  We investigate transport in a disordered reaction-diffusion (RD) model
consisting of particles which are allowed to diffuse, compete with one another
(2A->A), give birth in small areas called "oases" (A->2A), and die in the
"desert" outside the oases (A->0). This model has previously been used to study
bacterial populations in the lab and is related to a model of plankton
populations in the oceans. We first consider the nature of transport between
two oases: in the limit of high growth rate, this is effectively a first
passage process, and we are able to determine the first passage time
probability density function in the limit of large oasis separation. This
result is then used along with the theory of hopping conduction in doped
semiconductors to estimate the time taken by a population to cross a large
system.
