Fluctuation effects in an epidemic model

We study a discrete epidemic model $A+\overrightarrow{B}2A$ in one and two dimensions (1D and 2D). In 1D for low concentration θ, we find that a depletion zone exists ahead of the front and the average velocity of the front approaches $v=\theta /2.\mathrm{}$ In the 1D high concentration limit, we find that the velocity approaches $v=1\mathrm{}-e^{-\theta /2\mathrm{}}.$ In 2D, for low concentration we also find a depletion zone, and the velocity scales as $v\sim {\theta }^{0.6},$ which is different from the scaling expected from the mean field approximation, $v\sim {\theta }^{0.5}.$ Analysis of the interface width scaling properties demonstrated that the front dynamics of this reaction are not governed by the Kardar-Parisi-Zhang equation.