Vector/pest control is essential to reduce the risk of vector-borne diseases or losses in crops. Among all biological control tools, the sterile insect technique (SIT), which consists of massive releases of sterile insects to reach elimination or to lower a vector/pest population under a certain threshold, is the most promising one. The models presented here are minimalistic with respect to the number of parameters and variables. The first model deals with the dynamics of the vector population, while the second model tackles the interaction between treated males and wild female vectors. For the vector population model, equilibrium 0 is globally asymptotically stable when the basic offspring number, R=1, whereas 0 becomes unstable and one stable positive equilibrium exists, with well-determined basins of attraction, when R>1. For the SIT model, we obtain a threshold number of treated males above which the control of wild population is effective using massive releases. When the amount of treated males is lower than the aforementioned threshold, the SIT model experiences a strong Allee effect, that is, 0 becomes locally asymptotically stable, while a positive equilibrium still exists. Practically, massive releases of sterile males are only possible for a short period. That is why using the Allee effect, we develop a new strategy to maintain the wild population under a certain threshold, for a permanent and sustainable low level of SIT control. We illustrate our theoretical results with numerical simulations. In particular, we study the combination of SIT with other control tools, like mechanical control and adulticide.