A moment closure model of sexually transmitted disease spread through a concurrent partnership network is developed. The model employs pair approximations of higher–order correlations to derive equations of motion in terms of numbers of pairs and singletons. The model is derived from an underlying stochastic process of partnership network formation and disease transmission. The model is analysed numerically, and the final size and time evolution are considered for various levels of concurrency, as measured by the concurrency index K3 of Kretzschmar and Morris. Additionally, a new way of calculating R0 for spatial network models is developed. It is found that concurrency significantly increases R0 and the final size of a sexually transmitted disease, with some interesting exceptions.