  Mosquitoes are vectors of viral diseases with epidemic potential in many
regions of the world, and in absence of vaccines or therapies, their control is
the main alternative. Chemical control through insecticides has been one of the
conventional strategies, but induces insecticide resistance, which may affect
other insects and cause ecological damage. Biological control, through the
release of mosquitoes infected by the maternally inherited bacterium Wolbachia,
which inhibits their vector competence, has been proposed as an alternative.
The effects of both techniques may be intermingled in practice: prior
insecticide spraying may debilitate wild population, so facilitating subsequent
invasion by the bacterium; but the latter may also be hindered by the release
of susceptible mosquitoes in an environment where the wild population became
resistant, as a result of preexisting undesired exposition to insecticide. To
tackle such situations, we propose here a unifying model allowing to account
for the cross effects of both control techniques, and based on the latter,
design release strategies able to infect a wild population. The latter are
feedback laws, whose stabilizing properties are studied.
