  In order to prevent the propagation of human diseases transmitted by
mosquitoes (such as dengue or zika), one possible solution is to act directly
on the mosquito population. In this work, we consider an invasive species (the
mosquitoes) and we study two strategies to eradicate the population in the
whole space by a local intervention. The dynamics of the population is modeled
through a bistable reaction diffusion equation in an one dimensional setting
and both strategies are based on the same idea : we act on a moving interval.
The action of the first strategy is to kill as many individuals as we can in
this moving interval. The action of the second strategy is to release sterile
males in this moving interval. For both strategies, we manage to generate
traveling waves that propagate in the opposite direction relative to the one of
the natural invasive traveling wave. These cases correspond to succeeding in
eradicating the invasive species. Furthermore, for the first strategy, we fully
characterize the minimal size of the interval. All the results are illustrated
by numerical simulations.
