Laboratory experiments as well as some field essays have revealed that the intracellular bacterium Wolbachia, deliberately introduced in Aedes spp female mosquitoes, drastically reduces their vector competence for dengue virus and other pathogens. However, female mosquitoes infected with Wolbachia still need to ingest human blood while male mosquitoes, either wild or Wolbachia-carrying, do not bite people. Moreover, Wolbachia-carrying females may transmit the virus to people during blood-feeding, even though with a far less probability than the wild ones. Therefore, massive releases of Wolbachia-carrying females may increase both the nuisance and the epidemiological risk among human residents. In this paper, we propose a sex-structured model of Wolbachia invasion that brings forward the possibility of developing male-biased release strategies of Wolbachia-carriers leading to Wolbachia invasion. Thanks to this model, we study the minimal amount of mosquitoes necessary to complete this task, according to the relative sex-ratio of the released mosquitoes and to the release schedule. We also pay attention to the estimate of the time needed to achieve the ultimate population replacement.