Global suppression and periodic change of the mosquito population in a sterile release model with delay

In this paper, we study a mosquito population suppression model with a time-delay effect, which includes explicitly the growth stage and sex structure of the mosquito population. According to the release function of sexually active sterile male mosquitoes in the field, we determine a release threshold and obtain sufficient conditions to successfully suppress the wild mosquito population. When these conditions are not satisfied, we use the fixed point theorem to obtain the existence of positive periodic solutions and determine their existence region for the common periodic release case in practice. Finally, we present a numerical example to support our theoretical results.