  Vector control is critical to limit the circulation of vector-borne diseases
like chikungunya, dengue or zika which have become important issues around the
world. Among them the Sterile Insect Technique (SIT) and the Incompatible
Insect Technique (IIT) recently aroused a renewed interest. In this paper we
derive and study a minimalistic mathematical model designed for Aedes mosquito
population elimination by SIT/IIT. Contrary to most of the previous models, it
is bistable in general, allowing simultaneously for elimination of the
population and for its survival. We consider dierent types of releases
(constant, periodic or impulsive) and show necessary conditions to reach
elimination in each case. We also estimate both sucient and minimal treatment
times. Biological parameters are estimated from a case study of an Aedes
polynesiensis population, for which extensive numerical investigations
illustrate the analytical results. The applications of this work are twofold:
to help identifying some key parameters that may need further eld
investigations, and to help designing release protocols.
