Abstract: The reproduction number R(t) represents the average number of new infections caused by a single infected individual at time t. Estimation of the reproduction number R(t) is of vital importance during an epidemic outbreak, for example, to decide whether to implement control measures and to determine their effects once implemented. Typically, the reproduction number R(t) is inferred using only epidemic data, such as prevalence per day. However, prevalence data is often noisy, partially observed and biased. Genomic data is therefore increasingly being used to understand infectious disease epidemiology. We take a Bayesian approach to this problem to find the trajectory of R(t) given a dated phylogeny and partial prevalence data using particle Markov chain Monte Carlo methods. We have implemented a particle marginal Metropolis--Hastings algorithm with backward simulation to jointly infer the hyper-parameters of the model, the latent epidemic and the trajectory of R(t). The performance of this approach is analysed using simulated data. These simulations show that incorporating genomic data as well as epidemic data improves inference in a variety of cases.