Rift Valley fever (RVF) is an emerging, zoonotic, arboviral haemorrhagic fever threatening livestock and humans mainly in Africa. RVF is of global concern, having expanded its geographical range over the last decades. The impact of control measures on epidemic dynamics using empirical data has not been assessed. Here, we combined seroprevalence livestock and human RVF case data from the 2018-2019 epidemic in Mayotte, with a dynamic mathematical model. Using a Bayesian inference framework, we estimated viral transmission potential amongst livestock, and spillover from livestock to humans, through both direct contact and vector-mediated routes. Model simulations were used to assess the impact of vaccination on reducing the human epidemic size. Reactive vaccination immunising 20% of the livestock population reduced the number of human cases by 30%. To achieve a similar impact, delaying the vaccination by one month required using 50% more vaccine doses, and vaccinating only humans required 20 times as more as the number of doses for livestock. Finally, with 53. ) of livestock estimated to be immune at the end of the epidemic wave, viral re-emergence in the next rainy season (2019-2020) was unlikely. We present the first mathematical model for RVF fitted to real-world data to estimate virus transmission parameters, and able to inform potential control programmes. Human and animal health surveillance, and timely livestock vaccination appear to be key in reducing disease risk in humans. We furthermore demonstrate the value of a One Health quantitative approach to surveillance and control of zoonotic infectious diseases.