https://doi.org/10.1140/epjb/e2010-90977-6
Velocity of front propagation in the epidemic model A+B 
2A
Institute of Physics, Sachivalaya Marg, 751005 Bhubaneswar, India
Corresponding author: a n2kumar@ucsd.edu
Received:
16
December
2009
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
