Asymptotic stability in a mosquito population suppression model with time delay

In this paper, a delayed mosquito population suppression model, where the number of sexually active sterile mosquitoes released is regarded as a given nonnegative function, and the birth process is density dependent by considering larvae progression and the intra-specific competition within the larvae, is developed and studied. A threshold value r* for the releases of sterile mosquitoes is determined, and it is proved that the origin is globally asymptotically stable if the number of sterile mosquitoes released is above the threshold value r*. Besides, the case when the number of sterile mosquitoes released stays at a constant. level r is also considered. In the special case, it is also proved that the origin is globally asymptotically stable if and only if r > r* and that the model exhibits other complicated dynamics such as bi-stability and semi-stability when r <= r*. Numerical examples are also provided to illustrate our main theoretical results.