We consider the dynamics of a mosquito-transmitted pathogen in a multi-patch
Ross-Macdonald malaria model with mobile human hosts, mobile vectors, and a
heterogeneous environment. We show the existence of a globally stable steady
state, and a threshold that determines whether a pathogen is either absent from
all patches, or endemic and present at some level in all patches. Each patch is
characterized by a local basic reproduction number, whose value predicts
whether the disease is cleared or not when the patch is isolated: patches are
known as ``demographic sinks'' if they have a local basic reproduction number
less than one, and hence would clear the disease if isolated; patches with a
basic reproduction number above one would sustain endemic infection in
isolation, and become ``demographic sources'' of parasites when connected to
other patches. Sources are also considered focal areas of transmission for the
larger landscape, as they export excess parasites to other areas and can
sustain parasite populations. We show how to determine the various basic
reproduction numbers from steady state estimates in the patched network and
knowledge of additional model parameters, hereby identifying parasite
sources in the process. This is useful in the context of control of the infection on natural landscapes, because a commonly suggested strategy is to target focal areas, in order to make their corresponding basic reproduction numbers less than one, effectively turning them into sinks. We show that this is indeed a successful control strategy -albeit a conservative and possibly expensive one- in case either the human host, or the vector does not move. However, we also show that when both humans and vectors move, this strategy may fail, depending on the specific movement patterns exhibited by hosts and vectors.