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) have 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 different types of releases (constant, periodic or impulsive) and show necessary conditions to reach elimination in each case. We also estimate both sufficient 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 two-fold: to help identifying some key parameters that may need further field investigations, and to help designing release protocols.