The population of the species and reproduction is the system itself. You introduce a new genotype to the population. This new genotype has recessive gene that causes sterility. Because it is recessive and not dominate, this new genotype will produce offspring and further spread the gene amongst the population. A female mosquito with two modified parents will be sterile, bringing about the goal of eradication.

EDIT: Regarding the last sentence, two recessive parents are not guaranteed to produce a modified phenotype offspring. My bio is getting rusty. :)