  We investigate a time-dependent spatial vector-host epidemic model with
non-coincident domains for the vector and host populations. The host population
resides in small non-overlapping sub-regions, while the vector population
resides throughout a much larger region. The dynamics of the populations are
modeled by a reaction-diffusion-advection compartmental system of partial
differential equations. The disease is transmitted through vector and host
populations in criss-cross fashion. We establish global well-posedness and
uniform a prior bounds as well as the long-term behavior. The model is applied
to simulate the outbreak of bluetongue disease in sheep transmitted by midges
infected with bluetongue virus. We show that the long-range directed movement
of the midge population, due to wind-aided movement, enhances the transmission
of the disease to sheep in distant sites.
