Velocity of front propagation in the epidemic model $A+B\to2A$
  We study front propagation in the irreversible epidemic model $A+B\to 2A$ in one dimension. Here, we allow the particles $A$ and $B$ to diffuse with rates $D_A$ and $D_B$, which, in general, may be different. We find analytic estimates for the front velocity by writing truncated master equation in a frame moving with the rightmost $A$ particle. The results obtained are in reasonable agreement with the simulation results and are amenable to systematic improvement. We also observe a crossover from the linear dependence of front velocity $V$ on $D_A$ for smaller values of $D_A$ to $V\propto \sqrt{D_A}$ for larger $D_A$, but numerically still significantly different from the mean field value. The deviations reflect the role of internal fluctuations which is neglected in the mean field description. 
Niraj Kumar and Goutam Tripathy