  The Sterile Insect Technique (SIT) is one of the sustainable strategies for
the control of disease vectors, which consists of releasing sterilized males
that will mate with the wild females, resulting in a reduction and, eventually
a local elimination, of the wild population. The implementation of the SIT in
the field can become problematic when there are inaccessible areas where the
release of sterile insects cannot be carried out directly, and the migration of
wild insects from these areas to the treated zone may influence the efficacy of
this technique. However, we can also take advantage of the movement of sterile
individuals to control the wild population in these unreachable places. In this
paper, we derive a two-patch model for Aedes mosquitoes where we consider the
discrete diffusion between the treated area and the inaccessible zone. We
investigate two different release strategies (constant and impulsive periodic
releases), and by using the monotonicity of the model, we show that if the
number of released sterile males exceeds some threshold, the technique succeeds
in driving the whole population in both areas to extinction. This threshold
depends on not only the biological parameters of the population but also the
diffusion between the two patches.
