There is considerable uncertainty as to the effectiveness of Neisseria gonorrhoeae (NG) screening in men who have sex with men. It is important to ensure that screening has benefits that outweigh the risks of increased antibiotics resistance. We develop a mathematical model to estimate the effectiveness of screening on prevalence. Separable Temporal Exponential family Random Graph Models are used to model the sexual relationships network, both with main and casual partners. Next, the transmission of Gonorrhoea is simulated on this network. The models are implemented using the R package 'statnet', which we adapted among other things to incorporate infection status at the pharynx, urethra and rectum separately and to distinguish between anal sex, oral sex and rimming. The different screening programmes compared are no screening, 3.5% of the population screened, 32% screened and 50% screened. The model simulates day-by-day evolution for 10 years of a population of 10 000. If half of the population would be screened, the prevalence in the pharynx decreases from 11.9% to 10.2%. We conclude that the limited impact of screening on NG prevalence may not outweigh the increased risk of antibiotic resistance.