  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.
