Velocity of front propagation in the epidemic model A+B 2A
Institute of Physics, Sachivalaya Marg, 751005 Bhubaneswar, India
Corresponding author: a firstname.lastname@example.org
Revised: 15 July 2010
Published online: 22 November 2010
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 ϵ. 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 ≫ ϵ becomes independent of DA. For DA = DB, macroscopic description for the process is given by Fisher equation and one expects to get mean field dependence (V ~ ) 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.
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2010