESS-THAN 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.

Automated summary

By utilizing Monte Carlo simulation, the critical behavior of a three-dimensional stochastic lattice model describing a diffusive epidemic propagation process was studied, revealing an absorbing phase transition between different states. Three different diffusion regimes were explored, all showing second order transitions, contrary to predictions from field theory in first order approximation.