Velocity of front propagation in the epidemic model A + B → 2A

We study front propagation in the irreversible epidemic model A + B → 2A in one dimension with initially separated A and B, which diffuse with rates DA and DB respectively and B gets converted by neighbouring A with rate � . We find analytic estimates for the front velocity by writing truncated master equation in the frame moving with the leading A particle. The results obtained are in reasonable agreement with simulation results and are amenable to systematic improvement. We observe a crossover from the linear dependence of front velocity V on DA for smaller values of DA which, for DA � � becomes independent of DA .F orDA = DB, macroscopic description for the process is given by Fisher equation and one expects to get mean field dependence (V ∼ √ DA) in the reaction controlled limit, i.e. DA →∞ . However, the observed dependence of V on DA in the limit DA →∞ rules out such convergence to the naive mean field results.