The persistence mechanisms of Rift Valley fever (RVF), a zoonotic arboviral haemorrhagic fever, at both local and broader geographical scales have yet to be fully understood and rigorously quantified. We developed a mathematical metapopulation model describing RVF virus transmission in livestock across the four islands of the Comoros archipelago, accounting for island-specific environments and inter-island animal movements. By fitting our model in a Bayesian framework to 2004–2015 surveillance data, we estimated the importance of environmental drivers and animal movements on disease persistence, and tested the impact of different control scenarios on reducing disease burden throughout the archipelago. Here we report that (i) the archipelago network was able to sustain viral transmission in the absence of explicit disease introduction events after early 2007, (ii) repeated outbreaks during 2004–2020 may have gone under-detected by local surveillance, and (iii) coordinated within-island control measures are more effective than between-island animal movement restrictions.