  The purpose of this paper is to study a Markovian metapopulation model on a
directed graph with edge-supported transfers and deterministic intra-nodal
population dynamics. We first state tractable stability conditions for two
typical frameworks motivated by applications: constant jump rates with
multiplicative transfer amplitudes, and coercive jump rates with unitary
transfers. More general criteria for boundedness, petiteness and ergodicity are
then given.
