Recent evidence suggests that sexual contact may give rise to transmission of Ebola virus long after infection has been cleared from blood. We develop a simple mathematical model that incorporates contact transmission and sexual transmission parametrized from data relating to the 2013-2015 West African Ebola epidemic. The model explores scenarios where contact transmission is reduced following infection events, capturing behaviour change, and quantifies how these actions reducing transmission may be compromised by sexual transmission in terms of increasing likelihood, size and duration of outbreaks. We characterize the extent to which sexual transmission operates in terms of the probability of initial infection resolving to sexual infectiousness and the sexual transmission rate, and relate these parameters to the overall case burden. We find that sexual transmission can have large effects on epidemic dynamics (increasing attack ratios from 25% in scenarios without sexual transmission but with contact-transmission-reducing behaviour, up to 80% in equivalent scenarios with sexual transmission).