  In this paper, we propose a sex-structured entomological model that serves as
a basis for design of control strategies relying on releases of sterile male
mosquitoes (Aedes spp) and aiming at elimination of the wild vector population
in some target locality. We consider different types of releases (constant and
periodic impulsive), providing necessary conditions to reach elimination.
However, the main part of the paper is focused on the study of the periodic
impulsive control in different situations. When the size of wild mosquito
population cannot be assessed in real time, we propose the so-called open-loop
control strategy that relies on periodic impulsive releases of sterile males
with constant release size. Under this control mode, global convergence towards
the mosquito-free equilibrium is proved on the grounds of sufficient condition
that relates the size and frequency of releases. If periodic assessments
(either synchronized with releases or more sparse) of the wild population size
are available in real time, we propose the so-called closed-loop control
strategy, which is adjustable in accordance with reliable estimations of the
wild population sizes. Under this control mode, global convergence to the
mosquito-free equilibrium is proved on the grounds of another sufficient
condition that relates not only the size and frequency of periodic releases but
also the frequency of sparse measurements taken on wild populations. Finally,
we propose a mixed control strategy that combines open-loop and closed-loop
strategies. This control mode renders the best result, in terms of overall time
needed to reach elimination and the number of releases to be effectively
carried out during the whole release campaign, while requiring for a reasonable
amount of released sterile insects.
