Rift Valley fever is an endemic vector-borne disease in West Africa, which mainly affects domestic ruminants and occasionally humans. The aetiological mechanisms of its endemicity remain under debate. We used a simple spatially explicit model to assess the possibility of endemicity without wild animals providing a permanent virus reservoir. Our model takes into account the vertical transmission in some mosquito species, the rainfall-driven emergence of their eggs and local and distant contacts because of herd migration. Endemicity without such a permanent virus reservoir would be impossible in a single site except when there is a strictly periodic rainfall pattern; but it would be possible when there are herd movements and sufficient inter-site variability in rainfall, which drives mosquito emergence.