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

On the use of the sterile insect technique or the incompatible insect technique to reduce or eliminate mosquito populations