The sterile insect technique (SIT) is a technique to control pests and vectors of diseases by releasing mainly sterile males. Several challenges need to be solved before large-scale field application in order to guarantee its success. In this paper we intend to focus on two important issues: residual fertility in released (sterile) males and contamination of each release by sterile females. Indeed, sterile males are never 100% sterile, that is there is always a small proportion, ɛ, of fertile males (sperm of) within the sterile males population. Among the sterile insects that are released, a certain proportion of them are sterile females due to imperfect mechanical sex-separation technique. This can be particularly problematic when arthropod viruses are circulating, because mosquito females, even sterile, are vectors of diseases. Various upper bound values are given in the entomological literature for and ɛ without clear explanations. In this work, we aim to show that these values are related to the biological parameters of the targeted vector, the sterile insects release rate, and the epidemiological parameters of a vector-borne disease, like Dengue. We extend results studied separately in Aronna and Dumont (2020), Dumont and Yatat-Djeumen (2022). To study the impact of both issues, we develop and study a SIT-entomological-epidemiological mathematical model, with application to Dengue. Qualitative analysis of the model is carried out to highlight threshold values that shape the overall dynamics of the system. We show that vector elimination is possible only when ɛN<1, where N is the basic-offspring number related to the targeted wild population. To ensure the success of SIT control, we recommend that the issue of residual fertility be addressed as a priority and then that contamination by sterile females be minimized with each release.