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Gonorrhoea is among the most common bacterial sexually-transmitted infections in the UK, over 41,000 cases were recorded in 2015, with over half in men who have sex with men (MSM). As the bacterium has developed resistance to each first-line antibiotic in turn, we need improved quantification of fitness-benefits and costs of antibiotic resistance to inform control policy. Cefixime was recommended as a single-dose treatment for gonorrhoea from 2005–2010, during which time resistance increased, and then subsequently declined. We hypothesise that there is a net fitness-benefit to cefixime-resistance when cefixime is widely-prescribed and a net fitness-cost when cefixime-prescriptions decline.We developed a stochastic compartmental model representing the natural history and transmission of cefixime-sensitive and -resistant strains of gonorrhoea in UK MSM, which was fitted to data on diagnoses and prescriptions over 2008-2015 using particle Markov Chain Monte Carlo (pMCMC) methods.The model replicated the observed data and indicated that the fitness-benefit of cefixime-resistance exceeds its cost when cefixime is prescribed for >31% (95% CI [26%, 36%]) of gonorrhoea diagnoses, and that the resistant strain is fitter than the cefixime-susceptible strain when cefixime is prescribed for >51% (95% CI [43%, 62%]) of diagnoses.The use of state-of-the-art pMCMC methods provided significant evidence in favour of our hypothesis and insights into the dynamics of cefixime-resistance in gonorrhoea. Our findings have important implications for antibiotic-stewardship and public health policies, such as targeted prescriptions and combination therapy; as well as emerging resistance through similar mechanisms to the current first-line treatment, ceftriaxone.