Mosquito-borne diseases such as dengue and chikungunya have been co-circulating in the Americas, causing great damage to the population. In 2021, for instance, almost 1.5 million cases were reported on the continent, being Brazil the responsible for most of them. Even though they are transmitted by the same mosquito, it remains unclear whether there exists a relationship between both diseases. In this paper, we model the geographic distributions of dengue and chikungunya over the years 2016 to 2021 in the Brazilian state of Ceará. We use a Bayesian hierarchical spatial model for the joint analysis of two arboviruses that includes spatial covariates as well as specific and shared spatial effects that take into account the potential autocorrelation between the two diseases. Our findings allow us to identify areas with high risk of one or both diseases. Only 7% of the areas present high relative risk for both diseases, which suggests a competition between viruses. This study advances the understanding of the geographic patterns and the identification of risk factors of dengue and chikungunya being able to help health decision-making.