Fluctuation effects in an epidemic model.
We study a discrete epidemic model A+B-->2A in one and two dimensions (1D and 2D). In 1D for low concentration theta, we find that a depletion zone exists ahead of the front and the average velocity of the front approaches v=theta/2. In the 1D high concentration limit, we find that the velocity approaches v=1-e(-theta/2). In 2D, for low concentration we also find a depletion zone, and the velocity scales as v approximately theta(0.6), which is different from the scaling expected from the mean field approximation, v approximately 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.
Warren
C P
CP
Michigan Center for Theoretical Physics, Department of Physics, The University of Michigan, Ann Arbor, Michigan 48109-1120, USA.
Mikus
G
G
Somfai
E
E
Sander
L M
LM