Résumé
The development of sustainable vector/pest control methods is of utmost
importance to reduce the risk of vector-borne diseases and pest damages on
crops. Among them, the Sterile Insect Technique (SIT) is a very promising one.
In this paper, using diffusion operators, we extend a temporal SIT model,
developed in a recent paper, into a partially degenerate reaction-diffusion SIT
model. Adapting some theoretical results on traveling wave solutions for
partially degenerate reaction-diffusion equations, we show the existence of
mono-stable and bi-stable traveling-wave solutions for our SIT system. The
dynamics of our system is driven by a SIT-threshold number above which the SIT
control becomes effective and drives the system to elimination, using massive
releases. When the amount of sterile males is lower than the SIT-threshold, the
SIT model experiences a strong Allee effect such that a bi-stable traveling
wave solution can exist and can also be used to derive an effective long term
strategy, mixing massive and small releases. We illustrate some of our
theoretical results with numerical simulations , and, also explore numerically
spatial-localized SIT control strategies, using massive and small releases. We
show that this "corridor" strategy can be efficient to block an invasion and
eventually can be used to push back the front of a vector/pest invasion.