  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
(sterile) male fertility and contamination by sterile females. Indeed, sterile
males are never $100\%$ sterile, that is there is always a small proportion,
$\varepsilon$, of fertile males (sperm of) within the sterile male population.
Among the sterile insects that are released, a certain proportion,
$\epsilon_F$, 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. In this work, we extend results studied separately in [4,7]. To study
the impact of both issues, we develop and study a
SIT-entomological-epidemiological mathematical model, with application to
Dengue. In order to guarantee the success of SIT control, we recommend to solve
in priority the issue of residual fertility, and, then, to decay the
contamination by sterile females as low as possible.
