Asymptotic stability in a mosquito population suppression model with time delay

Abstract

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 [Formula: see text] 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 [Formula: see text]. Besides, the case when the number of sterile mosquitoes released stays at a constant level [Formula: see text] is also considered. In the special case, it is also proved that the origin is globally asymptotically stable if and only if [Formula: see text] and that the model exhibits other complicated dynamics such as bi-stability and semi-stability when [Formula: see text]. Numerical examples are also provided to illustrate our main theoretical results.