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Genital warts are a common and highly contagious sexually transmitted disease. They have a large economic burden and affect several aspects of quality of life. Incidence data underestimate the real occurrence of genital warts because this infection is often under-reported, mostly due to their specific characteristics such as the asymptomatic course. Genital warts cases for the analysis were obtained from the catalan public health system database (SIDIAP) for the period 2009-2016, covering 74\% of the Catalan population. People under 15 and over 94 years old were excluded from the analysis as the incidence of genital warts in this population is negligible. This work introduces a time series model based on a mixture of two distributions, capable of detecting the presence of under-reporting in the data. In order to identify potential differences in the magnitude of the under-reporting issue depending on sex and age, these covariates were included in the model. This work shows that only about 80\% in average of genital warts incidence in Catalunya in the period 2009-2016 was registered, although the frequency of under-reporting has been decreasing over the study period. It can also be seen that the under-reported issue has a deeper impact on women over 30 years old. The registered incidence in the Catalan public health system is underestimating the real burden in almost 10,000 cases in Catalunya, around 23\% of the registered cases. The total annual cost in Catalunya is underestimated in at least about 10 million Euros respect the 54 million Euros annually devoted to genital warts in Catalunya, representing 0.4\% of the total budget of the public health system.